(3) What is the likelihood of obtaining Mercury and Mars analogs in systems with Venus–Earth pair analogs? Recent terrestrial planet formation studies managed to statistically produce low-mass Mars analogs. In particular, there are currently five main competing models. (1) Grand Tack: the protoplanetary disk is truncated at ∼1 au by perturbations of an inward-then-outward gas-driven migrating Jupiter within the first 1–3 Myr of the solar system history, leaving a disk with mass concentrated within that distance after the disk gas dispersal (Walsh et al. 2011; Jacobson & Morbidelli 2014; Walsh & Levison 2016; Brasser et al. 2016a); (2) Empty Asteroid Belt: embryos and planetesimals in the protoplanetary disk formed concentrated within a narrow belt at ∼0.7–1 au (Hansen 2009; Drazkowska et al. 2016; Raymond & Izidoro 2017; Ogihara et al. 2018); (3) Early Instability: the protoplanetary disk is perturbed by the giant planets’ instability that occurred within ∼10 Myr after the disk gas dispersal, strongly depleting the disk mass beyond ∼1.3 au (Clement et al. 2018, 2019b); (4) Pebble Accretion: embryos and planetesimals form preferentially in the inner and outer regions of the protoplanetary disk, respectively, and the disk mass is concentrated within ∼1.5 au (Levison et al. 2015; Chambers 2016); (5) Sweeping Secular Resonance: the growth of embryos and planetesimals is inhibited beyond ∼1–1.5 au by perturbations of secular resonances that swept the disk during the disk gas dispersal (Bromley & Kenyon 2017). In all these models, Mars analogs may form as a result of the disk mass depletion or absence of mass beyond ∼1–1.5 au. Additionally, from the standpoint of the initial conditions of the disk after gas dispersal, models 1 and 2 are very similar, while models 3–5 probably also share similar properties. However, in the majority of those studies, it remains unclear whether these Mars analogs were obtained in systems that also contained Venus and Earth analogs. Moreover, even if they were, it is also unclear what fraction these three-planet analog systems would represent compared to all the systems obtained in those studies, because their results are often presented with all planets mixed (e.g., in plots of distance vs. mass). Furthermore, Mercury and Mars analogs in those studies are often defined as planets from the mixed population that satisfy an arbitrary distance range: e.g., 0.5 au and 1.2–2.0 au, respectively. However, this approach can lead to incomplete classifications in a given system (e.g., by failing to identify more massive Mars analogs at 1.2 au or failing to properly identify planet analogs). Indeed, it is difficult to discriminate Venus from Earth analogs, unambiguously identify Mercury/Mars analogs, and avoid misclassifications in past studies. If the five models described above are successful in reproducing a low-mass Mars, how can the best among them be discriminated without a proper system classification?


The effects of the wet air, the variable water vapour cells, are the main cause of the refraction at submillimetre/millimetre wavelengths. The dipole moment of water makes water vapour, the wet component in the troposphere, a strong absorber at submillimetre/millimetre wavelengths and significantly increases the refractive index of the air. Because the water vapour is not well mixed there are localised pockets of air with different refractive indices. In what is called the “frozen-screen” hypothesis (Taylor 1938), these pockets, or turbulent eddies, are assumed to be fixed in the atmospheric layer that advects over an interferometric array (Thompson et al. 2017). Thus, these cause various delays in the path length (variable in time and position) along the line of sight to each antenna. Interferometers are sensitive to the variations in path length, the interferometric phase difference, between pairs of antennas that form a baseline. For a given baseline (distance and orientation) the line-of-sight path to each component of an astronomical source has an intrinsic phase that relates the measured intensities to their location in an image. Thus any additional variable atmospheric delays that cause anomalous phase changes on many baselines making up an array have the effect of blurring the interferometric image; this is analogous to the effect of seeing at optical and infrared wavelengths. The introduced delays scale linearly with the difference in precipitable water vapour (ΔPWV) between an antenna pair (excluding dispersive effects) and linearly with frequency. The correlated signals between pairs of antennas (the visibilities V = V0eiφ) become partly decorrelated as a result of the phase noise. The reduced coherence for the visibilities is given by (1)\begin{equation} \label{eqn0} \langle V \rangle = V_0 \times \langle {\rm e}^{\rm i\phi} \rangle = V_0 \times {\rm e}^{-\phi^2_{\rm rms}/2} , \end{equation}⟨V⟩=V0×⟨eiφ⟩=V0×e−φrms2/2,


The global volume-weighted neutral fraction of hydrogen QH I in the high-resolution volume is presented as the thick blue line in Fig. 10. The reionization process starts when the first stars are born, and by z50 ≃ 7.63, half of the volume is reionized. We identify the redshifts at which 1%, 10%, 50%, 90% and 99% of the volume is ionized as z01 = 11.13, z10 = 8.68, z50 = 7.63, z90 = 6.58, and z99 = 5.92 respectively; corresponding to a reionization duration Δz = z99 − z10 = 2.8 (Δt ≃ 385 Myr), broadly consistent with the estimates of Robertson et al. (2015) The dark and light shaded areas in Fig. 10 correspond to the 1σ and 2σ constraints on the redshift of reionization from the cosmic microwave background measurements of the Planck mission (Planck Collaboration VI 2020), with a reionization midpoint zre = 7.67 ± 0.73. We also compare the OBELISK reionization history to a selection of observational constraints: Black hexagons correspond to the measurements of the Lyman-α forest transmission (Lyα forest, Fan et al. 2006b), the green circles show constraints on the IGM opacity from the fraction of Lyman-α emitters in Lyman-break galaxy samples (Schenker et al. 2014; Ono et al. 2012; Pentericci et al. 2014; Robertson et al. 2013; Tilvi et al. 2014), the purple diamonds show measurements from quasar damping wings by Mortlock et al. (2011), Schroeder et al. (2013), Bañados et al. (2018), Ďurovčíková et al. (2020), the red diamonds show similar measurements on gamma-ray bursts (GRB, Totani et al. 2006, 2016), and the black squares from Ouchi et al. (2010), Ota et al. (2008) represent constraints derived from the evolution of the Lyman-α luminosity function. Some of these data points come from the compilations of Bouwens et al. (2015). Overall, we find that the simulation agrees with most observations in terms of reionization history, despite the fact that we focus on an overdense region. Interestingly, the simulation manages to capture residual neutral fraction after reionization is complete at z  6 similar to what is observed. We discuss this point further below.


More recently, García-Bernete et al. (2022) found that the PAH molecules responsible for the 11.3 μm PAH emission band are more resilient in the hard environments often present in AGN. In particular, the authors found larger 11.3/7.7 μm and 11.3/6.2 μm PAH ratios in AGN-dominated systems compared to SF galaxies, indicating a larger fraction of neutral PAH molecules (as noted by Smith et al. 2007 using a sample of relatively weak AGN). However, these studies were limited by the spatial resolution (∼4″) and the low spectral resolution (R ∼ 60–130) of Spitzer/InfraRed Spectrograph (IRS). Previous sub-arcsecond angular resolution N-band (∼8–13 μm) ground-based spectroscopic studies investigated the 11.3 μm PAH feature in the nuclear and circumnuclear regions of AGN (e.g., Hönig et al. 2010; González-Martín et al. 2013; Alonso-Herrero et al. 2014, 2016; Ramos et al. 2014; Esquej et al. 2014; García-Bernete et al. 2015; Jensen et al. 2017; Esparza-Arredondo et al. 2018). However, these works were unable to provide definitive details regarding the effect of the AGN on the PAH molecules due to limited wavelength coverage and sensitivity. The changes in the PAH properties due to the presence of the AGN might be more prominent in their innermost regions of galaxies. Therefore, the unprecedented combination of high angular and spectral resolution (R ∼ 1500 − 3500) in the entire mid-IR range (4.9–28.1 μm) afforded by the James Webb Space Telescope (JWST)/Mid-Infrared Instrument (MIRI; Rieke et al. 2015; Wells et al. 2015; Wright et al. 2015) is key to investigating PAH properties. In this Letter we report on the first investigation of PAH emission in the nuclear regions of three luminous Seyfert (Sy) galaxies and compare them with emission from SF regions using JWST/MIRI Medium Resolution Spectrograph (MRS) data. This enables us, for the first time, to characterise the PAH properties of local luminous Sy galaxies (log (Lbol)> 44.46 erg s−1)1 at sub-arcsecond scales (∼0.45″, ∼142–245 pc).


In this study we are focusing on rest-frame UV emission red-wards of the strongest UV emission line, Lyα, partially motivated by the challenges of observing this line at high redshift (z ≳ 6) where the significantly neutral CGM and IGM absorbs the Lyα photons escaping the galaxy along the line of sight (e.g., Dijkstra et al. 2011; Laursen et al. 2011, 2019; Dijkstra 2017). Nevertheless, the Lyα line itself has improved our understanding of star-forming galaxies in the (early) Universe. In particular, the asymmetric Lyα line profile has enabled redshift confirmations of large samples of sources at both 2  z  6 (e.g., Steidel et al. 2014; Le Fevre et al. 2015; Herenz et al. 2017; Inami et al. 2017; Urrutia et al. 2019) and high redshift at z > 6 (e.g., Finkelstein et al. 2013; Oesch et al. 2015; Schmidt et al. 2016; Tilvi et al. 2016; Huang et al. 2016; Pentericci et al. 2018; Fuller et al. 2020). The resonant scattering of the photons and the resulting (occasional) multipeaked emission has been shown to relate closely to the column density and dynamics of the neutral hydrogen in the ISM and the CGM (Verhamme et al. 2015; Gazagnes et al. 2018, 2020). The fraction of galaxies with confirmed Lyα emission has been used to probe the evolution (or lack thereof) of the fraction of LAEs among Lyman-break galaxies from low redshift to the EoR (e.g., Treu et al. 2013; Pentericci et al. 2014; Tilvi et al. 2014; de Barros et al. 2017; Caruana et al. 2018; Kusakabe et al. 2020). Together with the observed velocity offset of the Lyα line resulting from resonant scattering (Schenker et al. 2013; Erb et al. 2014; Hashimoto et al. 2015; Stark et al. 2017; Verhamme et al. 2018), this has probed the amount of neutral gas in the IGM and has constrained the neutral fraction of the Universe during the EoR (Ouchi et al. 2010; Greig et al. 2017; Mason et al. 2018a,b; Banados et al. 2018; Hoag et al. 2019). Furthermore, comparisons between Lyα and Hα or UV emission line strengths have been used to study the production efficiency and escape of ionizing photons from LAEs (Nakajima et al. 2016; Matthee et al. 2017; Harikane et al. 2018; Lam et al. 2019; Maseda et al. 2020). It is therefore of interest to relate and compare the measured rest-frame UV emission lines red-wards of Lyα studied here, with the characteristics of the Lyα line itself and the properties of the LAEs in our sample.


In the context of solar wind turbulence, one crucial question concerns turbulence evolution and heating (Parashar et al. 2015; Chen 2016; Viall & Borovsky 2020). Numerous correlations exist between solar wind parameters and magnetic fluctuations, which can provide important indications and constraints on the physics of turbulence evolution and heating processes. Early observations showed that faster solar wind usually corresponds to higher proton temperature (e.g., Marsch et al. 1982; Elliott et al. 2012). The faster solar wind tends to be more imbalanced with greater wave energy flux antisunward than sunward (Tu & Marsch 1995), and can be characterized by larger inertial-scale magnetic energy density and steeper proton-scale magnetic spectrum (Bruno et al. 2014). A study by Wind observations revealed that higher proton temperature is associated with a steeper proton-scale magnetic spectrum (Leamon et al. 1998b). Statistical studies by Wind and Advanced Composition Explorer measurements later revealed that higher proton temperature is related to larger inertial-scale magnetic energy density (Smith et al. 2006; Vech et al. 2018). Recent statistical studies by Wind and Parker Solar Probe (PSP) observations further revealed that higher proton temperature is linked to larger proton-scale magnetic energy density (Zhao et al. 2020, 2022). On the other hand, cross and magnetic helicities at inertial and kinetic scales, respectively, are often employed to describe the imbalance and handedness of solar wind turbulence. A correlation between cross and magnetic helicities was reported, which was interpreted as the signature of cyclotron-resonant dissipation in solar wind turbulence (Leamon et al. 1998a). A strong correlation (with a correlation coefficient (CC) up to 0.8 occasionally) between the proton-scale spectral index and magnetic helicity was found (Pine et al. 2020; Zhao et al. 2021, 2022). Via PSP observations, a mild correlation (with a CC of 0.36) between the spectral index and cross helicity was displayed in the most recent literature (Huang et al. 2021). However, less attention has been paid to the relations between these correlations despite the large body of research.


Figure 1 shows the best fits of a multiple-Gaussian model to the T
90 distributions of distinct Swift/BAT GRB samples. Interestingly, we find from Figures 1(a)–(d) that the lognormal T
90 durations of all Swift GRBs except those with good spectra in sample V are triply distributed. It is confirmed in Figure 1(e) that the Swift/BAT GRBs with a well-measured peak energy are bimodally distributed at a boundary of ∼1 s, which is in good agreement with Zhang et al. (2020). Note that the third component remains controversial. On the other hand, Hakkila et al. (2000) suggested that the third subgroup proved by statistics was only a deviation caused by complex instrumental effects, which could reduce the duration of some weak long pulses. In addition, another classification scheme uses a scatter plot of flux and duration fitted with two-dimensional Gaussian functions (Bálazs et al. 2003). Some authors pointed out that there are more than two clusters (Mukherjee et al. 1998; Horváth 1998). Unfortunately, the physical origin of the extra components cannot be reasonably interpreted. The two-Gaussian fit to data in Figure 1(e) demonstrates that the duration distribution peaks at 0.21 ± 0.38 s with a spread of 0.93 dex for short bursts and at 43.97 ± 1.05 s with a spread of 1.12 dex for long GRBs. The best fit returns a good reduced Chi-square of

χν2

 ≈ 0.82, indicating that two classes are evidently reconfirmed and separated at T
90 ≈ 1.06 s instead of at T
90 = 2 s shown by CGRO/BATSE data. The dividing line of 1 s is consistent with some previous results of Swift/BAT GRBs (Berger et al. 2013; Gruber et al. 2014; Zhang et al. 2020). Additionally, the number of components in each T
90 distribution of Figure 1 has been accordingly tested by the traditional Bayesian information criterion (BIC) as we previously did (e.g., Zhang et al. 2016; Li et al. 2021b). Figure 1 demonstrates that the S/N level and the EE component are two important contributors to the third class of GRBs. In other words, one of them can separately confuse the classification of GRBs in terms of T
90 only.


Several qLMXBs have been identified in GCs and in the Galactic field (for some examples, see table 4 in Guillot et al. 2009 and references therein). While LMXBs in the field were detected following the onset of a bright accretion outburst, most qLMXBs in GCs, including all those with the highest flux at Earth, have not shown accretion activity.3 Most of these sources have only been spectrally identified based on their similarities to field LMXBs, observed during quiescence (e.g. Cen X-4 or Aql X-1). Previous works have confirmed that H-atmosphere models accurately describe the spectra of qLMXBs, with radii in the range 10–15 km, as expected for NSs, either from single sources (e.g. Heinke et al. 2006a; Webb & Barret 2007; Guillot, Rutledge & Brown 2011; Heinke et al. 2014; Bogdanov et al. 2016), or from statistical analyses of multiple qLMXBs (e.g. Guillot et al. 2013; Guillot & Rutledge 2014; Lattimer & Steiner 2014; Guillot 2016; Steiner et al. 2018). However, in some cases the accreted material may not be hydrogen, but helium (e.g. Servillat et al. 2012; Catuneanu et al. 2013; Heinke et al. 2014). One way to circumvent this is to identify the nature of the donor star, i.e. to determine the nature of the material transferred on to the NS (e.g. with the detection of an H α emission line, presumably originating in a faint accretion disc, Haggard et al. 2004). The possibility of helium (or heavier element) atmospheres is well-founded on the existence of ultracompact X-ray binaries (UCXB), with white dwarfs or helium-dominated donors4 (e.g. Zurek et al. 2009; Altamirano et al. 2010; Sanna et al. 2017; Cadelano et al. 2019). In fact, around 1/3 of the LMXBs in GCs with constraints on the companion nature, possess a white dwarf donor (Bahramian et al. 2014). Since NS He-atmosphere models have harder spectra than H-atmosphere models, using the incorrect composition for the observed thermal emission can result in biases of the inferred radii (Servillat et al. 2012; Heinke et al. 2014).


The second ingredient is the probability distribution of stellar mass at given SFR and redshift:
5

dpdlogM⋆(M⋆∣ψ,z)∝M⋆M⋆M⋆,MS(ψ,z)M⋆,MSexp−logM⋆−logM⋆,MSψ,z22σlogM⋆2M⋆≥M⋆,MS(ψ,z),

where M
⋆,MS(ψ, z) is the observed redshift-dependent galaxy main sequence with log-normal scatter

σlogM⋆≈0.2

 dex (we adopt the determination by Speagle et al. 2014 for an anlytic fit, see their Equation (28)). The main sequence is a relationship between SFR and stellar mass followed by the majority of star-forming galaxies, apart from some outliers located above the average SFR at given stellar mass (see Daddi et al. 2007; Rodighiero et al. 2011, 2015; Sargent et al. 2012; Speagle et al. 2014; Whitaker et al. 2014; Schreiber et al. 2015; Caputi et al. 2017; Bisigello et al. 2018; Boogaard et al. 2018). The expression in Equation (5) holds for an approximately constant SFR history, which is indicated both by in situ galaxy formation scenarios (see Mancuso et al. 2016b; Pantoni et al. 2019; Lapi et al. 2020) and by observations of ETG progenitors (that have on overage slowly rising star formation history with typical duration of ≲1 Gyr; see Papovich et al. 2011; Smit et al. 2012; Moustakas et al. 2013; Steinhardt et al. 2014; Cassará et al. 2016; Citro et al. 2016) and late-type galaxies (that have on the average slowly declining star formation history over a long timescale of several gigayears; e.g., see Chiappini et al. 1997; Courteau et al. 2014; Pezzulli & Fraternali 2016; Grisoni et al. 2017). In this vein, off-main-sequence objects can be simply viewed as galaxies caught in an early evolutionary stage that are still accumulating their stellar mass (which grows almost linearly with time for a constant SFR), and are thus found to be preferentially located above the main sequence or, better, to the left of it. As time goes by and the stellar mass increases, the galaxy moves toward the average main-sequence relationship, around which it will spend most of its lifetime before being quenched due to gas exhaustion or feedback processes.


LAE galaxies are defined by a high equivalent width (EW > 20 Å) Lyα line and are believed to be composed of extremely large regions of active star formation. Many efforts have been made to detect and characterize LAE galaxies (e.g., Conselice et al. 2003; Conselice 2004; Ravindranath et al. 2006; Shimasaku et al. 2006; Bournaud et al. 2007; Ouchi et al. 2008, 2017; Elmegreen et al. 2009a, 2009b; Tacconi et al. 2010; Gronwall et al. 2011; Kashikawa et al. 2011; Mandelker et al. 2014; Moody et al. 2014; Guo et al. 2015). In general, these galaxies appear as clusters of bright clumps, sometimes with a background of continuum emission. Evidence suggests that these clumps are larger and brighter than most star-forming regions in nearby low-redshift galaxies (Elmegreen et al. 2009a). Efforts have been made in quantifying mass, star formation rates, gas composition, and kinematics, as well as other LAE properties (e.g., Nilsson et al. 2009; Ono et al. 2010a, 2010b; Swinbank et al. 2010; Tacconi et al. 2010; Shibuya et al. 2014; Livermore et al. 2015; Nakajima et al. 2016; Hashimoto et al. 2017). These have revealed a wealth of information about the early universe, but they are ultimately limited by LAE surface brightnesses. Most studies rely upon stacks of galaxies and can draw only limited inferences about individual LAEs. Other studies show that LAE dust content, particularly clumpy dust, in the interstellar medium (ISM) can have an impact on most LAE observables (Kobayashi et al. 2007, 2010; Verhamme et al. 2008; Duval et al. 2014). Finkelstein et al. (2009) showed that clumpy dust models can provide a good fit to a set of z ∼ 4.5 LAEs, although they invoked a multiphase ISM that may be unlikely to form in nature (Laursen et al. 2013). Nevertheless, dust in LAE galaxy ISM could cause some of the irregularity in LAE surface-brightness profiles (Buck et al. 2017). With limited resolution, however, it is difficult to make this distinction. A further challenge to morphological studies is that the clump sizes are near the resolution limit of instrumental point spread functions (PSFs) and often cannot be distinguished from point sources (Guo et al. 2015). As a result, direct imaging studies cannot decisively determine whether the clumps are different in nature from star-forming regions in our local universe or if the larger apparent size is merely an artifact of insufficient resolution (Shibuya et al. 2014; Kobayashi et al. 2016; Tamburello et al. 2017; Fisher et al. 2017).


As clusters of galaxies assemble, they dynamically transform the physical properties of in-falling cluster members. Galaxies falling into a cluster experience ram pressure from dense intracluster medium (ICM) gas that can potentially unbind their individual gas reservoirs (Gunn et al. 1972). This process referred to as ram pressure stripping (RPS) can eventually remove a galaxy’s entire gas supply, making it an important quenching pathway for satellite galaxies (Vollmer et al. 2001; Tonnesen et al. 2007). Observationally, RPS results in disturbed galaxy morphologies and trailing tails of stripped gas (e.g., Kenney et al. 2004; van Gorkom 2004; Cramer et al. 2019). The most extreme examples have been dubbed “jellyfish” galaxies, due to the evocative morphologies of their star-forming tails (Ebeling et al. 2014; Boselli et al. 2016; Poggianti et al. 2016). Prior to complete gas removal, moderate values of ram pressure have also been shown to increase the star formation rate in galaxies both observed (Crowl & Kenney 2006; Merluzzi et al. 2013; Vulcani et al. 2018) and simulated (Kronberger et al. 2008; Kapferer et al. 2009; Tonnesen & Bryan 2009; Bekki 2014). In this picture, the increased pressure initially helps compress the gas and triggers increased star formation. Other proposed processes for accretion of gas to the centers of galaxies include gravitational instabilities and the inspiral of preferentially low angular momentum clumps that lose angular momentum to a wind: drag from the nonrotating ICM operating on dense clumps (Schulz & Struck 2001; Tonnesen & Bryan 2009; Ramos-Martínez et al. 2018). Over time, the interstellar medium (ISM) is fully stripped from the galaxy and star formation ceases. Recently, a very high incidence of AGN (5/7) has been observed in a sample of jellyfish galaxies (Poggianti et al. 2017), and comprehensive follow-up of this sample has led to the identification of AGN-driven outflows (Radovich et al. 2019) and a compelling case for AGN feedback in action (George et al. 2019). It is plausible that the same mechanisms that initially promote star formation can also fuel active galactic nuclei (AGN) during the ram pressure stripping process. Indeed, outside of cluster environments, ram pressure induced shocks are known to produce nuclear inflows that can fuel AGN in the context of galaxy merger simulations (Barnes 2002; Capelo & Dotti 2017; Blumenthal & Barnes 2018).


Many studies have been done to understand the dynamics and origin of such systems since the discovery of the first binary asteroid system, Dactyl orbiting around (243) Ida in 1993 (Chapman et al. 1995). Based on the structure of ‘rubble pile’ asteroids (a collection of gravitationally bound boulders with a distribution of size scales and very little tensile strength between them), a model for how they can disrupt due to close flybys of a planet was developed. However, close encounters with the planets proved not to be enough for creation of the current population of binary systems (Margot et al. 2002; Walsh & Richardson 2008). Another model for their formation is by increasing their spin rates due to incident and remitted solar photons, known as the Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) effect. The YORP effect on contact binary asteroids has been studied (Bottke et al. 2002; Merline et al. 2002; Scheeres 2002; Walsh & Richardson 2006). Using a model with an ellipsoid and a sphere in a planar case, Scheeres (2007) studied fission limits (spin limit to occur a fission) and the stability of that kind of system for different initial conditions. After that, the stability of a binary system was analysed using a two-ellipsoid model (Scheeres 2009). Pravec et al. (2010) made a complete study about formation of asteroid pairs through rotation fission. Jacobson & Scheeres (2011) studied the creation of binaries and other observed near-Earth asteroid (NEA) systems, including doubly synchronous binaries, high-e binaries, ternary systems and contact binaries. That study analysed the dynamics of a binary system just after rotational fission. Using a two-ellipsoid model taking into account mutual gravitational interactions and tidal dissipation, they analysed the dynamics for different mass ratios of the system under a planar assumption. The current work follows from these results, but looks at more likely, non-planar initial configurations. This extension is significant, as non-planar cases must take into account the complete rotational motion (rotation, precession and nutation) of each body. Our results are compared with the results obtained by Jacobson & Scheeres (2011).


Theoretically predicted magnetic field in the formation of the first stars. The evolution of a dynamo in a collapsing minihalo depends on a large number of parameters: the initial density, nH,0, the turbulent velocity, vt (which we parametrize in terms of the virial velocity, vt = ϕtvvir), the temperature, T, the mass of the collapsing cloud, M0, the rate of collapse (parametrized by ϕff), and the rate at which these quantities vary with density (denoted by qx for quantity x). (The initial value of the field, B0, enters only logarithmically, and is important only if it is many orders of magnitude less than our estimate of ∼10−16 G.) Choosing values of these parameters that are consistent with simulations (e.g. those of Greif et al. 2012), we find that the time for the field to grow from its initial amplitude of ∼10−16 G to equipartition at the viscous scale, Bν ∼ 10−8 G, is less than the virial time in the minihalo; hence, the exponential growth of the field occurs at approximately constant gas density. This rapid growth of the field is consistent with that found in previous work (e.g. Schleicher et al. 2010; Schober et al. 2012b). The subsequent non-linear dynamo amplification is sufficient to bring the field energy to within about an order of magnitude of equipartition; none the less, the overall amplification of the field is generally dominated by compression. We estimate that the field first reaches equipartition with turbulent velocities of the order of 2 km s−1 (taken from simulations) at a value of ∼10−4 G; the field subsequently grows as $n_{\rm H}^{1/2}$. The field reaches equipartition with the central 5 per cent of the mass of the gas. Our conclusion that the field reaches equipartition in a minihalo at z ∼ 25 differs from that of Xu & Lazarian (2016), who found that equipartition was not reached until a time of about 6 × 108 yr (the age of the Universe at z ≃ 8) since they did not consider the increase in density that occurs in star formation.


Thanks to the observations with high time resolution and high optical sensitivity from state-of-the-art facilities, various dynamic phenomena, and processes (e.g., magnetic reconnections, jet flows, and oscillatory waves) have been observed to be omnipresent in the multi-layers of solar atmosphere (Shibata et al. 2007; Tomczyk et al. 2007; He et al. 2010; Tian et al. 2014; Shen et al. 2018). In the past, magnetic reconnection and wave dissipation are viewed as two seemingly distinct mechanisms opposite to one another when dealing with the problems of coronal heating and solar wind origin (e.g., Cranmer & Van Ballegooijen 2010). Magnetic reconnection rapidly converts magnetic energy to particle energy, causing emission flare in multiple wave bands and even triggering coronal mass ejections (Priest & Schrijver 2000). Nano-jets are observed in closed loop system and have been suggested as being caused by the slingshot effect of newly reconnected magnetic field lines with a small angle of shear before reconnection (Antolin et al. 2021). Oscillatory wave signatures (e.g., oscillations in radiation intensity and Doppler velocities) have been considered as propagating or standing in both open strands or closed loops throughout the solar atmosphere (Wang et al. 2009). Flares are found to be often accompanied by quasi-periodic pulsations in multiband radiation intensities (Nakariakov et al. 2010; Van Doorsselaere et al. 2016; McLaughlin et al. 2018). The causal relation between reconnection and Alfvén waves was explored in 3D magnetohydrodynamic (MHD) simulations using the Walén test of the field-aligned current and parallel vorticity as emitting from the reconnection site (Ma et al. 1995). In the chromosphere, excitation of kink or Alfvénic waves, as well as compressive slow-mode waves, are also discovered to be associated with the formation of type-II spicules, which are launched by magnetic reconnection (He et al. 2009a, 2009b; Liu et al. 2014).


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


RX Cas is part of a group of interacting binaries showing light curves similar to β Lyrae and showing a long photometric cycle of unknown origin (Mennickent 2017). Few of these interacting binaries have been studied in terms of their physical changes during the long cycle. Here we provide a brief comparison with some of them. In RX Cas, we find that the long cycle of around 516 days can be explained in terms of changes of the physical parameters of the accretion disk, which was mentioned along with other possible causes in the past (Kříž et al. 1980). The disk turns out to be hotter and thicker at long-cycle maximum, but it does not change appreciably in radial extension. We note that a hotter disk during maximum was predicted by a simpler study in the past (Djurašević 1993). Contrarily, large changes in disk radius and thickness have been inferred in OGLE-BLG-ECL-157529, a binary characterized by orbital and long periods of 24

.

d

$ \overset{\text{d}}{.} $

8 and ∼850 days, while its long cycle can be reproduced by occultation of the gainer by a variable disk thickness (Mennickent & Djurašević 2021). On the other hand, the system OGLE-LMC-DPV-097 is characterized by a long-cycle length of ∼306 days and an amplitude of ∼0.8 mag in the I band. This binary has an orbital period of 7

.

d

$ \overset{\text{d}}{.} $

75 and relatively low stellar masses of 5.5 and 1.1 M⊙. In this system the orbital light curve changes in a systematic way during the long cycle. At the minimum of the long cycle the secondary eclipse practically disappears and during the ascending branch the system is brighter in the first quadrant than during the second quadrant. The disk radius is 7.5 R⊙ at the minimum and 15.3 R⊙ at the ascending branch of the long cycle; its temperature at the outer edge changes from 6870 to 4030 K in these two stages (Garcés et al. 2018). OGLE-LMC-DPV-065 is another interesting binary with a large amplitude of the long cycle. The long cycle is characterized by a double hump light curve in the I and V bands whose general shape is nearly constant with only minor variations. After a continuous decrease in the long-period from 350 to 218 d lasting about 13 yr, the long cycle remained almost constant for about 10 yr. However, the orbital light curve is fairly constant in shape, and no clear link between the disk structure and long cycle has been observed for this system, in a clear contrast to OGLE-LMC-DPV-097 and RX Cas (Mennickent et al. 2019). From the above we conclude that we cannot draw general conclusions about disk changes and photometric long cycles in these few systems as they show different behaviors that cannot be easily adapted to a global single picture.


Galaxy interactions represent a fundamental component of our current view of hierarchical galaxy evolution. Studies based on both observations and simulations have shown that galaxy collisions and mergers can dramatically affect the galaxies undergoing the interaction, by, e.g. triggering nuclear activity (e.g. Kennicutt 1984; Kennicutt et al. 1987; Ellison et al. 2011, 2013a; Silvermann et al. 2011; Satyapal et al. 2014), producing colour changes (e.g. Larson & Tinsley 1978; Darg et al. 2010; Patton et al. 2011), disrupting morphologies (e.g. Kaviraj et al. 2011; Patton et al. 2016; Lofthouse et al. 2017), and altering the metallicities (e.g. Rupke et al. 2010; Perez, Michel-Dansac & Tissera 2011; Scudder et al. 2012; Torrey et al. 2012). The most evident effect driven by galaxy encounters is probably the triggering of new episodes of star formation, which can occur both in the pre-merger regime between first pericentre and coalescence (e.g. Nikolic, Cullen & Alexander 2004; Ellison et al. 2008, 2013b; Patton et al. 2011; Scudder et al. 2012), and in the post-merger phase, where the two nuclei of the interacting galaxies have merged together (e.g. Kaviraj et al. 2012; Kaviraj 2014; Ellison et al. 2013a). The idea that galaxy mergers have a strong impact on the star formation activity is supported by studies of Ultra-Luminous InfraRed Galaxies (ULIRGs), i.e. galaxies with IR luminosities exceeding 1012 L⊙ and characterized by star formation rates (SFRs) up to ∼1000 M⊙ yr−1 (e.g. Barnes & Hernquist 1991; Mihos & Hernquist 1994; Daddi et al. 2010; Scoville et al. 2015). Observations have revealed that the majority of ULIRGs reside in interacting systems (e.g. Sanders & Mirabel 1996; Veilleux, Kim & Sanders 2002; Kartaltepe et al. 2010, 2012; Haan et al. 2011). Nevertheless, ULIRGs are rare and extreme examples of highly star-forming galaxies. Most galaxy–galaxy interactions result in SFR increases of at most a factor of a few, as shown in both numerical simulations (e.g. Di Matteo et al. 2008) and observations of galaxy pairs and post-mergers (Ellison et al. 2008; Martig & Bournaud 2008; Jogee et al. 2009; Robaina et al. 2009; Scudder et al. 2012).


The size–SFR relation has been already well-defined in the local Universe investigating H ii regions in nearby spiral and irregular galaxies by Kennicutt (1988). On the other hand, outliers are mainly hosted by interacting systems as shown in the case of the Antennae galaxy (Bastian et al. 2006), and have been thoroughly investigated on a larger samples with DYNAMO (Green et al. 2014) and LARS (Messa et al. 2019). In Fig. 10, we show the relation between the size and star formation rate of clumps, including samples across different redshifts (Swinbank et al. 2009, 2012; Jones et al. 2010; Livermore et al. 2012, 2015; Johnson et al. 2017). We consider samples where SFRs was estimated through SED fitting (as for our sample) or from H α, using the prescription by Kennicutt (1988). Our sample and the Sunburst clumps (Vanzella et al. 2021a), despite being at z ∼ 2–6, have sizes comparable to local H ii regions and GCs (Swinbank et al. 2009; Jones et al. 2010; Livermore et al. 2012; Johnson et al. 2017), but they have SFRs ∼300 times higher. They also have SFRs ∼100 times higher than clumps from Wuyts et al. (2014) and Livermore et al. (2015), which are part of a sample of lensed systems at z > 2. In particular, we compare our sample with two well-known H ii regions from the local Universe: 30 Doradus and II Zw40 (Vanzi et al. 2008). One possible explanation for the high SFR measured in our sample is enhanced interactions, or larger gas reservoirs at high redshift. Similar cases have been observed in the local Universe, for example, the Antennae galaxy which is a local merging system hosting six star-forming complexes whose SFR ranges from 0.2 to 1.4 M⊙ yr−1, significantly higher than other local star-forming regions. Three of those complexes show signatures of Wolf–Rayet stars, implying young ages of $\sim 5\, \rm Myr$ (Bastian et al. 2006). Similar properties are observed in the Sunburst 5.1 knot presented in detail in Vanzella et al. (2021a) and in some of our clumps shown in fig. D.1 of Vanzella et al. (2021b). Other scenarios, such as the fragmentation of gas-rich discs, are potentially responsible for the observed high SFR among high redshift clumpy structures (Noguchi 1999; Dekel et al. 2009). During this process, cold gas cools becoming unstable and the galactic disc starts to fragments and forms clumpy structures. Further on, such newly formed structures lead to the increased SFR as discussed in i.e. Immeli et al. (2004).

Uses Similarities Similarities Differences


For comparisons with the light curve YORP constraints, the YORP effect acting on Cuyo could be predicted by computing the total recoil forces and torques from reflected and thermally emitted photons from the asteroid surface using the ATPM. These calculations were made for both a smooth and rough surface, and were averaged over both the asteroid rotation and elliptical orbit (see Rozitis & Green 2012, 2013, for methodology). As demonstrated in Rozitis & Green (2012), the inclusion of rough-surface thermal-infrared beaming effects in the YORP predictions tends to dampen the YORP rotational acceleration on average but can add uncertainties of up to several tens of per cent if the roughness was varied across the surface. Since the light curve inversion produced convex shape models only, then shadowing and self-heating effects inside global-scale concavities (see Rozitis & Green 2013) were not possible to model. However, a study of non-convex shape models for fast two to four hour rotators in Rozitis & Green (2013) indicated that such asteroids have rather minimal levels of global-scale concavities, and the ~ 2.7 h rotation period of Cuyo implies that its shape could be similar. Furthermore, the Tangential-YORP effect, that is, a predicted rotational acceleration caused by temperature asymmetries within exposed rocks and boulders on the surface of an asteroid (Golubov & Krugly 2012), was also not included in the ATPM predictions. However, the very low thermal inertia value measured for Cuyo implies the absence of rocks and boulders on its surface of the quantity and size that are necessary to induce a significant Tangential-YORP component. As Cuyo is likely to be an S-type rubble-pile asteroid, a bulk density equivalent to that measured for the S-type rubble-pile asteroid (25143) Itokawa (Abe et al. 2006) of 2 g cm−3 was assumed for the YORP computations. Using the thermo-physical properties derived earlier, the ATPM predicts YORP rotational acceleration of (−6.39 ± 0.96) × 10−10 rad day−2 for the nominal shape model. The uncertainty given here corresponds to the standard deviation of results when the degree of surface roughness israndomly varied across the surface of Cuyo (see Lowry et al. 2014, for details of the Monte Carlo methodology used). These values lie well within the light curve rotational acceleration constraints determined previously.


The reasons for such a tight – and linear – correlation between \hbox{$L^{\prime}_{\rm CO(1{-}0)}$}LCO(1−0)′ and M∗ (or LK) observed consistently across different galaxy samples except in early type galaxies have been little explored in the literature. The interpretation favoured by Leroy et al. (2005) is that CO emission and stars are linked through the hydrostatic pressure in the disk, which depends mainly on the stellar surface density (Σ∗) and sets the rate at which Hi is converted into H2. An alternative explanation that we propose here goes back to the nature of the optically thick 12CO emission and to the approximately linear relation between 12CO luminosity and virial mass found for GMCs (see e.g. Scoville et al. (1987), Solomon et al. (1987), and Bolatto et al. (2013) for a more recent compilation). By extrapolating from the relation shown by Scoville et al. (1987), our observed \hbox{$L^{\prime}_{\rm CO(1{-}0)}-M_*$}LCO(1−0)′−M∗ correlation may be so tight and close to linear simply because the global 12CO luminosity is a very good tracer of the dynamical mass in star-forming galaxies, assuming that in this class of objects the bulk of the CO emission traces molecular gas clouds in virial motions (for example in a rotating disk). This explanation of course assumes that in most star-forming galaxies the stellar mass is also a good tracer of the dynamical mass. Following on from our hypothesis, a possible explanation for the break down of the \hbox{$L^{\prime}_{\rm CO(1{-}0)}-M_*$}LCO(1−0)′−M∗ relation in early types is that in these sources, even when CO is detected, the motions of the CO-emitting clouds are poor tracers of the total dynamical mass of the system. Interferometric CO observations of large samples of early type galaxies have indeed shown that the CO emission in these objects tends to be rather compact (on average extending over ~ 1 kpc) compared to the optical extent of the galaxy (Alatalo et al. 2013; Davis et al. 2013).


Combining these different velocity signatures, the data show strong signatures of two gas components at different velocities (around 6 km s−1 apart) that converge to a common intermediate velocity at the location of the infrared dark cloud and active star-formingregion, similar to filament formation via gravitationally driven, converging gas flows (e.g., Gómez & Vázquez-Semadeni 2014). We interpret these signatures as indicators of converging gas streams that may trigger the star formation event at its center (e.g., Vázquez-Semadeni et al. 2006; Heitsch et al. 2008; Banerjee et al. 2009; Gómez & Vázquez-Semadeni 2014). Position-velocity diagrams based on simulations of cloud-cloud collisions sometimes show a characteristic pattern of lower-level emission between two main velocity components, a so-called bridging feature (e.g., Haworth et al. 2015, 2018). Similar signatures were also reported in observations (e.g., Jiménez-Serra et al. 2010; Henshaw et al. 2013; Dobashi et al. 2019; Fujita et al. 2019). The pv-diagrams of the G28.3 region presented here (Fig. 9) show different signatures in the sense that there is not a lower-intensity bridge between the two well-defined components, but that the two velocity components converge at the center of the cloud toward a central, high-intensity velocity component. However, the absences of a bridging feature does not necessarily rule out the formation of G28.3 in a cloud-cloud collision, as this feature is not always visible in simulations. For example, simulations by Bisbas et al. (2017) show that the low-intensity bridge feature may merge into a centrally peaked pv-diagram during the evolution of the cloud-cloud collisions, while the colliding-cloud simulations of Clark et al. (2019) yield only a single central velocity component in CO or [CI], with multiple components only becoming apparent when the [CII] emission from the cloud is considered. In addition, the multiple components and bridging feature may not be visible in cases where our line of sight is oriented at a large angle to the direction of motion of the clouds. We return to the interpretation in Sects. 4.4 and 4.5.


We also present the correlation functions of centrals and satellites in Fig. 17. This is a worthwhile exercise for a variety of reasons, not least that there is information on the small-scale IA signal missed in the large-scale fits. While we cannot, at the present time, fit the IA signal on scales ∼1 h−1 Mpc, the qualitative comparison can be instructive. Given that there is some evidence that they behave differently, we consider blue and red satellites/centrals separately here. We also drop the full sample density tracer, and instead use one of the four (red/blue, satellite/central) subsamples. The motivation here is that, while on large scales, the density tracer is effectively just that: a probe of the large-scale matter distribution multiplied by a linear galaxy bias, on scales approaching the one halo regime this no longer holds. Fig. 17 shows these new data vectors. As shown we measure both wg + and w++, and recompute the covariance matrices with the appropriate densities. For reference, the dark red crosses also show the equivalent satellite/central red galaxy wg + correlations from KiDS×GAMA here (c.f. Johnston et al. 2019 fig. 7, red points/band). On large scales at least, our illustristng red sample is consistent with their measurements. There are a few interesting features here to note, however. First, we see a relatively strong red galaxy 1h contribution on scales 1 h−1 Mpc. Although the general trends match the real data, with ss and to a lesser extent cs exhibiting strong scale-dependent IAs in this regime, the magnitude is somewhat higher in our sample. This is particularly interesting, given that our sample characteristics are similar (〈L〉/L0 = 0.91 and 0.34 for our red and blue samples, respectively, compared with their ∼0.99 and 0.50). As discussed briefly in Section 6.2.1, we observe a persistent non-zero IA signal in blue galaxies on large scales; here we can see it is dominated by the cc correlation, with a smaller contribution from sc. Also notable is that, in line with some previous direct IA measurements (e.g. Singh et al. 2015), the large-scale satellite correlations do not appear to vanish on large scales. Focusing on the right-hand panels, the purple and pink points are consistently positive and non-zero. While small compared with the red central terms, and consistent with the dark red points from GAMA, there appears to be a detectable signal at the precision allowed by illustristng.

Uses Uses Similarities Compare/Contrast Similarities Differences Compare/Contrast


It is now well established that the weak lensing of distant galaxies by foreground mass provides a relatively clear window on to the large-scale structure of the Universe. This is true whether that foreground mass is in the form of discrete matter concentrations, as traced by galaxies (i.e. galaxy–galaxy lensing; Mandelbaum et al. 2013; Leauthaud et al. 2017; Joudaki et al. 2018; Prat et al. 2018; Blake et al. 2020), massive dark matter haloes (cluster lensing; Melchior et al. 2017; Dark Energy Survey Collaboration 2020), or the continuous large-scale matter distribution (cosmic shear; Heymans et al. 2013; Dark Energy Survey Collaboration 2016; Troxel et al. 2018; Chang et al. 2019; Hamana et al. 2020; Hildebrandt et al. 2020; Amon et al. 2021; Asgari et al. 2021; Secco, Samuroff et al. 2021). Though the measurement method and the exact form of the theory predictions differ slightly in the three cases, they are all fundamentally probes of the growth of structure at low redshift. Similarly cross-correlations between galaxy lensing and other observables can be powerful probes in their own right; recent examples include galaxy lensing × CMB lensing (Schaan et al. 2017), voids correlated with CMB lensing (Vielzeuf et al. 2021), and galaxy weak lensing crossed with gamma-ray emission (Ammazzalorso et al. 2020), each of which provide probes of dark matter with slightly different sensitivities. A measurement of cosmological weak lensing, however, is subject to a range of systematic effects; that is, observational effects that mimic a cosmological lensing signal, and so bias cosmological inference if one neglects them. Depending on the systematic in question, the most effective mitigation strategy may be quite different. In broad terms, however, the standard approach is to either (i) mitigate systematics where possible, either by applying a calibration to the data, or discarding the data points most strongly affected or (ii) marginalize over them with a parametric model. Often a combination of the two is appropriate, and the prior used in (ii) is informed by additional data or simulations, and detailed testing of the calibration step in (i).


For the first time, we detected [C ii] 158-μm emission from a GRB host galaxy at z > 2. This is the second detection of [C ii] 158-μm emission among known GRB host galaxies, following GRB 980425 (Michałowski et al. 2016). The [C ii] 158-μm fine structure line is the dominant cooling line of the cool interstellar medium, arising from photodissociation regions (PDR) on molecular cloud surfaces. It is one of the brightest emission lines from star-forming galaxies from FIR to metre wavelengths, almost unaffected by dust extinction. [C ii] 158-μm luminosity, L[C II], has been discussed as an indicator of SFR (e.g. Stacey et al. 2010). If L[C II] scales linearly with SFR, the ratio to FIR luminosity, L[C II]/LFIR, is expected to be constant, since LFIR is a linear function of SFR (e.g. Kennicutt 1998a). However, LC II/LFIR is not constant, but declines with increasing LFIR, known as the ‘[C ii] deficit’ (e.g. Luhman et al. 1998, 2003; Malhotra et al. 2001; Sargsyan et al. 2012; Díaz-Santos et al. 2013, 2017; Spilker et al. 2016). The [C ii] deficit persists when including high-z galaxies (e.g. Stacey et al. 2010; Wang et al. 2013; Rawle et al. 2014). In Fig. 5, we compare the [C ii] deficit in the GRB 080207 host and other star-forming galaxies. Two GRB hosts are shown by stars: GRB 080207 (orange star) and 980425 (blue star). The comparison sample is compiled from the literature up to z ∼ 3 (Malhotra et al. 2001; Cormier et al. 2010, 2014; Ivison et al. 2010; Stacey et al. 2010; Sargsyan et al. 2012; Farrah et al. 2013; Magdis et al. 2014; Brisbin et al. 2015; Gullberg et al. 2015; Schaerer et al. 2015). Active galactic nuclei are separated from star-forming galaxies based on either (i) the explicit description in the literature or (ii) EWPAH 6.2μm  0.1 (Sargsyan et al. 2012). As reported by previous studies (e.g. Maiolino et al. 2009; Stacey et al. 2010), high-z galaxies are located at a different place from local galaxies in the L[C II]/LFIR–LFIR plane.


Lithium is the only metal element produced during the Big Bang nucleosynthesis (BBN) due to the lack of stable nuclei with mass number eight (Fields, Molaro & Sarkar 2014). The element abundances predicted by the standard BBN theory for the baryonic density coming from the Planck mission agree well with those observed, except for 7Li (Fields 2011; Coc, Uzan & Vangioni 2014). Indeed, the abundance of lithium measured in the low-metallicity Galactic halo stars is A(7Li)  = log[N(7Li)/N(H)] + 12 = 2.25 (Spite & Spite 1982; Sbordone et al. 2010; Bonifacio et al. 2015), which is ∼3 times below the estimate of the standard cosmological model A(7Li) = 2.72 ± 0.06 (Cyburt et al. 2016). The latter value depends on the baryon-to-photons ratio $\eta = \frac{N_b}{N_{\gamma }} \propto \Omega _B h^2$, with Ωb is the cosmological baryon density and h is the dimensionless hubble parameter (Planck Collaboration XIII 2016). This problem is also known as the Cosmological Lithium problem (Fields et al. 2014). A possible solution can be ascribed to convective diffusion in the pre-main-sequence phase as well as during the lifetime of these halo stars (Fu et al. 2015) or to new physics beyond the standard model. On the other hand, the young stellar populations in our Galaxy show Li-abundances four times greater than the SBBN estimate and more than one order of magnitude greater than the halo stars (Spite 1990; Lambert & Reddy 2004; Lodders, Palme & Gail 2009; Ramírez et al. 2012; Fu et al. 2018). The evidence of a growth requires the existence of additional lithium factories. In the last decades several astrophysical Li sources have been proposed, like Galactic cosmic-rays, AGB stars, low-mass Carbon stars, type II supernovae, and classical novae (D’Antona & Matteucci 1991; Romano et al. 1999; Prantzos 2012; Matteucci 2021). The recent detection in the outburst spectra of classical novae of 7Li and 7Be ii, an isotope whose unique decay channel is into lithium through electron capture, have confirmed these objects as Li producers. The corresponding yields inferred have placed nova explosions as the main lithium factories in the Galaxy. The time-scales involved also match, as shown by detailed Galactic chemical evolution (Izzo et al. 2015; Tajitsu et al. 2015; Molaro et al. 2016; Izzo et al. 2018; Cescutti & Molaro 2019; Grisoni et al. 2019; Molaro et al. 2020a; Matteucci 2021).


A couple of years after the closure of the solar flare myth debate, Dere et al. (1997) and Thompson et al. (1998) reported on the presence of wavefronts observed on the solar disk that propagated away from the site of the flare. They were originally termed “EIT waves” (Thompson et al. 1999) after the instrument that first detected them (EIT on board the Solar and Heliospheric Observatory (SOHO) Delaboudiniére et al. 1995) and have now been intensely studied for over 15 years. Over that time they have been assigned different terms, such as flare waves (e.g., Thompson et al. 2000; Warmuth et al. 2003), extreme-UV (EUV) waves (e.g., Patsourakos & Vourlidas 2012; Muhr et al. 2014), coronal waves (e.g., Douglas & Ballai 2007; Webb & Howard 2012), and coronal bright fronts (e.g., Gallagher & Long 2011, and references therein). While there are differences in the precise definitions of these terms, broadly speaking they describe the same phenomenon: a bright front propagating away from a point-like origin on the solar disk. In many cases the origin appears to be from the site of a solar flare associated with a CME (e.g., Thompson 1999; Thompson & Myers 2009; Wills-Davey & Attrill 2009; Nitta et al. 2013), but some workers have reported a stronger correlation of wave occurrence with CMEs rather than flares (e.g., Wills-Davey & Attrill 2009, and references therein). For simplicity, henceforth in this paper we refer to them as EIT waves although we do not use the EIT instrument for any measurements in our study. We define EIT waves with the criteria described in Section 4. Nitta et al. (2013) provide a recent review of the various physical narratives that have been assigned to EIT waves, such as the coronal manifestations of Moreton waves (e.g., Thompson 1999; Warmuth et al. 2001, 2002), the base of expanding overhead CME magnetic structures (e.g., Delanée & Aulanier 1999), and solitons (Wills-Davey et al. 2007). Other reviews on EIT waves can be found by Wills-Davey & Attrill (2009), Gallagher & Long (2011), and Patsourakos & Vourlidas (2012).


The mass accretion onto the black hole is important for a better understanding of AGN evolution. The Eddington ratio, the ratio between the AGN bolometric luminosity and the Eddington luminosity (Lbol/LEdd), provides insight into the black hole growth because the bolometric luminosity reflects the mass accretion rate. We show AGN bolometric luminosity versus black hole mass for our sample of broad-line AGNs in the different redshift bins in the left panel of Figure 5. The different X-ray surveys are shown with different symbols as labeled. The dotted reference lines indicate constant Eddington ratios of 1, 0.1, 0.01, and 0.001. Our sample of broad-line AGNs covers the black hole mass range 7.0  log MBH/M⊙  9.5 and the bolometric luminosity range 43  log Lbol  47 with a wide dispersion in the Eddington ratio distribution. For comparison, we show published observations in the same redshift range from the literature in the right panel of Figure 5 (Gavignaud et al. 2008; Merloni et al. 2010; Shen et al. 2011; Nobuta et al. 2012; Matsuoka et al. 2013). The SDSS quasar sample (gray points; Shen et al. 2011) is limited to the high-mass and high-luminosity regime because the SDSS detection limit corresponds to a luminosity of log Lbol ∼ 46 at z ∼ 1. Compared to the SDSS quasar sample, our sample of broad-line AGNs shows a wider dispersion in the black hole mass, AGN bolometric luminosity, and Eddington ratio distribution, consistent with previous studies on deep AGN samples (Gavignaud et al. 2008; Merloni et al. 2010; Nobuta et al. 2012; Matsuoka et al. 2013), which fill in the low-mass and low-luminosity region. The figure shows contours at the 1σ level, together with the literature data, except the SDSS quasar sample. The figure also reveals that only a small number of AGNs exceed the Eddington limit by a small amount. AGNs with similar black hole masses show a broad range of bolometric luminosities spanning about two orders of magnitude, indicating that the accretion rate of black holes is widely distributed. This suggests that the AGN cosmic downsizing phenomenon could be explained by some more-massive black holes with low accretion rates, which are relatively fainter than less-massive black holes with efficient accretion. Lusso et al. (2012) suggest that AGNs show higher Eddington ratios at higher redshift at any given MBH, and the Eddington ratio increases with bolometric luminosity. We confirm that there is a tendency for low-luminosity AGNs (log Lbol ≲ 45.5) with less-massive black holes (log MBH/M⊙ ≲ 8) to have lower Eddington ratios than high-luminosity AGNs (log Lbol ≳ 45.5) with massive black holes (log MBH/M⊙ ≳ 8), consistent with Lusso et al. (2012). It is important to note that, when comparing with results in the literature, one should take into account the different methods of spectral line fitting and correction for bolometric luminosities. Nevertheless, they show similar distributions of the accretion rate of black holes over a wide range, consistent with previous studies.


The last column in Table 1 reports the number of OB stars minus the “diffuse” population estimated from their density in the Reference field (22.5 stars per square degree): as is immediately seen, the M-star statistics is much larger than the OB star statistics. This can hardly be considered surprising, if an ordinary IMF (e.g., that from Weidner et al. 2010) is assumed for the star-formation region. In Fig. 19 we show the density ratio between M and OB stars, which provides a consistency test between our results and a plausible IMF: this ratio varies however by a large factor, close to 20, among our subregions. This might reflect differences in the respective IMFs, but also differences in completeness among the stellar samples considered for the various regions. We first note that the ratio between M and OB stars in NGC 6231 is dramatically lower than anywhere else in Sco OB1. We can indeed expect that M stars are detected less efficiently in the inner parts of NGC 6231, where the density of bright stars is very large, and their diffuse glare raises the limiting magnitude locally. As already discussed above in Sect. 4.1, this causes our sample of M stars in NGC 6231 to be highly incomplete. Moreover, we determined above that NGC 6231 is significantly more extincted, by almost half a magnitude in V, than Tr 24, and this implies a higher minimum detectable mass among NGC 6231 M stars compared to Tr 24 (see the MDA diagrams in Fig. 5); this effect reduces the completeness of the M-star sample in NGC 6231 more than in Tr 24. If Tr 24 is also slightly younger than NGC 6231, as we argue below, our M-stars in Tr 24 will reach down to lower masses than in NGC 6231, with a steep increase in the detected M-star population: adopting the IMF from Weidner et al. (2010), the predicted number of cluster M stars doubles considering the mass interval 0.25–0.5 M⊙ rather than 0.35–0.5 M⊙. If Tr 24 is younger than NGC 6231, moreover, its stars in the mass range 2.5–3 M⊙ might not have yet reached their ZAMS position as B stars, and therefore would not be counted among OB stars; this would further raisethe M/OB star ratio there by up to 30%. Therefore, the proportions of both M and OB stars that are detected in a young cluster will depend on their age and extinction, in accordance with the MDA diagrams, even for a fixed, spatially uniform photometric sensitivity. We estimated using the Weidner et al. (2010) IMF the expected range for the observed M/OB number ratio. Siess et al. (2000) predict that the latest-type B stars have a mass of ~ 3.5 M⊙ at 2 Myr, and ~ 2.2 M⊙ at 10 Myr, that is, in the range of ages expected for Sco OB1 clusters. The MDA diagrams of Fig. 5 predict that the lowest-mass stars we are able to detect using the available Sco-OB1 data have ~ 0.2 M⊙, even assuming the most favorable (and unlikely) circumstances of an age less than 2 Myr and negligible reddening. The extreme values found for the M/OB ratio are then ~ 3.8 for a minimum M-star mass as high as 0.35 M⊙ and an old age of 10 Myr, and ~ 20 for a minimum M-star massas low as 0.2 M⊙ and age of 2 Myr. These extremes are also shown as horizontal lines in Fig. 19. We note that the M/OB ratio in NGC 6231 falls well within this range; however, both Tr 24 regions are significantly richer of M stars than expected, by more than a factor of two and well above (statistical) errors. If true, then paradoxically this part of the OB association would form preferentially lower-mass stars. Of course, more detailed studies are needed to confirm this result. In the G345.45+1.50 region the M/OB ratio is highest, and far above predictions from the IMF: we may tentatively explain this since this region is very young, and some of its most massive members, like IRAS 16562-3959, are still in formation, thus decreasing the number of optically revealed OB stars. The lowest M/OB ratio in NGC 6231 is unlikely to be real, since as discussed above our M-star sample in this densest subregion is likely incomplete.


Level crossing statistics is a pioneering approach for characterizing stochastic processes introduced by S. O. Rice (Rice 1944, 1945). Up-, down-, and conditional crossing statistics are modifications to the primary definition of level crossing (Bardeen et al. 1986; Bond & Efstathiou 1987; Ryden 1988; Ryden et al. 1989; Matsubara 1996, 2003; Brill 2000; Shahbazi et al. 2003; Movahed & Khosravi 2011; Ghasemi Nezhadhaghighi et al. 2017). Minkowski functionals, which are also closely related to the crossing statistics, provide 1 + D functionals to quantify the morphology in D dimensions (Hadwiger 2013) and have been utilized for cosmological random fields (Mecke, Bucheri & Wagner 1994; Schmalzing, Buchert & Kerscher 1995; Schmalzing & Górski 1998; Matsubara 2003, 2010; Hikage, Komatsu & Matsubara 2006; Codis et al. 2013; Ling et al. 2015; Fang, Li & Zhao 2017). A number of critical sets including peaks (hills), troughs (lakes), saddles, voids, skeleton, genus, and Euler characteristics, are more popular in cosmology for different purposes and they have been fully explored for Gaussian stochastic fields. Some extensions for non-Gaussian and anisotropic conditions have been done in some research (Matsubara 2003; Pogosyan et al. 2009; Pogosyan, Pichon & Gay 2011; Gay et al. 2012; Codis et al. 2013). More recently, Betti numbers, Euler characteristics, and Minkowski functionals for a set of cosmological 3D fields have been examined extensively (Pranav et al. 2019). The scaling approach for investigating cosmological stochastic fields has been discussed by Borgani (1995), Movahed et al. (2011). Standard estimators like three- and four-point functions in real space, bispectra and trispectra in harmonic space, multiscaling methods such as wavelets (Planck Collaboration 2014b, 2016d; and references therein), and regeneration of stochastic processes based on the Fokker–Planck equation (Ghasemi et al. 2006) have also been considered.


We can see how this is consistent with the development of small scales via phase mixing by introducing local wavenumbers for the variation with α and β, (3)\begin{eqnarray} \xi \propto \exp {\rm i}\left[ \int \kappa_\alpha {\rm d}\alpha + \int \kappa_\beta {\rm d}\beta \right]\!. \label{number3} \end{eqnarray}ξ∝expi∫καdα+∫κβdβ.Here κα and κβ are the wavenumbers in α and β and have units that are the inverse of the units of their respective coordinates. These wavenumbers should be distinguished from the perpendicular components of the usual wave vector k, which has units of 1/length. The different wavenumbers may be related through the scale factors (h) that relate elemental coordinate increments to physical distances: dr = eαhαdα + eβhβdβ + eγhγdγ, where eα is a unit vector in the α direction, etc. In this notation ∇⊥ = (eα/hα)∂/∂α + (eβ/hβ)∂/∂β, and noting that ∇⊥ξ ≈ ik⊥ξ, Eq. (3) yields \begin{eqnarray} \bdelp\xi &=& {\rm i} \vec{k}_\perp \xi = {\rm i} \left( \frac{\vec{e}_\alpha}{h_\alpha}\frac{ \partial}{\partial\alpha} +\frac{\vec{e}_\beta}{h_ \beta}\frac{ \partial}{\partial \beta}\right)\xi \\ &\equiv& {\rm i}\left( \frac{\vec{e}_\alpha}{h_\alpha}\kappa_\alpha +\frac{\vec{e}_\beta}{h_ \beta}\kappa_\beta\right)\xi. \label{number4} \end{eqnarray}∇⊥ξ=ik⊥ξ=ieαhα∂∂α+eβhβ∂∂βξ≡Equating components of the second and fourth expressions in Eq. (5) gives the expected relations between the various wavenumbers, (6)\begin{eqnarray} k_\alpha = \kappa_\alpha /h_\alpha, \qquad k_\beta = \kappa_ \beta /h_ \beta. \label{number5} \end{eqnarray}kα=κα/hα, kβ=κβ/hβ.Equations (2) and (5) give a direct and elegant expression for the perpendicular wave vector as (7)\begin{eqnarray} \vec{k}_\perp \approx -(\bdel \omega_{\rm c}) t, \label{number6} \end{eqnarray}k⊥≈−(∇ωc)t,which is a generalisation to three dimensions of the results of Mann et al. (1995), (Wright et al. 1999) and Kaneko & Yokoyama (2015) for lower dimensional systems, which developed phase mixing in only one perpendicular coordinate. The above expression allows phase mixing in both perpendicular directions, giving physical phase mixing lengths (or wavelengths) in the α and β directions of (8)\begin{eqnarray} L_{{\rm ph}\alpha} = \frac{2\pi}{|k_\alpha |} \equiv \frac{2\pi h_\alpha}{|\partial \omega_{\rm c}/\partial\alpha |t}, \qquad L_{{\rm ph}\beta} = \frac{2\pi}{|k_ \beta |} \equiv \frac{2\pi h_\beta}{|\partial \omega_{\rm c}/\partial \beta |t}\cdot \label{number7} \end{eqnarray}Lphα=2π|kα|≡2πhα|∂ωc/∂α|t, Lphβ=2π|kβ|≡2πhβ|∂ωc/∂β|t·If the phase mixing lengths are expressed in the same units as α and β, rather than physical length as in Eq. (8), slightly simpler expressions are found, i.e. (9)\begin{eqnarray} \ell_{{\rm ph}\alpha} = \frac{2\pi}{|\kappa_\alpha |} \equiv \frac{2\pi}{|\partial \omega_{\rm c}/\partial\alpha |t}, \qquad \ell_{{\rm ph}\beta} = \frac{2\pi}{|\kappa_ \beta |} \equiv \frac{2\pi}{|\partial \omega_{\rm c}/\partial \beta |t}\cdot \label{number8} \end{eqnarray}ℓphα=2π|κα|≡2π|∂ωc/∂α|t, ℓphβ=2π|κβ|≡2π|∂ωc/∂β|t·The development of the phase mixing length can be pictured simply as the tendency for each field line to oscillate with its own natural frequency. Even if all the field lines start to oscillate with the same phase, they soon drift out of phase with one another as time passes. Not only does the phase mixing process generate perpendicular scales, but points of constant phase can be seen to move across field lines. This phase motion has been seen in magnetospheric data of Alfvén waves (see the review by Wright & Mann 2006) and the simulations of coronal oscillations by Kaneko & Yokoyama (2015). These studies note that the direction of motion is related to the spatial variation of ωc. The results of these papers for the perpendicular phase velocity in physical space generalise to Vph = ωc/k⊥, giving the components (10)\begin{eqnarray} V_{{\rm ph}\alpha} = \frac{-\omega_{\rm c} h_\alpha}{(\partial \omega_{\rm c}/\partial\alpha )t}, \qquad V_{{\rm ph}\beta} = \frac{-\omega_{\rm c} h_ \beta}{(\partial \omega_{\rm c}/\partial \beta )t}, \qquad \label{number9} \end{eqnarray}Vphα=−ωchα(∂ωc/∂α)t, Vphβ=−ωchβ(∂ωc/∂β)t, If the excitation occurred at a time ti, the subsequent properties are found by replacing t with t−ti in the above formulae.


CME-driven shocks accelerate not just protons, but also the electrons in the solar corona (Holman & Pesses 1983; Schlickeiser 1984; Kirk 1994; Mann et al. 1995, 2001; Mann & Klassen 2005). These accelerated electron beams can be observed as type II bursts in the solar radio radiation in the metric wave range (Wild & McCready 1950; Uchida 1960). Type II bursts require electrons escaping from the shock front, and the lack of these bursts implicates the absence of accelerated electrons as type II bursts occur when 0.2–10 KeV electrons are accelerated in the shock front (see, e.g., Bale et al. 1999; Knock et al. 2001; Mann & Klassen 2005). Energetic electrons are unstable to Langmuir waves, thus they are converted into radio emission at the local plasma frequency and its harmonic (see Nelson & Melrose 1985). Therefore, type II radio bursts hold crucial information of both the shock and the surrounding ambient medium in which the CME-driven shock propagates (Gopalswamy et al. 2008a). Although almost every large SEP event is accompanied by a type II radio burst (Gopalswamy 2003; Cliver et al. 2004) that indicates CME-driven particle acceleration (Gosling 1993; Reames 1999), we have ten events in our sample that lack a type II burst: 14 August 2010, 03 August 2011, 04 March 2012, 26 May 2012, 27 May 2012, 14 June 2012, 08 September 2012, 14 December 2012, 21 April 2013, and 06 November 2013. Of the ten events, two originate in the west, three in the east, and five at the disk center. On average, these events have a maximum velocity of about 1000 km s−1 and maximum Mach number of about 0.94. The protons accelerated by these events have peak fluxes of about 23.2 cm−2 s−1 sr−1 in the > 10 MeV band, making these events the slowest and weakest SEPs in the sample. As the propagation of radio bursts does not depend on the magnetic connectivity, a possible explanation for their absence could be that the path of the radio burst did not coincide with the instrument on board the satellite or that the detection of the waves was below the range of the radio instrument, hence missing the signature. Detailed investigation is required to understand the absence of DH type II radio bursts in these events.


To provide enough galaxies to adequately train a neural network, EAGLE galaxies from the simulation snapshots with a redshift of less than 1.0 were used. Objects with M⋆ greater than 1010 M⊙ were selected while the merging partner of the merging systems must be larger than 109 M⊙. The merging partner must also be more than 10% of the M⋆ of the primary galaxy. Galaxies were deemed to have merged when they are tracked as two galaxies in one simulation snapshot and then tracked as one galaxy in the following snapshot in the EAGLE merger trees catalogue (Qu et al. 2017). This prevents the inclusion of chance flybys that may be selected as mergers if the EAGLE galaxies were selected based on proximity. Systems that are projected to merge, using a closing velocity extrapolation, within the next 0.3 Gyr (pre-merger) or are projected to have merged, again using a closing velocity extrapolation of the progenitors, within the last 0.25 Gyr (post-merger) were selected, along with a number of non-merging systems, and gri band images were created of these systems. Springel et al. (2005) have shown that the effects of a merger are visible for approximately 0.25 Gyr after the merger event while the pre-merger stage is much longer. However, we chose to have the pre and post merger period approximately equal as tests conducted with longer pre-merger times showed no improvement, see discussion in Sect. 4.2. We note, however, that the merger timing may suffer from imprecision as a result of the coarse time resolution of the EAGLE simulation, that is the time between snapshots, which becomes coarser at lower simulation redshift. Each galaxy was imaged at an assumed distance of 10 Mpc and each image contains all material within 100 kpc of the centre of the target galaxy and is 256 × 256 pixels, where 256 pixels corresponds to a physical size of 60 kpc. There are 537 pre-merger, 339 post-merger and 335 non-merging systems, each with six random projections to increase the size of the training set. Each of the six projections are treated as individual galaxies resulting in 3222 pre-merger, 2034 post-merger and 2010 non-merging galaxy images for training. The pre-mergers and post-mergers were combined to form the merger class, keeping the pre-merger image if the same galaxy appears in both sets.


In Table 3, we present a detail comparison of our theoretical energy values from the layer n = 7. For this purpose, we have taken four data sets available in the literature. First, we compare with the ab initio values of Fritzsche (1995) because they have used a larger configuration space than previous ab initio computations (Vajed-Samii & MacDonald 1981; Huang et al. 1983). Secondly, theoretical values from the CHIANTI V.8 (Landi et al. 1999; Del Zanna et al. 2015) because these are considered the most appropriate data for astrophysical applications (Träbert 2014). Thirdly, with the most recent semi-empirically predicted and tentative experimental data values of Del Zanna & Badnell (2016). Fourthly, with the NIST data base (NIST Atomic Spectra Database (ver. 5.3) 2017), which is considered as the most critically analysed data base. Comparison with observed energies (Del Zanna & Badnell 2016) and with the NIST values shows that the present ab initio values are not fully converged to experimental values. In order to achieve better accuracy relative to experimental values, we suggest more balanced and extended reference configuration sets as a starting point of the orbital expansion. This, however, results in very large expansions of wave functions, which is computationally very expensive. Nevertheless, with the present set of calculations for CV correlations, results for the lowest 31 levels are better than obtained before in any ab initio investigation. A very good agreement with experiment is achieved to an accuracy better than 0.5 per cent for low lying levels and 0.8 per cent for higher lying levels, whereas this accuracy is 1–2 per cent for the mcdf calculations of Fritzsche (1995) and for superstructure calculations available at CHIANTI V.8 (Landi et al. 1999; Del Zanna et al. 2015). In some more detail, there is no experimental connection in NIST data base to the 5 levels with J = 7/2 and two levels with J = 9/2 for the 3s23p43d configuration with other levels. The present results of energies for these seven levels with less than 0.45 per cent error with new tentative experimental assignments (Del Zanna & Badnell 2016) testify them. However, we suggest different level ordering than provided by semi-empirical formalism of Del Zanna & Badnell (2016). We briefly discuss later the shift in level ordering and reasons for it. We also note that there is 2100 cm−1 difference between the latest experimental energy (Del Zanna & Badnell 2016) and NIST data base for the level no. 31 (2D3/2). The present value of 683 070 cm−1 confirms the experimental energy (Del Zanna & Badnell 2016), and we suggest a replacement in the NIST data base with new experimental value.


Neutron star X-ray binaries are an important class of low-mass X-ray binaries to understand the radiative and dynamical configuration of the inner region of an accretion disc. Though from previous studies especially based on RXTE (Rossi X-ray Timing Explorer) data of Z sources, it was known that there must exist a corona/comptonization region to explain the observed hardtail in their X-ray spectra but the exact location and how it changes across the intensity variation is not yet properly understood. Among the two primary categories i.e. Z and Atoll sources, Z sources emit close to the Eddington luminosity (0.5–1.0 LEdd; Done, Gierliński & Kubota 2007a) and they exhibit ‘Z’ and ‘C’ shape intensity variation in the hardness intensity diagram (HID) or colour–colour diagrams (CCDs; Hasinger & Van der Klis 1989; Van der Klis 2006). The Z shape variation constitutes a horizontal branch (HB) at the top, a flaring branch (FB) at the bottom, and a normal branch (NB) connecting them diagonally. These are further classified into two broad groups, namely Sco and Cyg-like sources, due to their different appearance exhibited by the HB and FB i.e. less vertical orientation of HB and a weaker FB is seen among Cyg-like sources than in Sco-like (Kuulkers et al. 1994). The hybrid source XTE J1701–462 occupies a special place among NS LMXBs and is considered to be a remarkable source, as it displays all the characteristics exhibited by both Z and atoll sources (Homan et al. 2010, 2007; Lin et al. 2009). At the brightest state, the intensity variations were associated with HB, NB, and FB of Cyg-like and exhibited Sco-like variation at relatively lower brightness. During the decay phase, the variation closely resembles the soft state of an atoll source and later transits to the hard state of the atoll source just before going to the quiescent state. Many important results were noticed based on the spectral fitting of RXTE data of this source. The mass accretion rate was found to be constant along with the Z phase in Sco-like variation and different mechanisms were proposed to explain the spectral and timing variations during the Z phase variations (Lin et al. 2009). It was also found that mass accretion rate is the important driving parameter during the Z and all along with the atoll phases variation. Z sources are unique probes in the sense they provide a platform to understand the structure of accretion disc emitting close to Eddington luminosity because due to the radiation pressure the structure of the inner region of accretion is affected. The previous studies suggested that the interplay between the accretion disc and comptonization region mutually varies to produce the observed tracks in the HID. However, other physical components like a boundary layer (Popham & Sunyaev 2001) or a transition layer (TL) (Osherovich & Titarchuk 1999a, b; Titarchuk & Osherovich 1999) cannot be ruled out. The comptonization region can be in the form of a quasi-spherical cloud or it could be a base of a jet that causes the observed hard continuum in the X-ray spectrum (Migliari et al. 2007). But its association with dynamical features like various branch oscillations or band-limited noises is not known. The spectra of Z sources can also be explained by a structure known as the boundary layer over the NS surface but again, its association to the observed HBO, NBO, etc., is not properly understood (Popham & Sunyaev 2001; Gilfanov, Revnivtsev & Molkov 2003; Revnivtsev & Gilfanov 2006). Based on the detailed spectral modelling of GX 17 + 2, BL occupies a smaller area at the lower vertex (i.e. bottom of NB) in comparison to its area in other branches (Lin et al. 2012) and the comptonization dominates at the HB branch that fades away as source traverse to the FB. The inner disc radius was found to be moving towards the NS, as the Z track evolves from HB to FB. All these structural and radiative variations are found to be occurring at an almost constant mass accretion rate (Lin et al. 2009, 2012).


WASP-43b is the most heavily scrutinized phase curve, with four analyses of this data set already published (Stevenson et al. 2017; Mendonça et al. 2018; Morello et al. 2019; May & Stevenson 2020). Our phase curve semi-amplitude, eclipse depth, and radius are consistent with all of these works. The more contentious issue is that of the phase curve’s phase offset and nightside temperature. Stevenson et al. (2017) initially reported only a 2σ upper limit on the nightside temperature of 650 K, while all subsequent reanalyses (including ours) favour a significantly detectable nightside temperature of ∼800 K. As for the planet’s phase offset, Stevenson et al. (2017) and May & Stevenson (2020) favour a larger phase offset (21 ± 2 °E) than Mendonça et al. (2018) and Morello et al. (2019) (12 ± 3 °E and 11 ± 2 °E). May & Stevenson (2020) claimed that the differences between the retrieved phase offsets is the result of temporal binning which was not used by Stevenson et al. (2017) and May & Stevenson (2020) but was used by Mendonça et al. (2018), Morello et al. (2019), and this work. Fitting the temporally binned photometry for all 17 phase curves with each of our detector models already required more than 2000 CPU hours, and expanding this to unbinned photometry for all phase curve fits would require more than 125 000 CPU hours (or 434 d using our 12× multithreading computer) optimistically assuming all of detector models scaled linearly with the number of input data. However, we did try fitting just the WASP-43b unbinned phase curve with our preferred detector model (BLISS) and found that our phase offset and nightside temperature was unchanged. Including a linear slope in time also did not affect our phase offset or nightside temperature. Instead, we find that the phase offset inferred by our models depends on the choice of phase curve model, as our 4-parameter (v2) phase curve models are consistent with those of Stevenson et al. (2017) and May & Stevenson (2020), while our 2-parameter phase curve models (v1) are consistent with Mendonça et al. (2018) and Morello et al. (2019). Ultimately, we cannot decide between these two discrepant offsets as the ΔBIC between the two phase curve models for our preferred BLISS detector model is only 3.7 (insignificantly favouring the 20.4 ± 3.6 offset from the v2 model). For reference, Stevenson et al. (2014b) found phase offsets ranging from roughly −6 to 17 deg east in the Hubble/WFC3 bandpass.


Recently, forms of feedback that are fundamentally different from SNe have been shown to be essential to galaxy formation. Murray, Quataert & Thompson (2010) analysed the dynamical effects of several forms of stellar feedback on parent molecular clouds. In their models they include momentum input from ionized gas in H ii regions, shocked stellar winds, hot gas pressure, protostellar jets and cosmic rays. Murray et al. (2010) conclude that radiation pressure (RP) on dust grains is likely to be the dominant form of feedback in star-forming galaxies. A variety of other studies have reached the same conclusions, placing the combination of RP and photoionization of gas by massive stars as the dominant mechanism for disruption of molecular clouds and internal regulation of the SF process (Indebetouw et al. 2009; Krumholz & Matzner 2009; Murray et al. 2010; Andrews & Thompson 2011; Hopkins, Quataert & Murray 2011; Lopez et al. 2011; Pellegrini, Baldwin & Ferland 2011). RP alone might also be the only mechanism that explains galactic fountains and the warm gas outflows observed in absorption in high-redshift galaxies (Murray, Ménard & Thompson 2011). In addition, recent numerical work by Krumholz & Thompson (2012) shows that radiation feedback fully accounts for the large gas velocity dispersions measured in young star clusters in the MW. There are at least three reasons why radiative feedback is an essential ingredient of the galaxy formation process. First, observations show that molecular clouds begin to disperse shortly after the O stars form and before the first SNe explode and deposit their energy into the gas (Kawamura et al. 2009). Secondly, the total energy output of a stellar cluster is dominated by radiation. The rate of radiative energy output by O and B stars is ∼200 times larger than the average power injected by SNe and stellar winds during the lifetime of the most massive stars. Thirdly, it is difficult to explain the large gas turbulence values observed in star-forming regions without including the momentum input by radiation (Murray et al. 2010).


The Hubble Frontier Fields program1 (or HFF hereafter, Lotz et al. 2017) provides the most remarkably detailed examples of gravitational lensing by galaxy clusters, registering hundreds of multiply lensed galaxies for charting galaxy formation to unprecedented depths (see e.g. Jauzac et al. 2014, 2015a,b; Lam et al. 2014; Zitrin et al. 2014; Diego et al. 2015b,c, 2016; Kawamata et al. 2016; Limousin et al. 2016; Mahler et al. 2017). Furthermore, most of these HFF clusters are in a state of collision, enhancing their value for assessing the collisionality of dark matter (DM), a basic assumption of the standard particle interpretation of DM (Markevitch et al. 2002, 2004; Springel & Farrar 2007; Randall et al. 2008). Many clusters exhibit significant, but modest, offsets between the peak of the DM distribution and the centroid of the X-ray emission (Markevitch et al. 2004; Clowe et al. 2006; Mahdavi et al. 2007; Dawson et al. 2012; Menanteau et al. 2012), which is expected if DM is collisionless. These observations can provide a constraint on the DM cross-section (Markevitch et al. 2004; Randall et al. 2008). It is important that these differences are evaluated with the guidance of hydrodynamical models, as complex multibody interactions may also separate the DM from the plasma that can be explained without new physics, as is clearly evident in extreme cases of the bullet cluster (Mastropietro & Burkert 2008), and like the El Gordo cluster (Molnar & Broadhurst 2015), where high-speed collisions between pairs of clusters are ongoing. More direct evidence for collisional DM would be concluded from differences between the stellar and DM distributions as the stars behave like collisionless particles and we should expect the collisionless DM to follow the gravitational potential in the same way. Offsets between the position of the DM central peak and the peak of the luminous matter are difficult to explain with a standard Λcold dark matter but are naturally produced for reasonable values of the DM cross-section (Rocha et al. 2013). A difference of this nature has been claimed recently based on detailed lensing data in the centre of a cluster that contains four bright member galaxies (Massey et al. 2015). In case of the HFF clusters, it is interesting that our free-form analysis of MACS0146 also indicates a possible offset between the lensing-based centroids of the brightest galaxies and their luminous stellar centroids. These differences are subtle and it will be important to look at a larger sample and the model dependencies, and systematic uncertainties, in detail to support any claim of new physics.


There are several popular scenarios employed to explain the observational features of CL AGNs. One scenario is that the broad emission lines are obscured by the torus or moving clouds over the observer’s line of sight (Goodrich & Miller 1989), while only several CL AGNs can be explained by this scenario (Wang et al. 2019; Jaffarian & Gaskell 2020; Kokubo & Minezaki 2020). The features observed in most CL AGNs, e.g., the complex multiband spectral variabilities, and strong changes seen in the infrared or low level of polarization, strongly argue against the scattering (or obscuration) scenario (e.g., Sheng et al. 2017; Mathur et al. 2018; Stern et al. 2018; Hutsemékers et al. 2019; Kynoch et al. 2019, and the references therein). Another attractive scenario is that the CL AGNs are indeed tidal disruption events (Merloni et al. 2015; Kawamuro et al. 2016; Yang et al. 2019; Padmanabhan & Loeb 2020; Ricci et al. 2020; Zhang 2021), while it is not a general mechanism to explain all CL AGNs, such as repeating CL AGNs. The changing look phenomenon triggered by the change of the mass accretion rate of the accretion disk is a rather straightforward model (Husemann et al. 2016; Liu et al. 2019; Ruan et al. 2019; Ai et al. 2020; Sniegowska et al. 2020); however, it has a fatal problem that propagation timescale of the gas in a thin accretion disk is much longer than the observed timescale in CL AGNs, unless the viscous thin disk model is somewhat revised (Lawrence 2018). Dexter & Begelman (2019) proposed that the magnetically elevated disk model could help to explain the changing look timescale. Based on this scenario, Scepi et al. (2021) suggested that a magnetic flux inversion in a magnetically arrested disk is able to explain the CL event in 1ES 1927+654. Sniegowska et al. (2020) suggested that a narrow unstable zone between the outer thin disk and the inner ADAF could cause the periodic outbursts in repeating CL AGNs. Recently, the effects of large-scale magnetic fields on this scenario for repeating CL AGNs have been studied in detail by Pan et al. (2021), and Lyu et al. (2021) suggested that the change of broad emission lines in Mrk 1018 might be regulated by the evolution of accretion disk.


It was found that the complex dielectric function from Pecharromán et al. (1999) for the sample obtained by heating bayerite at 1273 K, assuming a spheroid with depolarization parameters of (0.35, 0.003), produced an opacity with 11, 20, 28, and 32 μm features, so this component was included in the models. However, with only this component, the observed 20 μm features in the residual spectra were found to be wider than those in the models. By adding the opacity of the sample obtained by heating boehmite at 1173 K, the width of the 20 μm feature could be matched. This was done using the complex dielectric function for the sample obtained by heating boehmite at 1173 K from Pecharromán et al. (1999), assuming a spheroid with depolarization parameters of (0.35, 0.035). The complex dielectric functions of the samples obtained by heating bayerite and boehmite to various temperatures (Pecharromán et al. 1999) were derived by modeling the reflectance spectra of pellets obtained by pressing powders of these materials under great pressure. This method required Pecharromán et al. (1999) to assume an effective medium theory, such that a pellet is a mixture of one of their samples with a matrix of air. Pecharromán et al. (1999) noted that heating bayerite at 500°C eliminates the XRD pattern of bayerite, and they note that at 700°C, the infrared reflectance spectrum of the boehmite sample no longer shows OH− stretching bands. This must mean that the samples obtained from heating bayerite at 1273 K and from heating boehmite at 1173 K are no longer bayerite or boehmite, respectively. XRD performed by Pecharromán et al. (1999) of the sample of bayerite prepared at 1273 K suggests only θ-alumina was present, and their infrared and NMR spectroscopy confirms this. XRD of their sample obtained from heating boehmite to 1173 K (Pecharromán et al. 1999) suggests δ-alumina to be present, though some amounts of θ-alumina and α-alumina are present, as they deduce from XRD and infrared and NMR spectroscopy.


Altogether, the approximately thirty molecules recently detected have confirmed the chemical complexity in the nebula, and generated our interest for the present study. Of these species, we will focus our attention on the seventeen species listed by molecular families in Table 1. As can be seen in this table, the WHISPER survey allowed the detection of some organic molecules in the Horsehead nebula, such as formaldehyde (H2CO) and methanol (CH3OH), which constitute key species in the likely synthesis of more complex organic molecules such as some prebiotic molecules (Bernstein et al. 2002; Muñoz Caro et al. 2002; Garrod et al. 2008). Because they are detected in a wide variety of interstellar sources – in hot cores (Sutton et al. 1995; Ceccarelli et al. 2000), dark clouds (Bergman et al. 2011), shocked regions (e.g. Sakai et al. 2012; Codella et al. 2012; Tafalla et al. 2010) and even in comets (Mumma & Charnley 2011; Cordiner et al. 2015) – it is of prime importance to understand well how these precursor molecules form. H2CO is commonly thought to form both in the gas-phase and on grain surfaces, while CH3OH is believed to be only formed on grain surfaces (Garrod et al. 2006; Geppert et al. 2006). Guzman et al. (2013) reported the observations of these two molecules toward the Horsehead nebula in both the PDR and Core positions. Unable to reproduce the observed abundances of either H2CO or CH3OH at the PDR position with only pure gas-phase models, they concluded that, for this region, both species are formed on grain surfaces and then photodesorbed into the gas phase. On the other hand, at the Core position, a pure gas-phase model can reproduce the observed H2CO abundance, while photodesorption of ices is still needed to explain the observed abundance of CH3OH. Other organic molecules were reported in the Horsehead nebula as first detections in a PDR environment, including HCOOH (formic acid), CH2CO (ketene), CH3CHO (acetaldehyde), and CH3CCH (propyne) (Guzman et al. 2014). Their abundances were found to be higher at the PDR position than at the Core, revealing that complex organic chemistry is also occurring in UV-illuminated neutral gas (Guzman et al. 2014). Of these molecules, some – HCOOH, CH2CO, and CH3CHO – have now also been detected in the Orion bar PDR (Cuadrado et al. 2016, 2017).


Once corrected for dust attenuation, Hα luminosities can be transformed into star formation rates (SFR, in M⊙ yr-1) using a factor that depends on the assumed IMF and stellar model7: (10)\begin{equation} {SFR = k({\rm H}\alpha) \times L({\rm H}\alpha)_{\rm cor}} . \end{equation}SFR=k(Hα)×L(Hα)cor.We recall that this relation is valid only under the assumption that the mean star formation activity of the emitting galaxies is constant on a timescale of a few Myr, roughly comparable to the typical time spent by the stellar population responsible for the ionisation of the gas on the main sequence (Boselli et al. 2009; Boissier 2013; Boquien et al. 2014). The ionising stars are O and early-B stars, whose typical age is ≲107 yr. The stationarity condition is generally satisfied in massive, normal, star-forming galaxies undergoing secular evolution. In these objects, the total number of OB associations is significantly larger than the number of HII regions under formation and of OB stars reaching the final stage of their evolution, thus their total Hα luminosity is fairly constant with time. This might not be the case in strongly perturbed systems or in dwarf galaxies, where the total star formation activity can be dominated by individual giant HII regions (Boselli et al. 2009; Weisz et al. 2012), and the IMF is only stochastically sampled (Lee et al. 2009; Fumagalli et al. 2011; da Silva et al. 2014). The HRS sample is dominated by relatively massive galaxies undergoing secular evolution. For these objects, Eq. (10) can thus be applied. The sample, however, also includes galaxies in the Virgo cluster region, where the perturbation induced by the cluster environment might have affected their star formation rate (e.g. Boselli & Gavazzi 2006, 2014). Models and simulations have shown that in these objects the suppression of star formation occurs on timescales of a few hundred Myr (Boselli et al. 2006, 2008a,b, 2014d). These timescales are relatively long compared to the typical age of O-B stars. The recent work of Boquien et al. (2014) has clearly shown that the Lyman continuum emission tightly follows the rapid variations in the star formation activity of simulated galaxies down to timescales of a few Myrs. We can thus safely consider that the linear relation between the Hα luminosity and the star formation rate given in Eq. (10) is satisfied in the HRS sample.