The uncertainty for most frequency determinations in the spectrum of NEFA is of a few kHz in view of the high S/N of the data (see Fig. 20). However, we have assigned an uncertainty of 10 kHz for all lines showing a single component and intensity larger than 20 mK (S/N ≥ 20). Unlike linear molecules with a nitrogen atom, for which hyperfine splittings rapidly collapse, symmetric or asymmetric tops can show significant hyperfine splitting even for high-J and high-Ka transitions. As an example, the bottom panel of Fig. 10 shows the hyperfine structure of K = 3 component of the J = 6 → 5 rotational transition of CH3CN. The K = 0 and 1 components of the same transition do not show any measurable splitting, while the K = 2 exhibits an emerging shoulder (clearly seen in that figure) due to its hyperfine structure. Using the diagonal elements of the 14N quadrupole coupling tensor in NEFA (Ohba et al. 2005), we have computed the expected hyperfine splitting of all lines in the W band. Most of the lines we have identified have the hyperfine splitting concentrated around ±10 kHz of the central frequency. However, several lines present three hyperfine components with similar intensities. Two of these components are at practically the same frequency, while the third component is always on the opposite side producing a global splitting of 60–100 kHz. Hence, some of the observed lines could have a two-component structure, with intensity ratio 1:2, with a strong feature accompanied by less intense shoulder (a factor of two lower), either left or right of the central frequency. Many other lines also show a complex profile due to blending with lines coming from the vibrationally excited states and the other conformers of NEFA (see, for example, the bottom right panel of Fig. 20). We have fitted in most cases one single Gaussian profile to the observed lines. However, when the line profile exhibits two components we fitted two Gaussians. Depending on the degree of overlap between these components, the assigned uncertainty varies between 20 and 80 kHz. When two components were obvious in the line profile, the feature assigned to NEFA was based on the expected intensity of the transition (determined with the MADEX code; Cernicharo 2012), and by comparison with the intensity of other nearby lines of NEFA.


To check for any spectral variation in the optical/IR bands, we looked for variation in the V − J band colour against the V-band brightness. This colour variation was analysed for the epochs A, B, D, and E. During epochs A and B, the source showed a ‘redder when brighter’ (RWB) behaviour. During epoch E, a bluer when brighter behaviour was observed. During epoch D, we observed a complex behaviour. Upto a V-band brightness of around 15 mag, the source showed a ‘bluer when brighter’ behaviour, but for optical brightness fainter than 15.0 mag, a ‘redder when brighter’ behaviour was observed. The colour–magnitude diagrams for all the four epochs are shown in Fig. 10. The spectral variations shown by the source are thus complex. From studies on the optical–IR colour–magnitude diagram, it is known that FSRQs in general show an RWB trend, which is attributed to them having a luminous accretion disc (Gu et al. 2006; Bonning et al. 2012). The observed optical emission is a combination of thermal blue emission from the accretion disc and non-thermal red emission from the jet. As the source gets brighter, the non-thermal emission has a more dominant contribution to the total flux, giving rise to the RWB behaviour (Bonning et al. 2012). During epochs A and B, there is a trend of the object to become RWB, irrespective of its optical brightness. The optical flares dominated by synchrotron emission processes during A and B have corresponding γ-ray flares that are produced by EC processes. However, during epochs D and E, the colour variations were found to depend on the optical brightness. During the epochs when this complex spectral behaviour was noticed, the source showed an optical/IR flare with no or a weak corresponding flare in the γ-ray band. The source showed a much larger amplitude of variability in the optical/IR bands, while in the γ-ray band it was either faint or below the detection limit of Fermi. This definitely points to some complex physical changes and could be due to a combination of changes in the bulk Lorentz factor, electron energy density, and magnetic field as seen from our SED modelling of the multiband data.


Although this penalty is small, we can still provide a quantitative estimate based on a few assumptions. The observations of M15 that measured the parallax to VLA J2130+12 (K14) employed an interferometric technique where the position of a weaker potential in-beam calibrator source (M15 S1 and VLA J2130+12) can be measured against a brighter primary calibration source, with the potential for using the in-beam calibrator to transfer more accurate calibration solutions to other in-beam targets. Based on a literature review for papers where VLBI parallax measurements were determined using an in-beam calibrator, we find 24 similar measurements, the majority of which have been used to measure parallaxes to pulsars (Fomalont et al. 1999; Brisken et al. 2003; Chatterjee et al. 2005, 2009; Ng et al. 2007; Middelberg et al. 2011; Deller et al. 2012, 2013; Ransom et al. 2014; Liu et al. 2016). As these measurements represent additional opportunities to detect the parallax of a VLA J2130+12-like object, they could be considered as potential trials. However, all of the reported in-beam calibrators were significantly brighter (4–86 mJy) than VLA J2130+12 (∼0.1–0.5 mJy). Given our conservative assumption of a uniform volume density of VLA J2130+12-like objects in the Galaxy, we should down-weight the number of trials from brighter sources by (fν,in-beam/fν,VLA J2130+12)−1.5. In that case, the number of trials penalty is only an additional ∼0.2 trials. In addition, we note that the PSRπ parallax project (a large VLBA program) has reported15

15

https://safe.nrao.edu/vlba/psrpi/

 111 additional in-beam calibrator sources that they used to measure parallaxes. Although they do not provide the flux densities of individual sources, they note that their median in-beam calibrator source is 9.2 mJy. We have measured the flux density function of secure 1–20 mJy FIRST sources (Helfand et al. 2015;

) to estimate the expected distribution of the flux densities of in-beam calibrators. We found that the minimum flux density is likely ∼3.2 mJy, and using the same down-weighting we estimate an additional penalty of ∼0.9 trials.


Recently Izotov et al. (2016a,b, 2018a,b) have discovered significant emission of Lyman continuum (LyC) ionizing radiation leaking with the escape fractions of 2–76 per cent in a sample of 11 low-z compact active star-forming galaxies (SFGs) observed with the Hubble Space Telescope (HST) in conjunction with the Cosmic Origins Spectrograph (COS). These galaxies hereafter referred to as LyC leakers, possess many properties similar to those of high-redshift galaxies both at z ∼ 2–3 and z$\gtrsim$ 6 such as compact morphology with similar galaxy radii (e.g. Bouwens et al. 2004; Ferguson et al. 2004; Oesch et al. 2010; Ono et al. 2012; Shibuya, Ouchi & Harikane 2015; Curtis-Lake et al. 2016; Paulino-Afonso, Sobral & Ribeiro 2018), strong emission lines with high equivalent widths (EWs; e.g. Schaerer & de Barros 2009; Smit et al. 2014, 2015; Roberts-Borsani et al. 2016; Bowler et al. 2017; Castellano et al. 2017; Fletcher et al. 2019; Bian & Fan 2020; Endsley et al. 2020), similar low stellar masses, low metallicities, and high specific star formation rates (SFRs; e.g. Jaskot & Oey 2013; Nakajima et al. 2013; Stark et al. 2013a; de Barros, Schaerer & Stark 2014; Duncan et al. 2014; González et al. 2014; Nakajima & Ouchi 2014; Becker, Bolton & Lidz 2015; Grazian et al. 2015; Salmon et al. 2015; Huang et al. 2016; Stark 2016; Santini et al. 2017; Stark et al. 2017; Dors et al. 2018), small dust content (e.g. Ouchi et al. 2013; Ota et al. 2014; Maiolino et al. 2015; Schaerer et al. 2015; Watson et al. 2015), and are considered as the main sources of reionization of the Universe after the cosmic ‘Dark Ages’. This makes low-z LyC leakers the best local analogues of reionization galaxies (see e.g. Schaerer et al. 2016; Stark 2016; Ma et al. 2020). Given their proximity, these galaxies represent excellent laboratories for a detailed study of their physical conditions, and the main mechanisms responsible for LyC leakage. Ground-based spectroscopic observations in the visible and near-infrared ranges are necessary for that.


A rough idea of the location of the inert Oort cloud can be obtained from previous works. Gladman et al. (2002) showed that the scattering effect by Neptune is significant over long timescales only for perihelion distances below about 45 astronomical units (au). The precise limit actually increases with the semi-major axis (Gallardo et al. 2012), because energy kicks result in larger variations of semi-major axis if the semi-major axis is large. In fact, some observed objects with perihelion beyond 45 au are known to experience scattering (Bannister et al. 2017). In any case, we look here for a rough limit only. The scattering process mostly affects the semi-major axis of small bodies, which diffuses chaotically, while the perihelion distance does not vary much. Later on, Gomes et al. (2005), Gallardo et al. (2012), and Saillenfest et al. (2016, 2017a), showed that the Lidov–Kozai mechanism raised by the giantplanets inside a mean-motion resonance with Neptune is able to raise the perihelion of small bodies beyond 60 au in a few thousands of million years. Contrary to scattering effects, this mechanism induces a variation of perihelion distance and inclination, while the semi-major axis remains at the resonance location. This mechanism, however, is only efficient for semi-major axes smaller than about 500 au. From these studies, one can deduce that the action of the planets is limited to orbits with perihelion distances smaller than about 80 au, and that for perihelion beyond 45 au, the semi-major axis should be smaller than 500 au for the planets to possibly have a substantial effect through mean-motion resonances. As regards the effects of the galactic tides, Fouchard et al. (2017) showed that an object with perihelion in the Jupiter-Saturn region, that is, below 15 au from the Sun, should have a semi-major axis larger than 1600 au for the tides to be able to raise its perihelion beyond 45 au in less than the age of the solar system. In other words, the tides can move its perihelion out of reach of any significant planetary scattering.


These signatures are inconsistent with ultra-low frequency waves, which have circular polarization and a period similar to the upstream ion gyroperiod. The waves are also inconsistent with ion Weibel instability, which generates linearly polarized waves. Interaction of reflected ions with incoming solar wind electrons or ions can cause foot instabilities that excite waves in the whistler mode branch. Modified Two Stream Instability (MTSI) due to relative drift between reflected ions and incoming solar wind electrons (fast drift), and incoming solar wind ions and electrons (slow drift) has been frequently considered (Matsukiyo & Scholer 2003; Comişel et al. 2011; Umeda et al. 2012; Marcowith et al. 2016; Wilson et al. 2016; Muschietti & Lembège 2017; Hull et al. 2020). This instability, however, if excited, creates significant ion heating throughout the foot and suppresses the reformation process (Shimada & Hoshino 2005; Matsukiyo & Scholer 2006), rather than creating episodic enhancements that we show in the foot. Furthermore, Gary et al. (1987) indicated that (fast drift) MTSI becomes dominant at low electron beta (βe  0.5), while at higher βe more resonant electrons stabilize this instability through increased electron Landau damping. Electron data for the time period we discussed in this paper show βe ≥ 1.2, and therefore fast drift mode MTSI is most likely not significant. The slow drift mode of MTSI could be a more viable candidate at high β plasmas. Wave properties around 1.6 Hz in the middle interval (purple segment) of Figure 6, indicate that the wave is in propagation toward the ramp (

 = −0.66, −0.71, 0.22) with Vph‐sc = 34 km s−1 and λwave = 21.4 km  ∼ 12λe, where λe is the upstream electron inertial length. The plasma rest-frame frequency of the wave is about 8 Hz  ∼ 2.5flh. Since these characteristics are somewhat consistent with model predictions for drift mode of MTSI (Muschietti & Lembège 2017), we do not rule out the possibility of some waves at certain frequencies and during some intervals being generated by the slow drift mode of MTSI.


A lower CB frequency in GCs than in the field has already been noticed by Rucinski (2000). It results most likely from a very low binary frequency of ~0.1 in GCs (but with a significant scatter among different clusters), compared to 0.5 in the field (Milone et al. 2012), together with a low percentage of binaries in the contact phase at a given age, as shown above. Any statistical comparison of models with observations is therefore extremely uncertain because we have so few observational data. Nevertheless, we can compare the predicted to observed fraction of BSs among all CBs in a GC. We used data for two clusters observed by Kaluzny and his collaborators with the highest number of CBs (except for ω Centauri). In M4, Kaluzny et al. (2013a) detected nine CBs with one BS among them, and in 47 Tuc, Kaluzny et al. (2013b) identified 15 CBs or NCBs, of which six are BS. The resulting fractions are 0.1 and 0.4, respectively. We did not take into account ω Cen with the richest population of CBs (Kaluzny et al. 2004) because it is highly atypical and the accurate number of member CBs is not well known, although the approximate data indicate a similarly high ratio as in case of 47 Tuc. The predicted fractions range from 0.08 to 0.2 for the three considered cluster ages. As we see, they are close to the lower observed value but are at odds with the higher value. This may indicate some deficiencies of the CCBM, for instance, too short initial cut-off period, a too high AML rate at short periods, or a too low mass-transfer rate. With the lower AML rate and/or higher mass transfer rate, a binary stays longer in contact and can reach a lower mass ratio before merging. Many of the short-period CBs have a rather high mass ratio of about 0.7−0.8 at the time of merging, whereas field CBs with P ≲ 0.3 d center around a value of 0.5 (Rucinski 2010; Stȩpień & Gazeas 2012). The lower mass ratio means more mass transferred to the gainer, hence its higher mass and higher position on the HRD, that is, a higher probability for entering the BS region. There may also still be another explanation of the discrepancy: strong fluctuations of this fraction among different clusters suggest a nonuniform BSs formation rate in some clusters, with individual bursts occurring in the recent past (see below). Regardless of the reason, it is apparent that profound differences occur among GCs, which makes a comparison of theoretical predictions with individual clusters uncertain.


HD 169142 is a very young Herbig Ae-Be star with a mass of 1.65–2 M⊙ and an age of 5–11 Myr (Blondel & Djie 2006; Manoj et al. 2007) that is surrounded by a gas-rich disk (i = 13°; Raman et al. 2006; PA = 5°; Fedele et al. 2017) that is seen almost face-on. The parallax is 8.77 ± 0.06 mas (Gaia DR2 2018). Disk structures dominate the inner regions around HD 169142 (see, e.g., Ligi et al. 2018). Figure 1 shows the view obtained from polarimetric observations: the left panel shows the QΦ image in the J band obtained by Pohl et al. (2017) using SPHERE on a linear scale, and the two rings are clearly visible. The right panel shows a pseudo-ADI image of the inner regions obtained by differentiating the QΦ image (see Ligi et al. 2018, for more details). Biller et al. (2014) and Reggiani et al. (2014) discussed the possible presence of a point source candidate at small separation (0.2 arcsec from the star). However, the analysis by Ligi et al. (2018) based on SPHERE data does not support or refute these claims; in particular, they suggested that the candidate identified by Biller et al. (2014) might be a disk feature rather than a planet. Polarimetricimages with the adaptive optics system NACO at the Very Large Telescope (VLT; Quanz et al. 2013b), SPHERE (Pohl et al. 2017; Bertrang et al. 2018) and GPI (Monnier et al. 2017) show a gap at around 36 au, with an outer ring at a separation >40 au from the star. This agrees very well with the position of the rings obtained from ALMA data (Fedele et al. 2017); similar results were obtained from VLA data (Osorio et al. 2014; Macías et al. 2017). We summarize this information about the disk structure in Table 1 and call the ring at 0.17–0.28 arcsec from the star Ring 1 and the ring at 0.48–0.64 arcsec Ring 2. We remark that in addition to these two rings, both the spectral energy distribution (Wagner et al. 2015) and interferometric observations (Lazareff et al. 2017; Chen et al. 2018) show an inner disk at a separation smaller than 3 au. This inner disk isunresolved from the star in high-contrast images and consistent with ongoing accretion from it onto the young central star.While the cavities between the rings seem devoid of small dust, some gas is present there (Osorio et al. 2014; Macías et al. 2017; Fedele et al. 2017). Fedele et al. (2017) and Bertrang et al. (2018) have suggested the possibility that the gap between Rings 1 and 2 is caused by a planet with a mass slightly higher than that of Jupiter. However, this planet has not yet been observed, possibly because it is at the limit of or beyond current capabilities of high-contrast imagers. On the other hand, Bertrang et al. (2018) found a radial gap in Ring 1 at PA ~ 50° that might correspond to a similar radial gap found by Quanz et al. (2013b) at PA ~ 80°. The authors noted that if this correspondence were real, then this gap might be caused by a planet at about 0.14 arcsec from the star. So far, this planet has not been unambiguously detected either.


Observational data from distant Type Ia supernovae (SNIa) revealed a hidden fact that the present Universe is expanding in an accelerated phase (Riess et al. 1998; Perlmutter et al. 1999; Kowalski et al. 2008). This important fact has been confirmed by other cosmological observations such as the cosmic microwave background (CMB) (Komatsu et al. 2009; Jarosik et al. 2011; Ade et al. 2016), large-scale structure (LSS), and baryonic acoustic oscillation (BAO) (Tegmark et al. 2004; Cole et al. 2005; Eisenstein et al. 2005; Percival et al. 2010; Blake et al. 2011; Reid et al. 2012), high-redshift galaxies (Alcaniz 2004), high-redshift galaxy clusters (Wang & Steinhardt 1998; Allen et al. 2004), and weak gravitational lensing (Benjamin et al. 2007; Amendola, Kunz & Sapone 2008; Fu et al. 2008). The accelerated phase of the expansion can be interpreted by modifying the standard theory of gravity on cosmological scales or by adding an exotic cosmic fluid with negative pressure, the so-called dark energy (DE) (Riess et al. 1998; Perlmutter et al. 1999; Kowalski et al. 2008). Historically, Einstein’s cosmological constant Λ with a constant equation of state (EoS) parameter equal to −1 is the first and simplest DE model to interpret the current accelerated phase of the expansion. The standard model of cosmology, the ΛCDM model, which accounts for about 70 per cent of the total energy density of the Universe from Λ and about 30 per cent from cold dark matter (CDM) is consistent with the most of the cosmological data. From a theoretical point of view, however, this model has two fundamental problems, namely the problem of fine-tuning and the problem of cosmic coincidence (Weinberg 1989; Sahni & Starobinsky 2000; Carroll 2001; Padmanabhan 2003; Copeland, Sami & Tsujikawa 2006). In addition, the standard model of cosmology suffers from the big tension between the local measurement values of Hubble constant H0 with that of the Planck CMB estimation. Moreover, there are big tensions between the Planck CMB data with weak lensing measurements and redshift surveys, concerning the value of non-relativistic matter density Ωm and the amplitude of the growth of perturbations σ8. The above observational tensions can make the standard model as an approximation of a general gravitational scenario yet to be found. For a recent review about the cosmological tensions of the standard model, we refer the reader to see (Abdalla et al. 2022). In this concern, a large family of dynamical DE models with time-varying EoS parameters has been proposed in the literature (for some earlier attemts, see Armendariz-Picon, Mukhanov & Steinhardt 2000; Caldwell 2002; Padmanabhan 2002; Elizalde, Nojiri & Odintsov 2004). Parallel to the solution of DE, the positive cosmic acceleration can be seen as the expression of a new theory of gravity on large cosmological scales. Indeed, modifying the standard Einstein–Hilbert action in the context of the Friedmann–Robertson–Walker (FRW) metric leads to the modified Friedmann equations, which can be used to justify the current accelerated expansion of the Universe without resorting to DE fluid. One of the most popular modified gravity theories is the f(R) scenario, in which the Lagrangian of the modified Einstein–Hilbert action is extended to the function of the Ricci scalar R (Capozziello, Stabile & Troisi 2007; Capozziello & Francaviglia 2008; Sotiriou & Faraoni 2010; Nojiri & Odintsov 2011). Besides the f(R) theories of gravity, the so-called f(T) theory of gravity is the other solution to solve the puzzle of cosmic acceleration. This theory is defined on the basis of the old definition of the teleparallel equivalent of general relativity (TEGR), first introduced by Einstein (Einstein 1928) and extended by (Hayashi & Shirafuji 1979; Maluf 1994). A comprehensive study on the theory of teleparallel gravity (TG) can be found in the recent review by (Bahamonde et al. 2021). In general, an extended theory of gravity involves curvature, torsion, and non-metricity components. If only torsion is non-vanishing, one can obtain the torsional teleparallel geometry which is the basic geometry for the most f(T) theories in literature. TG theory can be used to formulate a TEGR formalism, which is dynamically equivalent to GR but may have different behaviors for other scenarios, such as quantum gravity. The Horndeski gravity can also be formulated using the teleparallel geometry as a possible revival modes for regular Hordenski gravity models (see Bahamonde et al. 2021, for more detils). TG as a theory built on the tangent sapce must be invariant under general coordinate transformation and local lorentz transformation. In the first formulation of teleparallel theories, it was assumed that the spin connection was always zero and then torsion tensor depends on the tetrads. This torsion tensor is a particular case which is computed in the so-called Weitzenböck gauge (see section 2.2.3 of Bahamonde et al. 2021). By taking a local Lorentz transformation only in the tetrads, one can conclude that the torsion tensor is non-covariant quantity under the local Lorentz transformation. In this context, the action of TEGR has a total divergence term which can be removed as being a boundary term. Hence, the TEGR action is invariant under local Lorentz transformation up to a boundary term. In modified teleparallel theories of gravity like f(T) gravity, we have no boundary term anymore, meaning that f(T) gravity models break the local Lorentz invariance. Notice that the problem of breaking the local Lorentz invariance is related to the particular Weitzenböck gauge (spin connection zero) (Krššák & Saridakis 2016). If we take the simultaneous transformations in the tetrads and the spin connection, the teleparallel theories are then fully invariant (diffeomorphisms and local Lorentz). Thus, any action and consequently field equations constructed based on the torsion tensor will be fully invariant. In the context of cosmology, there is a large body of works that has examined the cosmological properties of various f(T) models. In this framework, the dynamics and various aspects of the Universe with homogeneous and isotropic background are studied in recent works (Bengochea & Ferraro 2009; Linder 2010; Wu & Yu 2011, 2010b; Bamba et al. 2011, 2012; Dent, Dutta & Saridakis 2011; Geng et al. 2011; Myrzakulov 2011; Zhang et al. 2011). In general, cosmological consequences for the various formulations of TG at both background and perturbation levels have been discussed in (Bahamonde et al. 2021). The f(T) models have been studied and constrained using the various cosmological data (Wu & Yu 2010a; Capozziello, Luongo & Saridakis 2015; Iorio, Radicella & Ruggiero 2015; Nunes, Pan & Saridakis 2016; Saez-Gomez et al. 2016). As a more recent study, we refer the work of Briffa et al. 2022, where the various versions of f(T) model have been studied observationally. Using the combinations of cosmological data including the cosmic chronometers, the SNIa observations from Pantheon catalogue, BAO observations, and different model-independent values for Hubble constant H0, Briffa et al. (2022) studied a detailed analysis of the impact of the H0 priors on the late time properties of f(T) cosmologies. They found a higher value of H0 compared to equivalent analysis without considering H0 priors. In addition, they showed that the f(T) model produces the higher value of H0 and slightly lower value of matter density Ωm0 as compared to standard ΛCDM model. In general, studies on the cosmological tensions and their possible alleviation in TG formalism have been addressed in section 10 of review article (Bahamonde et al. 2021). For a review of cosmological tensions H0 and σ8, we refer the reader to see the current studies in (Verde, Treu & Riess 2019; Di Valentino et al. 2021a, b, c; Perivolaropoulos & Skara 2021).


As part of this study, we investigate the 8 μm emission within our sample of galaxies using archival data from IRAC on the Spitzer Space Telescope (SST). The rest-frame 8 μm emission from galaxies has historically been used as a monochromatic SFR indicator. This is justified by the fact that polycyclic aromatic hydrocarbons (PAHs) and small dust grains can be heated by the photodissociation regions (PDRs) that surround actively star-forming regions and the subsequent emission from PAHs is brightest at about 8 μm (Draine & Li 2007; Smith et al. 2007; Kennicutt et al. 2009; Elbaz et al. 2011). However, there is an important caveat; PAHs are destroyed by ionizing radiation from newly formed stars (Helou et al. 2004; Povich et al. 2007; Bendo et al. 2008; Relaño & Kennicutt 2009), leading to a deficit in the 8 μm luminosity in galaxies with low metallicity, whereas PAHs are less well shielded by metals (Engelbracht et al. 2005; Calzetti et al. 2007; Smith et al. 2007; Cook et al. 2014; Shivaei et al. 2017). It has also been argued that metals can act as catalysts for the formation and growth of PAHs, leading to smaller average sizes in low-metallicity environments (Sandstrom et al.2012). More recently, Lin et al. (2020) find an anticorrelation between the dust-only 8 μm luminosity and the age of young stellar clusters, suggesting the 8 μm luminosity decreases with increasing age of the stellar population. The existence of a strong interstellar radiation field is also found to suppress the emission from PAHs, independent of metallicity (Madden et al. 2006; Gordon et al. 2008; Lebouteiller et al. 2011; Shivaei et al. 2017; Binder & Povich 2018). Adding to the complexity, spatially resolved studies have shown that a significant amount of 8 μm emission is associated with the cold, diffuse ISM, which suggests an important heating source other than recent (100 Myr) star formation (Bendo et al. 2008; Calapa et al. 2014; Lu et al. 2014). These results suggest that the luminosity at 8 μm is not a straightforward indicator of the SFR. In this work, we further investigate these issues by exploring how metallicity gradients within our sample affect the observed “red” side versus “blue” side IR color–color correlations—where we derive the “blue” side color from the flux density ratios at 8 and 24 μm.


Post-main-sequence mergers. Mergers of evolved stars with their MS companions originate from wider systems than main-sequence mergers (log P ≳ 0.7). We thus roughly estimate

f

P
,
i

∼

IPF

0.7

3.0

∼
0.66

$ f_{P , \mathrm{i}} \sim \mathrm{IPF}_{0.7}^{3.0} \sim 0.66 $

, using log10P = 3 as the maximum initial period for binary interaction (e.g., Claeys et al. 2011; Yoon et al. 2017). For merging to occur, a CEE phase needs to be initiated. Extreme mass ratio systems are prone to unstable mass transfer and thus to CEE, and although the exact value of the boundary is not well-constrained, we assume that this occurs for evolved donors in systems with q ≲ 0.4, following previous works such as Wellstein et al. (2001), Hurley et al. (2002) and de Mink et al. (2013). In principle, CEE can alternatively lead to the ejection of the envelope, but in this simple estimate we assume that all these systems eventually merge, leaving some hydrogen-rich layers on the surface of the formed star. This is consistent in most of the cases with the findings from our computational simulations for our standard assumption of using the entire orbital energy change to eject the envelope (αCEE = 1, as we will introduce and discuss in Sect. 4.1). Thus,

f

q
,
i

∼

IQF

0.1

0.4

∼
0.33

$ f_{q , \mathrm{i}} \sim \mathrm{IQF}_{0.1}^{0.4} \sim 0.33 $

. The projection of the initial parameter space for this channel at the log P − q plane is depicted in magenta on the left panel of Fig. 2. The donor star in such systems originate from a roughly similar part in M1 space as main-sequence mergers (

f

M
1

,i

~

IMF
7

25

~1.25

$ f_{M_1 , {\rm i}} \sim {\rm IMF}_7^{25} \sim 1.25 $

). In contrast, binaries of less extreme mass ratio are able to either follow a phase of stable mass transfer onto the secondary star or are assumed to always survive a CEE by ejecting the envelope, avoiding a merger. Such donors are expected to eventually produce a hydrogen-poor, stripped-envelope SN, not contributing to the SN II population that we focus on in this study. We find XpostMS + MS mergers ∼ C × 0.136 ∼ 15%.


It is also possible that these clusters have a smaller extent and can just be missed by our extent selection as our detection algorithm sets the extent to zero if it is smaller than 6 (Brunner et al. 2022). Following the method presented in Ghirardini et al. (2021a), we estimated several dynamical properties of the clusters in the point source sample and compared them with the extent-selected sample presented in Ghirardini et al. (2021a). In Fig. 5 we compare the distributions of the core radii (Rcore) constrained by the V06 model and the concentration parameter (cSB) between these two samples. The concentration parameter is defined as the ratio of the surface brightness within 0.1 R500 to the surface brightness within R500 (Ghirardini et al. 2021a; Santos et al. 2008; Maughan et al. 2012). Intuitively, the expectation is that the smaller the core radius, the more compact the cluster. The left panel of Fig. 5 clearly shows that the clusters in the point source sample have relatively smaller core radii, hence the emission is more concentrated in a smaller area. Consistently, the concentration of the point source sample shows a clear excess in higher values than the extent-selected sample, indicating that a significantly larger fraction of cool-core clusters and clusters host a central AGN. We performed the same experiment by applying cuts in flux 1.5 × 10−14 ergs s−1 cm−2 and in detection likelihood to test whether the clusters are missed by the extent selection because they are fainter and/or more compact than the extent-selected clusters. The distribution of number density, core radius, and concentration parameter remains the same, indicating that the population of clusters in the point source catalog is more compact than the extent-selected sample. The extent-selected sample does not show a clear bias toward cool-core clusters or clusters with a central AGN, but contains the fraction of cool-cores is similar to that of SZ surveys (Ghirardini et al. 2021a). In this sample, we observe the opposite trend.

Compare/Contrast Background Background Compare/Contrast


We further restricted our sample to well-defined N2H+ (1–0) spectra that we used to estimate the gas velocity dispersion. The N2H+ (1–0) emission of each clump was evaluated from the MALT90 data cubes by averaging the spectrum across all the pixels within one MALT90 beam, ≃ 38 arcsec. We assumed that all the N2H+ emission comes from the clumps, and we estimate the filling factor from the comparison of the radius of each Hi-GAL clump with the radius of a region equal to the MALT90 beam (Fig. 1). There is a strong correlation between these two quantities, and the size of the Hi-GAL clumps is systematically smaller than the radius estimated from the MALT90 beam for a factor of 0.64, on average. We assumed an average filling factor of 0.64 for the entire sample. The MALT90 data cubes are given in antenna temperature $T_{\rm A}^{*}$ and they have been converted to the main beam temperature $T_{\rm MB}=T_{\rm A}^{*}/\eta _{\rm MB}$, assuming a mean beam efficiency ηMB = 0.49 (Miettinen 2014). The properties of each N2H+ (1–0) averaged spectrum have been extracted in idl using a hyperfine fitting routine and the mpfitfun algorithm (Markwardt 2009), after smoothing the data to a spectral resolution of 0.3 km s−1 to enhance the signal-to-noise (S/N) ratio. We excluded all clumps with a S/N ratio below 5, where the rms in each smoothed data cube has been measured in a 100 km s−1 wide spectral window near the N2H+ emission. We further excluded clumps for which the fit converged but the spectrum was affected by spikes and/or by multiple components along the line of sight. Using these criteria, we obtained 308 clumps. We completed our selection by excluding all clumps without a clear distance assignation, in particular without a well-defined resolution of the near–far distance ambiguity. First, we have refined the kinematic distances in the Elia et al. (2017) catalogue (and the quantities that depend on them) with the newest set of distances developed for the Hi-GAL survey under the VIALACTEA project (Mege et al., in preparation). The method used by Elia et al. (2017) was the same as in Russeil et al. (2011): the brightest emission lines in the 12CO or 13CO spectra along the line of sight of each source are used to estimate the velocities of the local standard of rest and converted into heliocentric distances using the Brand & Blitz (1993) rotation curve. The distances in Mege et al. (in preparation) have been determined using a similar approach, but including all the recent surveys of the Galactic plane to trace structures along the line of sight, and using the more recent Reid et al. (2009) rotation curve. Then, in order to identify only clumps with a well-defined distance estimation, we have compared the distances assigned to our 308 clumps with the distances of the MALT90 sample estimated in Whitaker et al. (2017) and of the ATLASGAL sources published in Urquhart et al. (2018). We excluded from the sample all sources with a difference in the distance estimation larger than 20 per cent among the three surveys.


Benzene (C6H6), the simplest aromatic hydrocarbon, is a molecule that has raised great interest in the astrophysical community for almost four decades. This is mainly because C6H6 is one of the main precursors of polycyclic aromatic hydrocarbons (PAHs) reported to be present in interstellar dust particles (Leger & Puget 1984; Allamandola et al. 1989; Tielens 2013 and references therein), carbonaceous chondrites (Pering & Ponnamperuma 1971; Hayatsu et al. 1977; Hahn et al. 1988), and other astrophysical environments, such as carbon-rich, high-temperature environments (circumstellar and carbon-rich protoplanetary nebulae; Buss et al. 1993; Clemett et al. 1994). Benzene rings easily produce more complex, polycyclic structures by the one-ring build-up mechanism (Simoneit & Fetzer 1996). In space, an analogous process to carbon soot formation occurring on Earth can be initiated through the completion of that first aromatic ring and may also lead to the synthesis of PAHs (Tielens & Charnley 1997). Mechanisms involving the addition of hydrocarbons, such as acetylene onto aromatic rings as well as the attachment of other aromatic rings, or hydrocarbon pyrolysis, have been proposed to characterize the growth process of PAHs (Bittner & Howard 1981; Frenklach & Feigelson 1989; Wang & Frenklach 1997; Cherchneff 2011 and references therein). PAH synthesis from shocked benzene has also been reported (Mimura 1995). PAHs are crucial materials involved in a variety of cosmochemical processes. For example, amino acids could be synthesized by aqueous alteration of precursor PAHs in carbonaceous chondrites (Shock & Schulte 1990). PAHs are also produced in laboratory-simulated planetary atmospheres of Titan and Jupiter (Sagan et al. 1993; Khare et al. 2002; Trainer et al. 2004), and results from these studies indicate that the formation of aromatic rings and polyaromatics may be, among other sources, a possible chemical pathway for the production of the atmospheric solid particles (Lebonnois et al. 2002; Wilson et al. 2003; Trainer et al. 2004). The formation and evolution of benzene in planetary environments or other solar system objects thus represents a fundamental primary stage of the PAH production and other subsequent relevant chemical and prebiotic processes (like soot formation). In this context, several works related to benzene have been devoted to better understand the physico-chemical processes of irradiated C6H6, in its gaseous and solid phases, and the derived products, by acquiring high-resolution astronomical spectra, carrying out detailed laboratory studies or developing theoretical modeling (Allamandola et al. 1989  and references therein; Callahan et al. 2013; Materese et al. 2015; Mouzay et al. 2021). Laboratory astrophysical investigations have mostly focused on performing vibrational spectroscopy of ion, electron, or UV irradiated C6H6 gas and C6H6 ice. Such investigations aim to provide data on the spectral properties of the irradiated C6H6 materials, compare them with spectra obtained from astronomical observations (e.g., observations of the interstellar medium), or to study photoprocessed benzene ices to understand the fate of benzene ices in Titan’s stratosphere and help understanding the formation of aerosol analogs observed in Saturn’s moon’s stratosphere (Mouzay et al. 2021).


In the present work, we neglect the processes that generate the halo, but this topic deserves some review. Notably, the apparent growth of the halo at the expense of the anti-sunward suprathermal ‘strahl’ population may imply that the halo is locally formed in the inner heliosphere by scattered strahl electrons (e.g. Maksimovic et al. 2005; Štverák et al. 2009). This has led to significant theoretical development, focused on the resonant interaction of electrons with the whistler and fast-magnetosonic whistler (FM/W) modes (e.g. Vocks et al. 2005; Saito & Gary 2007; Vasko et al. 2019; Verscharen et al. 2019b; Micera et al. 2021; Zenteno-Quinteros, Viñas & Moya 2021; Tang, Zank & Kolobov 2022; Vo, Lysak & Cattell 2022). Observations have struggled to confirm these theories. Notably, whistlers are practically absent (occurrence rate 0.1 per cent) during PSP perihelion passes (Cattell et al. 2022). Additionally, the eVDFs sampled by Helios and PSP are stable with respect to the oblique FM/W mode (Jeong et al. 2022a). Theoretical calculations show that at r ≲ 1 AU, the strahl is stable to whistler fluctuations (Horaites et al. 2018b; Schroeder et al. 2021) and should be unaffected by whistler turbulence in the inner heliosphere (Boldyrev & Horaites 2019). High-resolution measurements of the strahl at 1 AU confirm that ‘anomalous diffusion’, e.g. from whistler waves, is not required to explain the strahl angular widths at resolvable energies ≲300 eV Horaites et al. (2018a), Horaites, Boldyrev & Medvedev (2019). Similar results were found from simulations at distances r ≲ 20RS (Jeong et al. 2022b), which showed that near the corona the strahl is adequately described by a combination of Coulomb collisions and expansion effects. This all suggests that a mechanism besides local wave particle scattering may account for the halo’s presence in the inner heliosphere. Such theories have been proposed (e.g. Leubner 2004; Lichko et al. 2017; Che et al. 2019; Horaites et al. 2019; Scudder 2019), though no consensus has emerged.


The currently accepted cold dark matter dominated model with the cosmological constant (ÎCDM) predicts that structures in our Universe assemble hierarchically, with more massive systems forming later through accretion and mergers of smaller, self-bound dark-matter halos (e.g., Tormen 1997; Moore etÂ al. 1999; Klypin etÂ al. 1999; Springel etÂ al. 2001). In N-body cosmological simulations, dark matter halos of all masses converge to a roughly âuniversalâ and cuspy density profile that steepens with radius, the so-called NavarroâFrenkâWhite profile (NFW profile; Navarro etÂ al. 1996, 1997). Moreover, the degree of central concentration of a halo depends on its formation epoch and hence on its total mass (e.g., Wechsler etÂ al. 2002; Zhao etÂ al. 2003). Within this scenario, early virialized objects are compact when they get accreted into a larger halo. Such objects are usually referred to as subhalos or substructures of their host and, as they orbit within the host potential well, they are strongly affected by tidal forces and dynamical friction, causing mass, angular momentum, and energy loss (e.g., Ghigna etÂ al. 1998; Tormen etÂ al. 1998; De Lucia etÂ al. 2004; Gao etÂ al. 2004). In the ÎCDM framework, more massive halos are predicted to have a larger fraction of mass in subhalos than lower mass halos because in the former there has been less time for tidal destruction to take place (e.g., Gao etÂ al. 2004; Contini etÂ al. 2012). On galaxy cluster scales, observational tests of these predictions have been attempted in some previous works (e.g., Natarajan etÂ al. 2007, 2009), but highly accurate analyses are becoming possible only now, thanks to the substantially improved quality of the available photometric and spectroscopic data. From an observational point of view, more investigations are still required to fully answer key questions on the formation and evolution of subhalos. How much mass of subhalos is stripped as they fall into the host potential? How many subhalos survive as bound objects? What are the spatial and mass distributions of the subhalos?


There are additional lines of evidence suggesting that accretion in HD 100546 could be magnetospheric, and not through a BL. Equation 3 in Johns-Krull, Valenti & Koresko (1999) provides a lower limit to the magnetic field necessary to drive MA, in terms of the stellar parameters and accretion rate. Assuming a mass accretion rate of ∼10−7 M⊙ yr−1, the minimum stellar mass and maximum stellar radius allowed by the uncertainties provided by Fairlamb et al. (2015), and a minimum rotation period of 0.26 d (from a maximum projected rotational velocity vsin i = 65 km s−1 and a minimum inclination i = 22°, from Guimarães et al. 2006, and TAT11), HD 100546 could require a magnetic field of only several tens of Gauss to drive accretion magnetospherically.1 This is consistent with the magnetic field measured by Hubrig et al. (2009), 89 ± 26 G, although non detections have also been reported (Donati et al. 1997; Hubrig et al. 2013). In addition, if accretion in HD 100546 is actually magnetospheric the Keplerian gaseous disc should be truncated at a stelleocentric radius that increases with the stellar magnetic field and radius, and decreases with the accretion rate and stellar mass (Elsner & Lamb 1977). Using equation 6 in Tambovtseva et al. (2014), the disc truncation radius of HD 100546 should be ≲ 0.01 au (Fig. 3). This value is consistent with the Keplerian radius inferred from the width of the Br γ line profile (∼ ± 200 km s−1; Section 3); once this value is de-projected using the inclination in TAT11, the corresponding Keplerian distance is ≲ 0.02 au. It is noted that, in contrast to optically thick lines like H α, Br γ is mainly broadened by the Doppler effect (Tambovtseva et al. 2014). If the Keplerian disc is truncated by the stellar magnetic field, the gas would then fall ballistically on to the stellar surface. This could eventually be traced from the presence of redshifted absorptions at free-fall velocities in the profiles of several lines. In fact, previous spectroscopic analysis involving optical/UV lines suggest MA/ejection processes in HD 100546 (Vieira et al. 1999; Deleuil et al. 2004), with redshifted absorptions at velocities comparable to free-fall (Guimarães et al. 2006). However, those signatures are not observed in the Br γ profile of HD 100546. The unresolved component contributing ∼35 per cent to the visibility (Section 4.1) could be related to magnetospheric infall, but the small spatial scales involved cannot be probed from our observations.


The earliest observations of magnetic fields in astrophysics were sunspot field strength measurements at the Mount Wilson Observatory (MWO) in California, USA, in 1908 (Hale 1908). Observations employed the Zeeman effect and were based on measuring the separation (splitting) between the two components of a spectral line, first Fe I 6173 Å and later Fe II 5250 Å. Daily observations of sunspot magnetic fields have been conducted since 1917 (Hale et al. 1919). In the early 1950s, the invention of an electronic magnetograph (Babcock 1953) allowed the measurement of regions with weaker magnetic fields than in sunspots, such as plages. Regular full-disk magnetograms have been observed since early 1960, first at MWO (Howard 1974) and then at the National Solar Observatory (NSO) at Kitt Peak starting in 1973 (Livingston et al. 1976). In our long-term project aimed at reconstructing the past magnetic activity on the Sun (Pevtsov et al. 2016, 2019; Virtanen et al. 2017, 2018, 2019a,b), we also use indirect measurements of magnetic fields obtained, in particular, from chromospheric spectroheliograms. Recently, Chatzistergos et al. (2021) and Shin et al. (2020) have used chromospheric observations to reconstruct the solar magnetic activity in the past. Reconstructing past magnetic fields is important for understanding the long-term behavior of the Sun since it is the main factor affecting space climate. Ca II K spectroheliograms are essential for this task, since the first ones were taken already in the 1890s in Europe (Paris and Meudon Observatories, France; Deslandres 1909; Malherbe & Dalmasse 2019) and in the United States (Kenwood Observatory; Hale 1893). Continuous observation campaigns in the Ca II K line started in the early 20th century in Kodaikanal (India), Mount Wilson Observatory (USA), the National Observatory of Japan (Japan), Paris-Meudon Observatory (France), the Arcetri Astrophysical Observatory (Italy), and the Astronomical Observatory of Coimbra University (Portugal) (for a historical overview see, e.g., Bertello et al. 2016; Chatzistergos et al. 2020a). Chromospheric spectroheliograms, together with flux transport simulations, have also been successfully used to study the evolution of large-scale solar magnetic fields, particularly the polar fields, which are only partially observable (Virtanen et al. 2019a).


We ignore the density stratification effect in Case I, II, and IIa, because the width of the horizontal current sheet in our simulations is much shorter than the length. The simulation domain extends from x = 0 to x = L0 in the x-direction, and from

y
=
−
0.5

L

0

 to

y
=
0.5

L

0

 in the y-direction, in the three cases, with

L

0

=

10

6

 m. Outflow boundary conditions are used in the x-direction and inflow boundary conditions in the y-direction. For the inflow boundary conditions, the fluid is allowed to flow into the domain but not to flow out; the gradient of the plasma density vanishes; the total energy is set such that the gradient in the thermal energy density vanishes; a vanishing gradient of parallel components plus divergence-free extrapolation of the magnetic field. For the outflow boundary conditions, the fluid is allowed to flow out of the domain but not to flow in, and the other variables are set by using the same method as the inflow boundary conditions. The horizontal force-free Harris current sheet is used as the initial equilibrium configuration of magnetic fields in Case I,
13

B

x
0

=
−

b

0

tanh
[
y

/

(
0.05

L

0

)
]

14

B

y
0

=
0

15

B

z
0

=

b

0

/

cosh
[
y

/

(
0.05

L

0

)
]
.

The magnetic fields in the low solar atmosphere could be very strong (Jin et al. 2009, 2012; Khomenko et al. 2014; Peter et al. 2014; Vissers et al. 2015) and the magnetic field can exceed 0.15 T in both the intranetwork and the network quiet region (e.g., Orozco Suárez et al. 2007; Martínez González et al. 2008; Jin et al. 2009, 2012). In the work by Jin et al. 2012, the maximum of the field strength was found to be 0.15 T. The magnetic field could be even stronger in the active region near the sunspot. Therefore, we set b0 = 0.05 T in Case I and Case II, and b0 = 0.15 T in Case IIa. Due to the force-freeness and neglect of gravity, the initial equilibrium thermal pressure is uniform. The initial temperature and plasma density are set as T0 = 4200 K and ρ0 = 1.66057 × 10−6 kg m−3 in Case I, and T0 = 4800 K and ρ0 = 3.32114 × 10−5 kg m−3 in Case II and Case IIa. Therefore, the initial plasma β is calculated as β ≃ 0.0583 in Case I, β ≃ 1.332 in Case II, and β ≃ 0.148 in Case IIa. The initial ionization degree is assumed as Yi = 10−3 in Case I, and Yi = 1. 2 × 10−4 in Case II and IIa. The magnetic diffusion in this work matches the form computed from the solar atmosphere model in Khomenko & Collados (2012), and we set

η
=

[

5
×

10

4

(
4200

/

T
)

1.5

+
1.76
×

10

−
3

T

0.5

Y

i

−
1

]

 m2 s−1 in Case I, and

η
=
[
5
×

10

4

(
4800

/

T
)

1.5

+
1.76

×

10

−
3

T

0.5

Y

i

−
1

]

 m2 s−1 in Case II and IIa. The first part ∼ T−1.5 is contributed by collisions between ions and electrons, the second part

∼

T

0.5

Y

i

−
1

 is contributed by collisions between electrons and neutral particles. Small perturbations for both magnetic fields and velocities at t = 0 make the current sheet to evolve and secondary instabilities start to appear later in the three cases. The forms of perturbations are listed below:
16

b

x
1

=
−
pert
·

b

0

·
sin

2
π

y
+
0.5

L

0

L

0

·
cos

2
π

x
+
0.5

L

0

L

0

17

b

y
1

=
pert
·

b

0

·
cos

2
π

y
+
0.5

L

0

L

0

·
sin

2
π

x
+
0.5

L

0

L

0

18

v

y
1

=
−
pert
·

v

A
0

·
sin

π

y

L

0

·

random

n

Max

(

∣

random

n

∣

)

,

where pert = 0.08, vA0 is the initial Alfvén velocity, randomn is the random noise function in our code, and

Max
(
∣

random

n

∣
)

 is the maximum of the absolute value of the random noise function. This random noise function makes the initial perturbations for the velocity in the y-direction to be asymmetric, and such an asymmetry makes the current sheet gradually become more tilted, especially after secondary islands appear. The reconnection process is not really symmetrical in nature (Murphy et al. 2012), this is one of the reasons that we use such a noise function. Another reason is that the asymmetric noise function makes the secondary instabilities develop faster. Figure 1(a) shows the distributions of the current density and magnetic fields at t = 0 in case I.


Finally, the multiphase nature of galactic outflows implies that measurements of the outflow properties based on a single gas phase can lead to misleading conclusions (for a discussion, see e.g., Cicone et al. 2018b). Historically, systematic studies of galactic outflows in nearby and high-z galaxies have focused on the ionized gas – for example, as observed as broad wing emission in the spectra of the Hα, [O III] or Paα lines – (e.g., Heckman et al. 1990; Rupke & Veilleux 2013a; Woo et al. 2016; Harrison et al. 2016; Förster Schreiber et al. 2019; Ramos Almeida et al. 2019) and the atomic phase – based on the Na D or Mg II lines in absorption (e.g., Heckman et al. 2000; Rupke et al. 2002, 2005; Weiner et al. 2009; Roberts-Borsani & Saintonge 2019). The molecular component of outflows, on the other hand, has been much more difficult to study. Great progress was made with the Herschel Space Observatory using the OH 119 μm line in absorption to study molecular outflows in Seyfert and luminous infrared galaxies (Fischer et al. 2010; Sturm et al. 2011; Veilleux et al. 2013; Bolatto et al. 2013; Spoon et al. 2013; George et al. 2014; Stone et al. 2016; González-Alfonso et al. 2017; Zhang et al. 2018). More recently, the advent of powerful millimeter-wave interferometers such as the Atacama Large Millimeter/submillimeter Array (ALMA) and the NOrthern Extended Millimeter Array (NOEMA) are rapidly increasing the number of molecular outflows detected based on observations of the CO line (e.g., Combes et al. 2013; Sakamoto et al. 2014; García-Burillo et al. 2014; Leroy et al. 2015; Feruglio et al. 2015; Morganti et al. 2015; Dasyra et al. 2016; Pereira-Santaella et al. 2016, 2018; Veilleux et al. 2017; Fluetsch et al. 2019; Lutz et al. 2020). At high-z, so far only a handful of large-scale, molecular outflows have been studied in QSOs (e.g., Cicone et al. 2015; Vayner et al. 2017; Feruglio et al. 2017; Carniani et al. 2017; Fan et al. 2018; Brusa et al. 2018), sub-millimeter galaxies (e.g., Spilker et al. 2018), and main-sequence, star-forming galaxies (e.g., Herrera-Camus et al. 2019).


Several studies have discussed the radio luminosity of GLEAM-X J1627 during its radio outburst in comparison with the limits of its rotational energy (Erkut 2022; Hurley-Walker et al. 2022). In particular, assuming isotropic emission, the radio luminosity of the brightest single peaks (L
radio ∼ 1030–1031 erg s−1; Hurley-Walker et al. 2022) exceeds the limits on the rotational power of the source by a few orders of magnitude. Figure 6 shows those peak radio luminosities and the rotational power of GLEAM-X J1627 in comparison with other pulsars, rotating radio transients (RRATs) and radio-loud magnetars. For the radio-loud magnetars, given their large variability, we have chosen the brightest radio pulses reported in the literature (data collected from Camilo et al. 2006, 2007; Weltevrede et al. 2011; Deller et al. 2012; Lynch et al. 2015; Majid et al. 2017; Pearlman et al. 2018; Lower et al. 2020, and Esposito et al. 2021). It is well known that assuming isotropic radio emission is not realistic, and a beaming factor necessarily has to be present (see, e.g., Erkut 2022). However, the relation between the duty cycle and the spin period of canonical pulsars has a large spread (Manchester et al. 2005). Moreover, it is observed that this relationship does not apply to radio-loud magnetars, which in general show larger duty cycles than what one would expect from the extrapolation of this tentative relation for radio pulsars to magnetars (see, e.g., Camilo et al. 2006, 2007). To avoid the uncertainty of beaming models, which for magnetars are mostly unknown even theoretically, we plotted the isotropic radio luminosity for all the different pulsar classes in Figure 6. From this plot, at variance with canonical radio pulsars, we see how the brightest single peaks for radio-loud magnetars might exceed their rotational powers, in line with what is possibly observed for GLEAM-X J1627. While not resolving uncertainties related to the exact mechanism of radio emission or the beaming factor, Figure 6 shows that, under the assumption of isotropic emission, even for magnetars the brightest single peaks exceed their rotational energy budget. Considering all the uncertainties in the assumptions used to derive the radio luminosities plotted in Figure 6, GLEAM-X J1627’s radio luminosity excess over its rotational power cannot be used as an argument for or against its neutron star nature.


Starting from the four aforementioned materials, we consider several composition mixtures and grain structures. For the sake of comparison, we first consider compact grains of purely a-Sil, a-C, or a-C:H. Subsequently, according to Köhler et al. (2015), we consider compact grains made of two thirds a-Sil and one third a-C (Mix 1) or one third a-C:H (Mix 2), in terms of volume fractions. These allow reproduction of the mass fractions derived by Jones et al. (2013) for the diffuse ISM. The effect of porosity is tested for the Mix 1 mixture, with a porosity degree of 50% (Mix 1:50). We also evaluate theimpact of the presence of a water ice mantle on compact Mix 1 grains (Mix 1:ice). We further consider two material compositions defined in Pollack et al. (1994) based on depletion measurements: (i) 21% a-Sil and 79% a-C (Mix 3); and (ii) 8% a-Sil, 30% a-C, and 62% water ice (Mix 3:ice). The various grain compositions are summarised in Table 1. For each grain composition, we derive the absorption and scattering efficiencies Qabs and Qsca, respectively, and the asymmetry factor of the phase function g = ⟨cosθ⟩. To allow fast calculations, we make the major assumption that the grains are spherical and compute their optical properties using the Mie theory (Mie 1908; Bohren & Huffman 1983) with the Fortran 90 version of the BHMIE routine given in Bohren & Huffman (1998). For grains consisting of two or three materials, we first derive effective optical constants following the Maxwell Garnett mixing rule (Maxwell Garnett 1904; Bohren & Huffman 1998). Indeed, we assume that in Mix 1 grains, for example, carbon appears as proper inclusions in the silicate matrix rather than assuming a completely random inhomogeneous medium. Mishchenko et al. (2016a,b) performed exhaustive studies of the applicability of the Maxwell Garnett mixing rule to heterogeneous particles. These latter authors showed that this rule can provide accurate estimates of the scattering matrix and absorption cross-section of heterogeneous grains at short wavelengths (typically up to the visible for a 0.1 μm grain and to the mid-infrared(MIR) for a 10 μm grain) if twocriteria are met: both the size parameter of the inclusions and the refractive index contrast between the host material and the inclusions have to be small. Moreover, Mishchenko et al. (2016a) demonstrated that the extinction and asymmetry-parameter errors of the Maxwell Garnett mixing rule are significantly smaller than the scattering-matrix errors, remaining small enough for most typical applications and in particular the kind of applications we perform here. It is however well known that this kind of mixing rule systematically underestimates the absorption efficiency in the FIR to millimetre wavelength range, the implications of which are discussed in Sect. 3.2. We perform our computations with the emc routine of V. Ossenkopf3. For Mix 1 and Mix 2, we assume a matrix of a-Sil with inclusions of a-C or a-C:H, and for Mix 3 a matrix of a-C with inclusions of a-Sil. For grains surrounded by an ice mantle, the optical properties are derived with the core-mantle Mie theory using the BHCOAT routine given in Bohren & Huffman (1998).


In the optical range, several proxies can serve as indicators of LyC leakage. In particular, line ratios involving ions with different ionization potentials, produced at different depths, have been proposed as indicators to discriminate between radiation-bounded and density-bounded H II regions. Radiation-bounded regions correspond to ionized spheres delimited by their Strömgren radii set by the equilibrium between production of photons by stars and ionization of the surrounding gas. Density-bounded regions are instead delimited by the lack of matter, which sets their outer radius before the Strömgren radius. Hence, they allow part of the LyC-photons produced by stars to escape from H II regions. The oxygen line ratio [O III]λ 5007 Å/[O II] λλ3726, 3728 Å (O32) proposed by Jaskot & Oey (2013) and Nakajima & Ouchi (2014) was successfully used to select LyC-leaking candidates but no strong correlation was found with the measured values of escape fraction (see Izotov et al. 2018b; Naidu et al. 2018; Bassett et al. 2019; Nakajima et al. 2020, and discussions therein). Based on a similar idea, the lack of emission from ions with low ionization potentials like [S II] λλ6716,6731 Å has also been proposed to target leaking candidates (Wang et al. 2019, 2021; Katz et al. 2020). This lack of emission of some low ionization species was first interpreted as the signature of a density-bounded galaxy where the outer part of H II regions were completely stripped out. However, using simple photoionization models, Stasińska et al. (2015) have shown that on average galaxies with high O32 cannot have massive escapes of ionizing photons, since low ionization lines like [O I]6300 Å are often also detected in these galaxies, implying the presence of radiation-bounded regions. Subsequently Plat et al. (2019) and Ramambason et al. (2020) noted that several strong LyC-emitters show surprisingly strong [O I]6300 Å emission, and proposed several explanations. While Stasińska et al. (2015) and Plat et al. (2019) suggested that such emission could be powered by the presence of AGN or radiative-shocks, we proposed in Ramambason et al. (2020) a 2-component model combining both density- and ionization-bounded regions.


We emphasize that 7Be/H remains larger by at least one order of magnitude than predicted by nova models (Starrfield et al. 1978; Hernanz et al. 1996; José & Hernanz 1998). We note, however, that the final amount of 7Be is sensitive to the amount of 3He in the donor star as a higher abundance of 3He is expected to result in a higher 7Be abundance. Boffin et al. (1993) and Hernanz et al. (1996) found a logarithmic dependence of the 7Be output to the initial 3He abundance. The non-linearity of 7Be yields results from 3He(3He, 2p)4He and its importance increases as the square of the initial 3He abundance. Therefore, it produces a leaking of the available 3He for the 3He(α, γ) 7Be, whose rate increases only linearly for the initial 3He abundance. For 3He enhancements up to 100 solar, Boffin et al. (1993) derive X(7Be)/X(7Be0) = 1 + 1.5log X(3He)/X(3He⊙), where 7Be0 is the 7Be final mass fraction obtained with a solar initial 3He mass fraction. From the theoretical point of view, it is believed that low-mass main-sequence stars synthesize 3He through the p–p chains with peak abundances of few 10−3 by number (Iben 1967). As the star ascends, the red giant branch convection dredges up 3He-enriched material to the surface, which is later expelled into the interstellar medium by wind or during the planetary phase. 3He is a particularly difficult element to measure. It can be measured in H ii regions by using measurements at a frequency of 8.665 GHz (i.e. 3.46 cm), which is emitted naturally by ionized 3He (Bania, Rood & Balser 2010; Balser & Bania 2018) or in the stellar atmospheres of hot stars (Geier et al. 2012). Surprisingly, interstellar medium observations indicate that there is far less of this element in the Galaxy than the current models predict. In order not to overproduce 3He in the course of chemical evolution, it has become customary to assume that some unknown 3He-destruction mechanism is at work in low-mass giants (Dearborn, Steigman & Tosi 1996; Galli et al. 1997; Chiappini, Renda & Matteucci 2002; Romano & Matteucci 2003). For instance, Charbonnel & Zahn (2007) suggested a thermohaline mixing during the red giant branch phase of low-mass stars. However, in a few planetary nebulae, 3He/H is found to be high at the level of 10−3, consistent with predictions from standard stellar models (Rood, Bania & Wilson 1992; Balser & Bania 2018).


The presented model calculations provide two-dimensional images for the scattered intensity I(x, y), azimuthal polarization Qφ(x, y), and other radiation parameters. It is useful for the comparison with observations to deduce disk-integrated radiation parameters from these model images that are scaled to the stellar intensity, as in ${{\bar I\left( i \right)} \mathord{\left/ {\vphantom {{\bar I\left( i \right)} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}{{,{{\bar Q}_\varphi }\left( i \right)} \mathord{\left/ {\vphantom {{,{{\bar Q}_\varphi }\left( i \right)} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$I¯(i)/I⋆,Q¯φ(i)/I⋆, the disk-averaged fractional polarization 〈pφ〉, or quadrant polarization values Qxxx(i)/I⋆ or Uxxx(i)/I⋆ which can also be deduced from observations without introducing significant ambiguities by the diversity of disk morphologies. We note that the measured values must be corrected for instrumental effects, in particular for the signal convolution with the instrumental PSF, which can introduce significant cancellation of the disk signal (Schmid et al. 2006; Avenhaus et al. 2014, Avenhaus et al. 2017; Heikamp & Keller 2019; Tschudi & Schmid 2021). Unfortunately, available observational data with high accuracy and quantified uncertainties are still very limited and often only some of the radiation parameters can be determined for a given disk. Therefore, the derivation of disk parameters from the comparison with model results can be rather ambiguous. The model results presented in this work allow us to carry out a detailed investigation of the important parameter ambiguities involved in the interpretation of observations of transition disks and provide diagnostic relations that can be used to constrain key model parameters for different types of observational data. For example, Fig. B.1 shows that, for a given inclination $i,{{\bar I} \mathord{\left/ {\vphantom {{\bar I} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}{{,{{\bar Q}_\varphi }} \mathord{\left/ {\vphantom {{,{{\bar Q}_\varphi }} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$i,I¯/I⋆,Q¯φ/I⋆, and ${{\bar Q} \mathord{\left/ {\vphantom {{\bar Q} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$Q¯/I⋆ all strongly correlate with the angular wall height α and single scattering albedo ω , and anti-correlate with wall slope χ and scattering asymmetry parameter ɡ. In addition, the polarization parameters ${{{{\bar Q}_\varphi }} \mathord{\left/ {\vphantom {{{{\bar Q}_\varphi }} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$Q¯φ/I⋆ and ${{\bar Q} \mathord{\left/ {\vphantom {{\bar Q} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$Q¯/I⋆ also correlated with pmax. If only the scattered intensity ${{\bar I} \mathord{\left/ {\vphantom {{\bar I} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$I¯/I⋆ or only the polarized intensity is measured then it is almost impossible to constrain individual disk parameters without additional information. Therefore, it is important to select and obtain more observational information and better diagnostic parameters with more diagnostic power.


Filippenko & Chornock (2001) first presented the dynamical estimate of mass of the source to be around 7.4 ± 1.1 M⊙. Recently, Radhika & Nandi (2014) claimed that the mass of XTE J1859+226 is perhaps in between 6.58 and 8.84 M⊙ which is similar to the prediction of Shaposhnikov & Titarchuk (2009), although the lower mass limit is estimated as 5.4 M⊙ by Corral-Santana et al. (2011). However, we consider the typical mass of the source as 7 M⊙. The distance of this source is around d ∼ 11 kpc (Filippenko & Chornock 2001). Steiner et al. (2013) measured the spin as ak ∼ 0.4; however, Motta et al. (2014b) recently reported that the spin of the source is ak ∼ 0.34. Since the spin predictions are quite close, we use ak ∼ 0.4 for this analysis. We estimate the fluxes Fx (see Table 1) of LHS and HIMS of the 1999 outburst of the source (Radhika & Nandi 2014). The corresponding disc luminosities are calculated as $L_{\rm disc}^{{\rm LHS}}=8.26 \times 10^{37}\ {\rm erg\ s^{-1}}$ and $L_{\rm disc}^{{\rm HIMS}}=1.85 \times 10^{38}\ {\rm erg\ s^{-1}}$, respectively. Now, it is reasonable to assume the accretion efficiency for rotating BH as η = 0.3 which corresponds to the accretion rate of the inflowing matter as ${\dot{M}}_{{\rm acc}}^{{\rm LHS}} = 0.304 {\dot{M}}_{{\rm Edd}}$ in LHS and ${\dot{M}}_{{\rm acc}}^{{\rm HIMS}} = 0.680 {\dot{M}}_{{\rm Edd}}$ in HIMS. For LHS, we use $R_{\dot{m}}=9.83$ per cent following our theoretical estimate where xs = 64.6rg for ak = 0.4, ${\mathcal {E}}=0.001\,98$ and λ = 3.18. Incorporating these inputs in equation (15), we obtain the jet kinetic power as $L^{{\rm LHS}}_{{\rm jet}} = 2.52\times 10^{37}\ {\rm erg\ s^{-1}}$. The maximum mass outflow rate for HIMS corresponding to ak = 0.4 is obtained from Fig. 9 as $R^{\rm max}_{\dot{m}}=17.5$ per cent for ${\mathcal {E}}=0.005\,47$ and λ = 3.1, where the shock transition occurs at 21.9rg. Using these values in equation (15), we obtain the maximum jet kinetic power as $L^{{\rm HIMS}}_{{\rm jet}} = 1.08\times 10^{38}\ {\rm erg\ s^{-1}}$ which we regard to be associated with the HIMS of this source.


In this study, we examine the stellar populations of NGC 5053 using the UVIT, on-board the AstroSat. NGC 5053 is a galactic GC that lies in the northern constellation of Coma Berenices, having Galactic coordinates l = 335${_{.}^{\circ}}$70, b = 78${_{.}^{\circ}}$95. This cluster is located at a distance of 17.54 ± 0.23 kpc (Baumgardt & Vasiliev 2021) and the metallicity is estimated to be [Fe/H] = −2.27 (Harris 2010). It is, therefore, placed amongst the metal-poor galactic GCs. The tidal radius of this cluster has been estimated as rt = 15.2 ± 3.3 arcmin by de Boer et al. (2019). When it was discovered in 1784, it was not classified as a GC because of its appearance and structure; there was no densely packed nucleus, and the central region was resolvable (Herschel 1786). These observations placed this GC in a grey-area between globular and open clusters. It was only in 1928 that Baade first classified it as a GC owing to its high latitude, richness in faint stars and presence of variable stars (Baade 1928). The variable stars in this cluster include RR Lyrae variables and SX Phoenicis (SX Phe) stars (Sawyer 1946; Nemec, Mateo & Schombert 1995a; Nemec et al. 1995b; Nemec 2004). The cluster is known to have a HB that is extended predominantly towards the blue flank of the RR Lyrae instability strip, which is an archetypal feature in many metal-poor GCs (Sarajedini & Milone 1995). A rich population of BSSs has been identified in this cluster (Sarajedini & Milone 1995). The presence of relatively large number of BSSs in such low density GCs has been examined to propose alternate formation mechanisms of BSSs (Leonard & Fahlman 1991). The cluster has been examined in the UV regime by Schiavon et al. (2012) using photometric data from GALEX, and they have published a catalogue of the UV bright stars present in this cluster. The location of this cluster in the sky and its velocity have given rise to a debate on whether it belongs to the Milky Way or Sgr dSph (e.g. Law & Majewski 2010; Boberg, Friel & Vesperini 2015; Sbordone et al. 2015; Tang et al. 2018).


Situated in the closest vicinity of their host stars (0.05 AU) and having no counterparts in our Solar system, ultra-hot Jupiters (Arcangeli et al. 2018; Bell & Cowan 2018; Parmentier et al. 2018) are ideal testbeds for studying the impact of 3D effects on high-resolution spectra. There are two important reasons for this. First, ultra-hot Jupiters are accessible objects to observe. Their short orbital periods (1–2 d) and hot, extended atmospheres make them perfect targets for transmission spectroscopy (Hoeijmakers et al. 2019; Von Essen et al. 2019; Ehrenreich et al. 2020; Borsa et al. 2021), emission spectroscopy (Evans et al. 2017; Arcangeli et al. 2018; Mikal-Evans et al. 2020) and phase-curve studies (Zhang et al. 2018; Bourrier et al. 2020b; Mansfield et al. 2020). Secondly, ultra-hot Jupiters display extreme variations across their atmospheres, because they are expected to become tidally locked soon after their formation (Rasio et al. 1996; Showman & Guillot 2002). As a result, their atmospheres virtually consist two different worlds: a permanently irradiated dayside and a permanently dark nightside. The scorching, cloud-free dayside (T ≳ 2500 K) nearly resembles a stellar photosphere, where most molecules are dissociated1 and metals become ionized (Parmentier et al. 2018; Hoeijmakers et al. 2019). On the other hand, the nightside is substantially cooler (T ≲ 1000 K) and may even serve as a stage for cloud formation (Helling et al. 2019; Ehrenreich et al. 2020). Ultra-hot Jupiters also exhibit large differences in their thermal structures: the dayside is expected to show strong thermal inversions (Haynes et al. 2015; Evans et al. 2017; Kreidberg et al. 2018; Pino et al. 2020; Yan et al. 2020), whereas nightside temperatures are expected to monotonically decrease with altitude. Furthermore, ultra-hot Jupiters feature strong winds in the order of 1–10 km s−1 (Tan & Komacek 2019), which arise as a result of the continuous day-night forcing. Many observational studies have measured Doppler shifts due to winds on ultra-hot Jupiters (Casasayas-Barris et al. 2019; Bourrier et al. 2020a; Cabot et al. 2020; Ehrenreich et al. 2020; Gibson et al. 2020; Hoeijmakers et al. 2020; Nugroho et al. 2020; Stangret et al. 2020; Borsa et al. 2021; Kesseli & Snellen 2021; Rainer et al. 2021; Tabernero et al. 2021), yet inferring the underlying 3D circulation pattern is a formidable challenge.


Therefore, the kinetics characteristics of the star could be the only piece to judge whether or not the SM star is the surviving companion of SN 1006. If its space velocity is significantly different from the other stars in the remnant of SN 1006, the probability to be the surviving companion would become high. Otherwise, the probability becomes low. We check the proper motion of the stars within 5 arcmin of the remnant centre from Gaia DR2, as shown in Fig. 19. From the figure, it seems that there is not difference between the SM star and other stars in the remnant of SN 1006 in the aspect of proper motion, i.e. the proper motion of the SM star only slightly deviates from the median value of the proper motions of the stars at the direction of the SNR centre of SN 1006, and such a proper motion disfavours the SM star as the surviving companion of SN 1006 (Schweizer & Middleditch 1980; Burleigh et al. 2000). So, a 3D space velocity is helpful to judge the nature of the SM star. However, unfortunately, some data of the SM star in Gaia DR2 are so uncertain that we cannot use them to constrain its 3D space velocity, otherwise we could obtain a complete wrong conclusion.5 For example, the parallax of the SM star is ϖ = 0.0736 ± 0.1244, and then σϖ/ϖ = 1.69 which is much larger than the threshold value of 0.2 for distance estimation from GAIA DR2 data (Astraatmadja & Bailer-Jones 2016; Katz et al. 2018). The distance of the SM star from this parallax is much larger than all the previous measurements from spectrum by at least a factor of 2 (see summary in Burleigh et al. 2000). Considering that some other astrometric measurements of the SM star are also very uncertain, we applied the measurements in the previous literatures as the distance of the SM star. Based on a radial velocity of $-13\pm 17\, {\rm km^{\rm -1}}$ and a distance of 2.07 ± 0.18 kpc (Schweizer & Middleditch 1980; Winkler et al. 2003; Kerzendorf et al. 2018), we can calculate the UVW velocities of the SM star, i. e. $U=-5.2\pm 14\, {\rm km^{\rm -1}}$, $V=197\pm 10\, {\rm km^{\rm -1}}$, and $W=3.1\pm 5\, {\rm km^{\rm -1}}$. The V value of the SM star is smaller than that of a normal disc star. We then transform these velocities into the Galactic rotational velocity at a Galactocentric distance of ∼6.67 kpc, i.e. $V_{\rm c}=196\pm 12\, {\rm km^{\rm -1}}$, which is smaller than the Galactic rotational velocity of the disc stars at the Galactocentric distance by $50\pm 19\, {\rm km^{\rm -1}}$ (Huang et al. 2016). This velocity difference is marginally consistent with the predicted orbital velocity here (see Fig. 7). In addition, the smaller rotational velocity of the SM star may explain its small proper motion shown in Fig. 19. So, the SM star is still possible to be the surviving companion of SN 1006.


Active galactic nuclei (AGN) are thought to be powered by an accretion disc around a supermassive black hole, mostly emitting in the optical/ultraviolet (UV) band. According to the standard paradigm, the X-ray emission is due to thermal Comptonization of the soft disc photons in a hot region, the so-called corona (Haardt & Maraschi 1991; Haardt, Maraschi & Ghisellini 1994, 1997). This process explains the power-law shape of the observed X-ray spectrum of AGN. A feature of thermal Comptonization is a high-energy cut-off, which has been observed around ∼100 keV in several sources thanks to past observations with Compton Gamma-Ray Observatory (CGRO)/Oriented Scintillation Spectrometer Experiment (OSSE; Zdziarski, Poutanen & Johnson 2000), BeppoSAX (Perola et al. 2002) and more recently Swift/Burst Alert Telescope (BAT; Baumgartner et al. 2013) and INTEGRAL (Malizia et al. 2014; Lubiński et al. 2016). From the application of Comptonization models, such high-energy data allow to constrain the plasma temperature, which is commonly found to range from 50 to 100 keV (e.g. Zdziarski et al. 2000; Lubiński et al. 2016). Furthermore, the cut-off energy is now well constrained in an increasing number of sources thanks to the unprecedented sensitivity of NuSTAR up to ∼80 keV (e.g. Ballantyne et al. 2014; Brenneman et al. 2014; Marinucci et al. 2014; Baloković et al. 2015; Matt et al. 2015; Ursini et al. 2015). The primary X-ray emission can be modified by different processes, such as absorption from neutral or ionized gas (the so-called warm absorber), and Compton reflection from the disc (e.g. George & Fabian 1991; Matt, Perola & Piro 1991) or from more distant material, like the molecular torus at pc scales (e.g. Matt, Guainazzi & Maiolino 2003). A smooth rise below 1–2 keV above the extrapolated high-energy power law is commonly observed in the spectra of AGN (see e.g. Bianchi et al. 2009). The origin of this so-called soft excess is uncertain (see e.g. Done et al. 2012). Ionized reflection is able to explain the soft excess in some sources (e.g. Crummy et al. 2006; Ponti et al. 2006; Walton et al. 2013), while Comptonization in a ‘warm’ region is favoured in other cases (e.g. Mehdipour et al. 2011; Boissay et al. 2014).


To search for transit events, we will make use of our custom pipeline SHERLOCK (Pozuelos et al. 2020)5. This pipeline provides the user with easy access to Kepler, K2, and TESS data for both SC and LC. The pipeline searches for and downloads the pre-search data conditioning simple aperture (PDC-SAP) flux data from the NASA Mikulski Archive for Space Telescope (MAST). Then, it uses a multi-detrend approach in the WOTAN package (Hippke et al. 2019), whereby the nominal PDC-SAP flux light curve is detrended several times using a biweight filter or a Gaussian process, by varying the window size or the kernel size, respectively. This multi-detrend approach is motivated by the associated risk of removing transit signals, in particular, short and shallow signals. Each of the new detrended light curves, jointly with the nominal PDC-SAP flux, is then processed through the transit least squares (TLS) package (Hippke & Heller 2019) in the search for transits. In contrast to the classical box least-squares (BLS) algorithm (Kovács et al. 2002), the TLS algorithm uses an analytical transit model that takes the stellar parameters into account. Then, it phase folds the light curves over a range of trial periods (P), transit epochs (T0), and transit durations (d). It then computes the χ2 between the model and the observed values, searching for the minimum χ2 value in the 3D parameter space (P, T0, and d). The TLS algorithm has been found to be more reliable than the classical BLS in finding any type of transiting planet, and it is particularly well suited for the detection of small planets in long time series, such as those coming from Kepler, K2, and TESS. The TLS algorithm also allows the user to easily fine-tune the parameters to optimize the search in each case, which is particularly interesting for shallow transits. In addition, SHERLOCK incorporates a vetting module that combines the TPFplotter (Aller et al. 2020), LATTE (Eisner et al. 2020), and TRICERATOPS (Giacalone et al. 2021) packages, which allows the user to explore any contamination source in the photometric aperture used, momentum dumps, background flux variations, x–y centroid positions, aperture size dependences, flux in-and-out transits, each individual pixel of the target pixel file, and to estimate the probabilities for different astrophysical scenarios such as transiting planet, eclipsing binary, and eclipsing binary with twice the orbital period. Collectively, these analyses help the user estimate the reliability of a given detection.

Uses Uses Compare/Contrast Compare/Contrast


It has been claimed that, for solar-type stars, CA models could face some difficulties (in principle) explaining the presence of giant planets around metal-poor stars, or massive planets at long radial distances (see e.g., Helled et al. 2014). In particular, HR 8799 is a metal-poor A5 star included in our sample, hosting three giant planets orbiting beyond 10 AU (Marois et al. 2008). Then, some authors proposed that the planets orbiting HR 8799 are likely formed by GI, given that GI models can take place at large radii and in low metal environments (Marois et al. 2008; Dodson-Robinson et al. 2009; Meru & Bate 2010). Other works cast some doubts about the planet formation around HR 8799, showing that CA models are also possible (Currie et al. 2011) or even a combination of GI and CA (Marois et al. 2010). For the case of β Pictoris and HD 169142, also having giant planets at long distances, CA models seem to be favored (GRAVITY Collaboration 2020; Nowak et al. 2020; Pérez et al. 2019). However, an important word of caution about these works is in order. Some of the stars mentioned (HR 8799 and HD 169142) display (superficial) metal-poor abundances, showing in fact a λ Boötis pattern (see for example Fig. 8). As previously mentioned, the most accepted idea about the origin of this peculiar signature, suppose a solar-like composition for the original molecular cloud where the stars born, and then some kind of selective accretion to obtain a λ Boötis pattern. In this way, it would be not entirely appropriate to assume a metal-poor natal environment for stars like HR 8799, as assumed by some works to support a GI planet formation (e.g., Meru & Bate 2010). This fact was early noted by Paunzen et al. (2014), in their comparison of λ Boötis stars and Population II type stars. Numerical simulations of planet formation around λ Boötis stars should assume a solar-like composition (rather than a metal-poor natal environment), and this could have important consequences for the subsequent results.


The flux calibration was performed from two calibration sources: (1) the spectrum of the spectrophotometric standard star GD71 (Bohlin 2003), obtained in 2016 January, which is used to eliminate as much as possible any strong wavelength dependence; (2) the median combination of a set of 10 images of the standard star HZ 4 (Bohlin, Dickinson & Calzetti 2001) obtained right after the end of the cube observation with photometric conditions similar to the observation conditions. The exact value of the interferometer’s modulation efficiency (ME), which acts essentially as an additional throughput loss, is the major source of uncertainty on the absolute flux calibration (Martin & Drissen 2016). Interferometric images of the laser source have been obtained before and after the observation of the target in order to measure the variation of ME at the calibration laser wavelength (543.5 nm) with respect to its nominal value (85 per cent). We have measured a loss of 11.7 per cent. The initial flux calibration of M 31 in the SN3 filter has been corrected for this loss (thus multiplied by a factor 1.13). But given the possible uncertainty on this estimate, we have double-checked it using Hubble Space Telescope (HST) narrow-band images of the target. The advantage of HST’s narrow-band filters is that they can easily be simulated by integrating the spectral cube over the filter’s well-known transmission curve. As SITELLE’s cube flux is expressed in erg cm−2 s−1 Å−1 and given the filter transmission curve F(σ), the integrated flux $\tilde{\phi }_{\rm F}$, expressed in erg cm−2 s−1 Å−1, is
(15)
\begin{equation}
\tilde{\phi }_{\rm F} = \frac{\int _{-\infty }^{+\infty }\phi (\sigma )F(\sigma ){\rm d}\sigma }{\int _{-\infty }^{+\infty }F(\sigma ){\rm d}\sigma }\, .
\end{equation}
If one converts the flux in terms of surface brightness, expressed in erg cm−2 s−1 Å−1 per HST pixel surface (SHSTCamera), i.e.
(16)
\begin{equation}
\tilde{B}_{\rm F} = \frac{\tilde{\phi }_F }{S_{\rm SITELLE}}S_{\rm HSTCamera},
\end{equation}
with SSITELLE = 0.322 arcsec2, the image $\tilde{B}_{\rm F}$, once properly aligned, can be directly compared with the HST frame. We have made this comparison for three different regions of the FOV (called WFC3, ACS1 and ACS2, shown in Fig. 9) and four different filters (F656N, F658N, F665N and F660N). Histograms of the flux ratio between the integrated frames and the HST frames are presented in Fig. 10 and the first moments of their distributions are listed in Table 3.


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


Galaxies are surrounded by vast gaseous haloes which extend well beyond the hosts’ stellar components: Early observations of quasar sight lines attributed the presence of absorption at multiple intermittent redshifts to gaseous haloes of intervening galaxies (e.g. Bergeron 1986; Bergeron & Boissé 1991; Lanzetta et al. 1995; Tripp, Savage & Jenkins 2000; Chen, Lanzetta & Webb 2001). In the past decade, owing to the rise of large spectroscopic surveys of galaxies with well-determined physical properties (e.g. SDSS), all sky UV surveys (e.g. GALEX), and improved sensitivity of UV spectrographs (e.g. COS), studies of the gaseous haloes of galaxies could systematically connect gas absorption properties to galaxy properties in statistically meaningful samples (e.g. Cooksey et al. 2010; Prochaska et al. 2011; Tumlinson et al. 2013; Liang & Chen 2014; Lehner, Howk & Wakker 2015). The aforementioned gaseous haloes are commonly referred to as the circum-galactic medium (CGM) and are ubiquitous in galaxies regardless of mass or star formation activity: even sub-L* galaxies (Bordoloi et al. 2014), and passive galaxies host a CGM (Thom et al. 2012). The current model of the CGM suggests the presence of a clumpy multiphase medium which extends beyond the virial radius of the host galaxy, with a declining radial density profile, containing a substantial amount of gas and metals (e.g. Werk et al. 2013, 2014; Liang & Chen 2014; Lehner et al. 2014, 2015; Prochaska et al. 2017). Observational studies targeting the CGM of L* galaxies showed that the CGM gas content is comparable to the mass of the interstellar medium (ISM; e.g. Chen et al. 2010; Tumlinson et al. 2011; Werk et al. 2014; Prochaska et al. 2017) and correlates positively with ISM properties (Borthakur et al. 2015). Additionally, CGM observations infer a significant amount of metals (e.g. Werk et al. 2013; Peeples et al. 2014) where CGM metallicities can extend to supersolar metallicities (Prochaska et al. 2017). The clumpy multiphase CGM consists of a warm gas T ∼ 104 − 5 K (clumpy in nature) embedded within a hot diffuse T ∼ 106 K medium (e.g. Heitsch & Putman 2009; Armillotta et al. 2017; Bordoloi et al. 2017). The multiphase structure of the CGM is corroborated by the variety of observed ionic species which survive at a vast range of temperatures: While the warm gas hosts the low ionization species (e.g. H i, Si ii, Si iii, C ii, C iv), the hot medium is home for the most highly ionized species (e.g. O vi, O vii). Additionally, the spectral line profiles of absorbers in the CGM can be reproduced by invoking a patchy medium (e.g. Stern et al. 2016; Werk et al. 2016), i.e. multiple high density gas clouds contribute to the optical depth along the line of sight thus leaving their kinematic imprint on the absorption line profile. For a review of the CGM, see Putman, Peek & Joung (2012) and Tumlinson, Peeples & Werk (2017).


Ever since the initial measurements of the cosmic infrared background (CIB; for a review, see Hauser & Dwek 2001) revealed that the amount of energy radiated in the far-infrared (IR) and submillimeter spectral windows is comparable to that measured at ultraviolet (UV) and optical wavelengths, it has been widely recognized that one of the keys to a comprehensive understanding of the star formation history of the universe is the study of the multiwavelength properties of dusty star-forming galaxies (DSFGs), whose integrated radiation produces the CIB. These systems host intense star-forming activity obscured by large columns of dust, which re-emit the UV radiation of young hot stars at longer wavelengths, so that the peak of their rest-frame spectral energy distribution (SED) falls in the far-IR. In the local universe, DSFGs are typically identified as luminous or ultraluminous infrared galaxies (LIRGs/ULIRGs; Sanders & Mirabel 1996), whereas more distant DSFGs’ emission can be redshifted into the submillimeter domain, allowing many to manifest as submillimeter galaxies (SMGs; Blain et al. 2002; Casey et al. 2014). SMGs were first detected with the Submillimeter Common-User Bolometer Array (SCUBA; Holland et al. 1999) on the James Clerk Maxwell Telescope both in blank-field surveys (e.g., Hughes et al. 1998; Barger et al. 1999; Scott et al. 2002; Serjeant et al. 2003; Webb et al. 2003; Coppin et al. 2006) and behind galaxy clusters (e.g., Smail et al. 1997; Chapman et al. 2002; Cowie et al. 2002; Knudsen et al. 2008). With the subsequent advent of comparable single-dish telescopes and larger format instruments covering the 870 μm atmospheric window like the Large APEX Bolometer Camera (LABOCA; Siringo et al. 2009) on the 12 m Atacama Pathfinder Experiment telescope (APEX; Güsten et al. 2006), and more recently SCUBA-2 (Holland et al. 2013), the number of known SMGs is now of the order of a few thousand (e.g., Weiß et al. 2009; Johansson et al. 2011; Chen et al. 2013; Hsu et al. 2016; Geach et al. 2017), and intensive observational efforts have been devoted to understanding their physical properties. In this quest, one of the main challenges has been the coarse (15″–20″) resolution of single-dish observations, which hinders the identification of counterparts at different wavelengths and can result in the blending of multiple, fainter SMGs into a single brighter object. However, the persistence of the local radio–FIR correlation to higher redshifts (e.g., Condon 1992) allows accurate SMG positions from deep radio imaging obtained with the Very Large Array (VLA) at 1.4 GHz and the Australia Telescope Compact Array (ATCA) at 2.1 GHz (e.g., Ivison et al. 1998, 2000, 2002; Smail et al. 2000; Chapman et al. 2002) to be determined, thus enabling the identification of optical and near-IR counterparts, determination of photometric and spectroscopic redshifts (e.g., Chapman et al. 2005), modeling of SEDs, analysis of individual morphologies, and characterization of dust and stellar components (for full reviews of these results, see Blain et al. 2002 and Casey et al. 2014). The general picture derived from such studies is that SMGs are massive, gas-rich galaxies with high IR luminosities (

) and complex optical/near-IR morphologies, in which respects they resemble the local ULIRG population. However, SMGs have a median redshift z ∼ 2.5 (Chapman et al. 2005) and a significantly higher number density than ULIRGs. Complementary observations with centimeter and (sub)millimeter telescopes have been used as well to study the cool, molecular gas of SMGs (e.g., Carilli & Walter 2013), an effort that has been transformed in recent years thanks to the exceptional spatial resolution and sensitivity provided by the Jansky VLA and the Atacama Large Millimeter/submillimeter Array (ALMA). Moreover, high-resolution continuum imaging at 870 μm with ALMA has made it possible to resolve the structure of the dust emission from SMGs and identify their counterparts in an unbiased way, revealing that a large fraction of bright single-dish detections actually “break up” into multiple, fainter (

 mJy) SMGs blended together at the coarse resolution of the maps in which they were detected (Hodge et al. 2013; Karim et al. 2013; Simpson et al. 2015a, 2015b).