Hierarchical structure formation scenarios (e.g. Fall & Efstathiou 1980; van den Bosch et al. 2002; Agertz, Teyssier & Moore 2011) predict that massive galaxies acquire much of their stellar mass through a combination of continuous cold gas accretion and mergers with smaller objects (e.g. Press & Schechter 1974; Moster, Naab & White 2013; Kaviraj et al. 2015; Rodriguez-Gomez et al. 2016; Martin et al. 2018b; Davison et al. 2020; Martin et al. 2021). As a consequence, mergers are also expected to play a significant role in driving the evolution of galaxy properties, for example, by triggering (Schweizer 1982; Mihos & Hernquist 1996; Duc et al. 1997; Elbaz & Cesarsky 2003; Kaviraj et al. 2011; Lofthouse et al. 2017; Martin et al. 2017) or quenching (Schawinski et al. 2014; Barro et al. 2017; Kawinwanichakij et al. 2017; Pontzen et al. 2017) star formation in the host galaxy or by driving its morphological evolution (e.g. Toomre 1977; Conselice, Yang & Bluck 2009; Dekel, Sari & Ceverino 2009; Taranu, Dubinski & Yee 2013; Naab et al. 2014; Fiacconi, Feldmann & Mayer 2015; Graham, Dullo & Savorgnan 2015; Deeley et al. 2017; Gómez et al. 2017; Welker et al. 2017; Martin et al. 2018a; Jackson et al. 2019). Signatures of past mergers take the form of faint extended tidal features such as tails (e.g. Pfleiderer 1963; Toomre & Toomre 1972; Peirani et al. 2010; Kaviraj 2014; Kaviraj, Martin & Silk 2019), or plumes (e.g. Lauer 1988) – which are typically produced by major mergers – and streams (e.g. Johnston, Sigurdsson & Hernquist 1999; Shipp et al. 2018; Martinez-Delgado et al. 2021) or shells (e.g. Malin & Carter 1983; Quinn 1984) – which mainly arise from minor interactions – as well as in the structure of the surrounding diffuse light (e.g. Choi, Guhathakurta & Johnston 2002; Graham 2002; Johnston, Choi & Guhathakurta 2002; Seigar, Graham & Jerjen 2007; Kaviraj et al. 2012; Monachesi et al. 2016, 2019; Iodice et al. 2019; Montes 2019). These features, which arise from many different types of encounter, hold a fossil record of the host galaxy’s past interactions and mergers which can be used to reconstruct its assembly history and dynamical history (Johnston et al. 2008; Martínez-Delgado et al. 2009; Belokurov et al. 2017; Montes et al. 2020; Ren et al. 2020; Spavone et al. 2020; Vera-Casanova et al. 2021). However, the majority of tidal features are expected to have surface brightnesses fainter than 30 mag arcsec−2 in the r-band (Johnston et al. 2008). Although pushing towards these kinds of limiting surface brightnesses remains extremely challenging, it is nevertheless desirable to do so, being necessary to uncover a more detailed history of local Universe. This is not only vital for our understanding of hierarchical galaxy assembly (e.g. Johnston, Sackett & Bullock 2001; Wang et al. 2012), but also serves as a novel galactic scale probe of more fundamental physics such as theories of gravity (e.g. Gentile et al. 2007; Renaud, Famaey & Kroupa 2016) and dark matter (Dubinski, Mihos & Hernquist 1996; Kesden & Kamionkowski 2006; Dumas et al. 2015; van Dokkum et al. 2018; Montes et al. 2020). In particular, tidal structure is a powerful tracer of the underlying galactic halo potential (e.g. Dubinski, Mihos & Hernquist 1999; Varghese, Ibata & Lewis 2011; Bovy et al. 2016; Ibata et al. 2020; Malhan, Valluri & Freese 2021).


Comparison to a sample of inactive galaxies is also key to demonstrating that an observed merger fraction is actually related to AGN activity. Large samples of inactive galaxies are observed at all merger stages, so it is clear that a major merger alone is not a sufficient condition for quasar activity. Thus, to conclusively demonstrate that mergers are an important channel for quasar fueling, we would need to observe an enhancement to the merger fraction in quasar hosts relative to a matched sample of inactive galaxies. Several studies of lower-luminosity AGN host morphologies with inactive control samples have been conducted in HST extragalactic survey fields (e.g., Grogin et al. 2005; Gabor et al. 2009; Cisternas et al. 2011; Schawinski et al. 2011; Kocevski et al. 2012; Böhm et al. 2013; Villforth et al. 2014). In particular, we designed our study methodology following Cisternas et al. (2011), who used visual classification to compare strong distortion signatures in moderate-luminosity X-ray selected AGN hosts to a comparison sample of inactive galaxies in the redshift range z = 0.3–1.0. They found no significant enhancement to the merger fraction of AGN hosts relative to inactive galaxies, demonstrating that the majority of cosmic black hole mass accretion at

, i.e., in AGN with inferred SMBH masses

 (Vestergaard & Osmer 2009), is not merger driven. How do we then reconcile this result with the results from the red quasar and radio galaxy studies? One possibility is that certain sub-classes of AGN may be preferentially merger driven, even though the bulk of all objects are not. In particular, a downsizing trend has been observed, such that near the peak of quasar activity at z = 2, higher-mass SMBHs dominate the cosmic mass accretion (

, Vestergaard & Osmer 2009). It is possible that forming these most massive black holes requires major mergers, as a particularly efficient gas transport mechanism, and that the declining major merger rate of galaxies is one of the driving forces behind this downsizing trend.


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.


For an informed opinion on the expected fluxes and durations of short transients, we have to understand coherent emission processes. What we know from incoherent emission physics is that the intrinsic brightness temperature of sources is likely limited to 1011 − 12 K (e.g. Kellermann & Pauliny-Toth 1969; Singal 1986, where brightness temperature is defined as the value of T in the Rayleigh–Jeans formula that yields the correct flux of the source). Sources having brightness temperatures above about 1012 K must emit coherently, have their emission relativistically boosted, or both. However, we understand the processes underlying such sources very poorly, and so in this paper, we shall take the approach of expecting a wide range of known and unknown types of source, and exploring as much of parameter space as our experiment allows. One important thing to note, that is particularly relevant here, is that most of those coherent emitters for which we know the properties of the radio spectrum have quite steep spectra, typically going as ν−2 or even ν−3 (see e.g. Melrose 2009; Lorimer & Kramer 2012), in contrast with a typical ν−0.8 for optically thin synchrotron emission. This means that low-frequency instruments such as LOFAR may be intrinsically at an advantage to find coherent emitters (in addition to having larger fields of view). While known coherent transients have mostly been found in beam-formed searches and last milliseconds to seconds, more recently fast transients have been discovered in low-frequency image plane surveys. For example, the sources GCRT J1745-3009 (Hyman et al. 2005) and GCRT J1746-2757 (Hyman et al. 2002) were detected at 330 MHz with the VLA, while GCRT J1742-3001 (Hyman et al. 2009) was discovered at 235 MHz with the Giant Metrewave Radio Telescope. These sources showed bright flares lasting from minutes to a few hours. More recently, the low-frequency radio transient ILT J225347+862146 (Stewart et al. 2016) was discovered at 60 MHz with LOFAR, lasting about 10 min. The only significant population of transient radio sources previously known in this duration range are relatively nearby and low-luminosity flare stars, having fluxes of about 1 Jy at 1.2 GHz (Osten & Bastian 2006).


The hard X-ray band has been crucial to studying some of the most powerful blazars (see e.g., Tavecchio et al. 2000; Massaro et al. 2004a, 2004b, 2006; Donato et al. 2005). More recently, the outstanding sensitivity of the Nuclear Spectroscopic Telescope Array (NuSTAR, 3–79 keV, Harrison et al. 2013) has enabled us to find and study some of the most distant and luminous ones (e.g., Sbarrato et al. 2013; Tagliaferri et al. 2015; Ajello et al. 2016; Paliya et al. 2016; Sbarrato et al. 2016; Marcotulli et al. 2017). Harboring highly relativistic jets pointed closely at the observer (θV  1/Γ, θV being the viewing angle and Γ the bulk Lorentz factor, Γ ∼ 10−15, Urry & Padovani 1995), this subclass of the Active Galactic Nuclei (AGNs) is home to some of the most energetic particle acceleration and radiation processes known in astrophysics. The boost in flux ascribed to relativistic beaming, arising from the peculiar orientation of the jets, renders them visible at redshifts well beyond z = 2 (the farthest blazar detected so far is at z = 5.47, Romani et al. 2004), making them extraordinary beacons with which to explore the early universe. Their typical double-hump spectral energy distribution (SED) spans the whole electromagnetic spectrum and is shaped by the nonthermal processes occurring in the jets. Relativistic electrons, spiraling along the magnetic field lines, undergo both synchrotron and inverse Compton (IC) processes. The first produces a peak in the SED located between infrared and X-ray frequencies. The second instead results in a peak located between X- and γ-ray energies. If the electrons interact with a source of low-energy photons within the jet, this is referred to as Synchrotron Self Compton (SSC, e.g., Ghisellini & Maraschi 1989), whereas if the photons are external to the jet (i.e., the accretion disk, the torus, and/or the broad line region, BLR), it is referred to as External Compton process (EC, e.g., Sikora et al. 1994). Based on their optical spectra, blazars are usually classified either as BL Lacertae objects (BL Lacs) or flat spectrum radio quasars (FSRQs), the first showing weak or no emission lines, the second showing broad (EW > 5 Å) ones. Following Abdo et al. (2010a), these sources can also be classified according to the position of the synchrotron peak (

), with low-, intermediate-, and high-synchrotron peak (LSP, ISP, HSP) blazars having, respectively,

 Hz,

 Hz, and

 Hz. FSRQs usually belong to the LSP class and at the high-luminosity end of such subclass are the so-called “MeV blazars,” whose high-energy peak falls in (or close to) the MeV band. With bolometric luminosities exceeding 1048 erg s−1, these are among the most powerful objects in the universe. In fact, they host powerful relativistic jets (Ghisellini et al. 2014), are usually found at high-redshift (z > 2, e.g., Ajello et al. 2009; Ghisellini et al. 2010; Ackermann et al. 2017; Marcotulli et al. 2017), and typically host billion solar mass black holes (e.g., Ghisellini et al. 2010; Paliya et al. 2017a).


NGC 2110. NGC 2110 is another nearby (z = 0.00779, Gallimore et al. 1999), X-ray bright Seyfert galaxy. Diniz et al. (2015) report a black hole mass of

2
.

7

−
2.1

+
3.5

×

10
8

M
⊙

$ 2.7^{+ 3.5}_{- 2.1} \times 10^{8}\,{{M}_{\odot}} $

, from the relation with the stellar velocity dispersion. From BeppoSAX data, Malaguti et al. (1999) found the X-ray spectrum to be affected by complex absorption. This has been later confirmed by Evans et al. (2007), who find the Chandra+XMM–Newton data to be well fitted with a neutral, three-zone, partial-covering absorber. Rivers et al. (2014) find the Suzaku data to be well fitted with a stable full-covering absorber plus a variable partial-covering absorber. A soft excess below 1.5 keV is also present (Evans et al. 2007), and possibly due to extended circumnuclear emission seen with Chandra (Evans et al. 2006). No Compton reflection hump has been detected with Suzaku (Rivers et al. 2014) or NuSTAR (Marinucci et al. 2015), despite the presence of a complex Fe Kα line. According to the multi-epoch analysis of Marinucci et al. (2015), the Fe Kα line is likely the sum of a constant component (from distant, Compton-thick material) and a variable one (from Compton-thin material). Concerning the high-energy cut-off, ambiguous results have been reported in literature (see Table 1). Ricci et al. (2017) report a value of

448

−
55

+
63

$ 448^{+63}_{-55} $

 keV, while Lubiński et al. (2016) report a coronal temperature of

230

−
57

+
51

$ 230^{+51}_{-57} $

 keV and an optical depth of

0
.

52

−
0.13

+
0.14

$ 0.52^{+ 0.14}_{- 0.13} $

. From 2008–2009 INTEGRAL data, Beckmann & Do Cao (2010) report a cut-off of ∼80 keV with a hard photon index, but these results are not confirmed by NuSTAR (Marinucci et al. 2015). Indeed, only lower limits to the high-energy cut-off have been found with NuSTAR (210 keV: Marinucci et al. 2015), Suzaku (250 keV: Rivers et al. 2014) and BeppoSAX (143 keV: Risaliti 2002). No hard X-ray spectral variability has been detected by Caballero-Garcia et al. (2012) and Soldi et al. (2014) from BAT data, despite the significant flux variability.


The physical nature of the X-structures themselves is also an open question, although significant progress has already been made in this direction. The spatial resolution of the models was not very good in the first numerical studies of 3D bar structure (≈103−104 particles represented the disc component). X-structures were only distinguished in unsharp masked images constructed from such models. Some authors (Friedli & Pfenniger 1990; Pfenniger & Friedli 1991) therefore suggested that X-structures are akin to an optical illusion due to the tendency of eyes to perceive the intensity gradients instead of actual intensity values. However, with an increase of spatial resolution, it became evident that the X-structures are real density enhancements that can be observed even without unsharp masking processing (see Smirnov & Sotnikova 2018 for many representative examples). The question then is why such density enhancements are observed. Studies of orbit composition of B/PS bulges and X-structures in different numerical and analytical models (Patsis, Skokos & Athanassoula 2002; Quillen 2002; Quillen et al. 2014; Patsis & Katsanikas 2014a; Parul, Smirnov & Sotnikova 2020) showed that an X-shape is observed in these models due to a tendency of a star to spend more time near turning points of its trajectory. More specifically, 3D bars are constituted by different types of periodic, quasi-periodic, and sticky chaotic orbits (Pfenniger 1984; Pfenniger & Friedli 1991; Patsis et al. 2002; Skokos, Patsis & Athanassoula 2002; Patsis & Katsanikas 2014a,b; Patsis & Harsoula 2018; Patsis & Athanassoula 2019). Stars that move along such orbits spend different periods of time in different parts of their trajectories. For example, stars moving along banana-shaped orbits (Pfenniger & Friedli 1991) spend more time at the highest points of their trajectory (Patsis et al. 2002; Patsis & Katsanikas 2014a). Therefore, the bulk of such orbits produces a density profile with visible density enhancements at the highest points of such orbits. For an X-structure to be observed, these density enhancements should be aligned along an almost straight line for orbits with different apocentric distances. This is indeed the case for the realistic bar potential (Patsis et al. 2002; Quillen 2002; Quillen et al. 2014; Patsis & Katsanikas 2014a). Parul et al. (2020) showed that the orbits of a more complicated morphology than banana-shaped orbits can build an X-structure in a similar manner. In general, cited works showed that X-structures and B/PS bulges are produced by the same orbits. They are not constituted by different types of orbits like, for example, disc and classical bulge components. The open question that has to be answered in the upcoming studies is what types of orbits are actually presented in real galaxies.


Lempo–Paha—Hiisi is a trans-Neptunian hierarchical triple system composed of a tight inner binary with components of similar size and an outer companion about half their size orbiting 10 times further away (Trujillo & Brown 2002; Benecchi et al. 2010). All large trans-Neptunian objects like Pluto have multiple small moons, but Lempo’s structure is unique in the Solar system. The place and timing of its origin are still a subject of debate (Nesvorný, Youdin & Richardson 2010; Correia 2018). In contrast to the Lempo system, all other known triples in the Solar system have their orbits almost regularly spaced, with one component much smaller than the others, with the most distant component being the largest (Johnston 2020). Unveiling the possible origin of the Lempo system is relevant, as the architecture of multiples holds clues to their formation story and the conditions prevailing in the primitive outer Solar system, but its origin is still unclear. Capture theories proposed so far failed to reproduce the orbital characteristics of observed binaries, especially the distribution of their orbital inclinations (Nesvorný et al. 2010; Brunini 2020). Also, triple formation requires multiple captures, a very unlikely event. Gravitational collapse of pebble clouds in a turbulent gas disc would be efficient in producing binaries and, in some particular conditions, can also produce triple systems. However, such triples do not seem to match the orbital structure of Lempo–Paha–Hiisi (Nesvorný et al. 2010). The non-detection of triple systems in the cold classical Kuiper belt, where the number of known binaries is much higher than in the resonant populations (Noll et al. 2020), argues against this formation mechanism of triple systems. The fragile dynamical stability of Lempo–Paha–Hiisi (Correia 2018) also casts doubt on the place and time of its origin, leading to speculations about a possible recent formation at the place in which it currently resides.


The Nançay Radio Telescope (NRT) is a meridian telescope equivalent to a 94 m parabolic dish located near Orléans (France). Owing to its design, the NRT can track objects with declinations δ >  −39° for approximately one hour around culmination, and is thus well suited for the long-term timing of pulsars, for example, for the study of individual objects (see, e.g., Cognard et al. 2017; Octau et al. 2018, for recent examples) or for searching low-frequency gravitational waves from supermassive black hole binaries, using pulsar timing arrays (PTAs; see, e.g., Desvignes et al. 2016). With the goal of identifying new exotic pulsar systems or highly stable MSPs suitable for PTA studies, the SPAN512 pulsar survey (Desvignes et al. 2013; Octau et al. 2016; Desvignes et al., in prep.) was conducted between 2012 and 2018 at the NRT. As part of this survey, new pulsars were searched for at intermediate Galactic latitudes (3.5 °  |b|  5°) and away from the inner Galaxy (Galactic longitudes 74 °  l   150°). Observations were conducted at 1.4 GHz with 0.5 MHz frequency channels over a total bandwidth of 512 MHz and a fine time resolution of 64 μs, to be sensitive to faint and distant MSPs. We used PRESTO pulsar searching routines (Ransom et al. 2002) to search the data for pulsars with dispersion measures (DMs) up to 1800 pc cm−3, and a moderate acceleration search in the Fourier domain (the zmax parameter was set to 50 in PRESTO analyses) to be sensitive to pulsars in binary systems. Searches for periodic signals in the data from this survey so far led to the discovery of one “ordinary” (i.e., non-millisecond) pulsar, PSR J2048+49, and two MSPs, PSRs J2055+3829 and J2205+6012. Details on the survey, the data analysis, and the discovered pulsars will be reported in Desvignes et al. (in prep.). In the present paper we report on the results from the timing of PSR J2055+3829, an MSP in an eclipsing BW system, and from the analysis of the radio eclipses of the pulsar. In Sect. 2 we describe the radio timing observations and the results from the analysis of the timing data. In Sect. 3 we present observations of eclipses of PSR J2055+3829 at 1.4 GHz, and analyses of the data taken around superior conjunction of the pulsar. In the following section (Sect. 4), we present comparisons of the mass function distributions for eclipsing and non-eclipsing BWs, and for Galactic disk and globular cluster BWs. Finally, Sect. 5 summarizes our findings.


In addition to the unconstrained optimization problems of (11) and (12), many CS-based approaches consider constrained forms of the analysis and synthesis models, which are, respectively, given by
(14)
\begin{eqnarray*}
\min _{\boldsymbol{x}} \Vert \boldsymbol {\mathsf {\Psi }}^\dagger {\boldsymbol{x}}\Vert _1, \quad {\rm s.t.} \ \ \Vert {\boldsymbol{y}}-\boldsymbol {\mathsf {\Phi }} {\boldsymbol{x}}\Vert _2^2 \le \epsilon
\end{eqnarray*}
and
(15)
\begin{eqnarray*}
\min _{\boldsymbol{a}} \Vert {\boldsymbol{a}}\Vert _1, \quad {\rm s.t.} \ \ \Vert {\boldsymbol{y}}-\boldsymbol {\mathsf {\Phi }}\boldsymbol {\mathsf {\Psi }} {\boldsymbol{a}}\Vert _2^2 \le \epsilon ,
\end{eqnarray*}
where ε is an upper-bound related to the noise level present in . CS approaches based on constrained optimization problems, solved via convex optimization techniques, have been applied broadly in RI imaging (Wiaux et al. 2009a,b; McEwen & Wiaux 2011; Li et al. 2011a,b; Carrillo et al. 2012, 2014; Onose et al. 2016; Pratley et al. 2018). These techniques have shown promising results, with improvements in terms of image fidelity and flexibility compared to traditional approaches such as clean-based methods and MEM. For these constrained regularization approaches, parallel implementation structures have also been explored (Carrillo et al. 2014; Onose et al. 2016). Compared with the unconstrained analysis and synthesis models, constrained approaches are parametrized by ε (related to noise level) which controls the error of the reconstruction explicitly; in contrast, unconstrained models use regularization parameter μ to impose a tradeoff between the prior and data fidelity. The constrained approach therefore avoids the problem of unknown regularization parameter μ, replacing it with the problem of estimating the noise bound ε. The latter can be performed in a principled manner by noting that for Gaussian noise the ℓ2 norm data fidelity term follows a χ2 distribution with 2M degrees of freedom (see e.g. Carrillo et al. 2012). While constrained problems do not afford a straightforward Bayesian interpretation, the constrained and unconstrained models are closely related (Nikolova 2016).


The most general third-order statistics is the three-point correlation function (hereafter referred to as 3PCF), which is defined in configurations space. Alternatively, one can study its Fourier space counterpart, the bispectrum. These two statistics contain, in principle, the same information. However, their analyses implicate different limitations and challenges, which can affect the physical interpretation of the results. A main advantage of the bispectrum is that an analysis in Fourier space allows for a clear exclusion of high-frequency modes in the density fluctuations, which are difficult to interpret theoretically due to their highly non-linear evolution. In configuration space, these high-frequency modes contribute to the 3PCF, in principle, at all scales. In practice, one therefore needs to restrict the analysis to large scales, where their contribution is negligible, lavishing a lot of valuable data. Another advantage of the bispectrum is that its covariance is diagonal for Gaussian density fluctuations. This approximation works well, even for evolved density fields, while deviations from Gaussianity can also be taken into account (Scoccimarro 2000; Sefusatti et al. 2006; Chan & Blot 2017). The covariance of the 3PCF, on the other hand, is not diagonal, even for Gaussian fluctuations, which makes the modelling more difficult (Srednicki 1993; Slepian & Eisenstein 2015; Byun et al. 2017; Gualdi et al. 2017). An additional difference in the analysis of the bispectrum and the 3PCF lies in the fact that the computation of the latter is more expensive. However, this aspect can be tackled by employing advanced algorithms and appropriate computational resources, as done in this work (see also, Barriga & Gaztañaga 2002; McBride et al. 2011a; Jarvis 2015; Slepian & Eisenstein 2015, and references therein). Besides its disadvantages, there are some arguments that speak for the 3PCF. One of them is the fact that the amplitude of the 3PCF (but not its errors) is not affected by shot-noise, whereas the latter affects the bispectrum amplitude at all scales and hence needs to be modelled for correcting the measurements. In addition, an analysis in configuration space has the advantage that complicated survey masks can be easily taken into account in the analysis of observational data, while in Fourier space such masks impose complicated effects on the measured bispectrum, which are difficult to model (e.g. Scoccimarro 2000). A more general consideration is that it is easier to interpret effects such as redshift space distortions or baryon acoustic oscillations (BAOs) on the statistics in configuration space, since that is where the physical processes that cause these effects happen. Studies of third-order correlations in the literature usually focus on either Fourier or configuration space (e.g. McBride et al. 2011b; Marín et al. 2013; Gil-Marín et al. 2015). However, it is worthwhile studying both statistics and cross-check the results, since their different advantages and disadvantages are quite complementary.


Other examples of AGN variability are given by the so-called changing-look AGN, which present a change in the AGN type (e.g. from Type 1 to Type 1.9) due to broadening or narrowing of the Balmer lines4 (Denney et al. 2014; LaMassa et al. 2015; Ruan et al. 2015; Gezari et al. 2016; Husemann et al. 2016; McElroy et al. 2016; MacLeod et al. 2016; Runnoe et al. 2016; Stern et al., in preparation). The appearance or disappearance of broad emission lines is often accompanied by a change in luminosity of a factor ∼10 over ∼10 yr time-scales. As described above, these time-scales are much shorter compared to time-scales expected for accretion state changes (e.g. Sobolewska, Siemiginowska & Gierliński 2011; Hickox et al. 2014), and possible alternative explanations of the changing-look behaviour are variable absorption due to a clumpy torus (e.g. Elitzur 2012), transient events, e.g. tidal disruption of a star by the central black hole (e.g. Eracleous et al. 1995; Merloni et al. 2015), or major changes in the photoionization balance. The magnitude of the drop in luminosity measured in IC 2497 is at least a factor of ∼2 higher than what has been observed in a changing-look AGN. Moreover, the Chandra  and NuSTAR data do not show significant variability, and the upper limits obtained from archival WISE, NEOWISE and IRAS data seem to exclude that the total drop in luminosity happened within the last decades. For these reasons, we argue that the AGN in IC 2497 should not be classified as a changing-look AGN. On the other hand, we suggest that a changing-look AGN corresponds to a short-time (∼10–100 yr) variability which is superimposed on the long-term (∼105–6 yr) AGN phases suggested by this work and other observations (e.g. Schawinski et al. 2015), high resolution (sub-kpc) simulations (Hopkins & Quataert 2010; Bournaud et al. 2011; Novak, Ostriker & Ciotti 2011; Gabor & Bournaud 2013; DeGraf et al. 2014; Sijacki et al. 2015) and theoretical models (Siemiginowska & Elvis 1997; Sanders 1981; Di Matteo, Springel & Hernquist 2005; Hopkins et al. 2005; Springel, Di Matteo & Hernquist 2005; King & Pringle 2007; King & Nixon 2015).


According to simulations, blue galaxies infalling from the field reach pericenter in about 2.4 Gyr (McGee et al. 2009; see also Oman et al. 2013), and we can hypothesize that, by the time they get there, they lose most of their gas. In the first part of this time frame, they can start feeling the action of the ram pressure, and their neutral gas content, which is less bound, starts being stripped. No signs at optical wavelengths are visible yet, but the stripping has started (Tonnesen & Bryan 2010). In some galaxies, ram pressure stripping might be able to unwind the spiral arms (Bellhouse et al. 2021), while in other galaxies it just strips the gas that at some point collapses and starts forming new stars (e.g., Poggianti et al. 2019a). In this phase, tails shine at optical wavelengths, as OB massive stars are very bright. We can assume the visibility of this phase lasts on the order of ∼6 × 108 yr (Fumagalli et al. 2011; Poggianti et al. 2019a). Stripping and star formation consume the available gas and galaxies first appear as truncated disks (Koopmann & Kenney 2004; Fritz et al. 2017) and then become passive, showing k+a spectra (Vulcani et al. 2020). Galaxies typically maintain blue colors for 0.5 Gyr after becoming passive and then move to the red sequence (Poggianti et al. 2004). In these phases, tails are not visible anymore at optical wavelengths. So to summarize, an infalling galaxy maintains its blue color for at least 2.4 + 0.5 ∼3 Gyr since infall and a tail is visible only for 6 × 108yr. We can assume that the sum of RS+SC+UG samples corresponds to all the noninteracting blue late-type galaxies in the clusters and that the tailed galaxies are either only SC or SC+UG. In the first case, ∼15% of the blue cluster galaxies currently show signs of stripping, but since the visibility phase is 6 × 108/3 × 109 ∼ 0.2, the total amount of galaxies undergoing stripping is 15%/0.2 ∼ 75%. In the second case, the incidence of blue cluster galaxies currently showing signs of stripping is even higher. On one hand, this suggests that all blue cluster galaxies undergo a stripping phase during their life in clusters, and on the other hand, it indicates that most likely we are overestimating the number of ram pressure stripped galaxies only using optical imaging.


Andromeda is a galaxy that lies in the green valley (Mutch et al. 2011; Tempel et al. 2011; Jin et al. 2014). According to Belfiore et al. (2016), it is typically a low-ionisation emission-line region (LIER), as first observed by Rubin & Ford (1971) and discussed by Heckman (1996). González-Martín et al. (2015) discussed that the torus is disappearing in LIER: there is indeed little gas in the inner part of M31 (Melchior et al. 2000; Melchior & Combes 2011, 2013). It is the closest external large galaxy in which we can explore the mechanisms that quenched the star formation activity. Optical ionised gas has been observed by Menezes et al. (2013) next to the black hole in a field of view1 of 5′′ × 3.5′′, but this emission is weak. Jacoby et al. (1985) estimated the ionised gas mass in the bulge (10′ × 10′) to be of the order of 1500 M⊙. It also hosts a very massive black hole of 1.4 × 108M⊙ (Bender et al. 2005), but as studied by Li et al. (2011a), it is non-active and only murmurs at a level of 10-10LEdd. It hosts very little star formation of the order of 0.25−0.3 M⊙ yr-1, mainly located in the 10 kpc ring of the disc (e.g. Ford et al. 2013; Rahmani et al. 2016). Inside the central region (10′ × 10′), no obvious sign of star formation is detected (e.g. Kang et al. 2012; Azimlu et al. 2011; Amiri & Darling 2016), except for a central cluster of A stars formed 200 Myr ago that is located next to the black hole (within 1′′) (Lauer et al. 2012), designated by P3 by Bender et al. (2005). Viaene et al. (2014) estimated the star formation rate (SFR) on a pixel basis with panchromatic spectral energy distribution modelling. This infrared-based SFR estimated in the central pixel (36′′ × 36′′) is 4 × 10-5M⊙ yr-1, while an integration over the central region with a radius of 1 kpc corresponds to 1.25 × 10-3M⊙ yr-1. This negligible SFR is much lower than the value predicted by Rimoldi et al. (2016), considering supernovae remnants expected within the sphere of influence of quiescent supermassive black holes. For M31, an SFR of 0.13 M⊙yr-1 is expected in the sphere of influence (RSOI = 14 pc = 3.7”) of its supermassive black hole. A past AGN activity is also expected, and the associated molecular torus, if it survives, should have a radius RMT = 25 pc = 6.7′′. In parallel, Chang et al. (2007) expected next to the black hole an accumulation of molecular gas (about 104M⊙) originating from stellar feed-back. Melchior & Combes (2013) estimated a minimum molecular mass of 4.2  ×  104M⊙ within 30″ from the centre, while about 106M⊙ of gas is expected from stellar feedback (e.g. Gallagher & Hunter 1981).


Alongside the above theoretical uncertainties in the physics of core formation in ellipticals, there have also been observational challenges. In particular, determining the size of the core has proven to be a non-trivial task. The light profiles of ellipticals are well described by the 3-parameter Sérsic profile (Sérsic 1963, 1968) over a large radial range. The most luminous ellipticals, however, show a departure from the Sérsic law in their central regions, at a radius widely known as the ‘break’ or ‘core’ radius. In these galaxies, the profiles break downward from the inward extrapolation of the outer Sérsic law. Initially the core size of a galaxy was determined by fitting the so-called ‘Nuker-profile’ (Lauer et al. 1995) to the surface brightness profile, a method that however depends sensitively on the radial fitting range and yields unreliable results when fit to surface brightness profiles with a large radial extent (e.g. Graham et al. 2003; Dullo & Graham 2012). In more recent years, it has become customary to incorporate a central flattening in the light profile by adopting a 6-parameter core-Sérsic profile (Graham et al. 2003; Trujillo et al. 2004) which provides a reliable measurement of the core size even over a large radial range (e.g. Dullo & Graham 2012, 2013, 2014). Furthermore, it has been shown that adopting a multicomponent model rather than a single core-Sérsic model over the entire radial range provides a more reliable estimate of the core size (Dullo & Graham 2014; Dullo 2019). Measured core sizes for massive ellipticals – derived in this way – are typically tens to a few hundred parsecs (e.g. Dullo & Graham 2014), while cores larger than $1{\, \mathrm{kpc}}$ are rare. A study by Lauer et al. (2007) considered a large sample of brightest cluster galaxies (BCGs) and found that fewer than 10 systems had a core size of $\sim 1\rm {kpc}$ or greater, with the largest cored system being NGC 6166 which has a core size of $\sim 1.5{\, \mathrm{kpc}}$. More recently, Dullo (2019) considered the largest sample of ‘large-core’ galaxies to date, finding that only 13(7) galaxies have core sizes larger than $0.5(1){\, \mathrm{kpc}}$.


The mechanism(s) driving the transport of angular momentum (e.g., Aerts et al. 2019a) and chemical elements (e.g., Salaris & Cassisi 2017) within stars are still not understood from stellar evolution theory. Discrepancies between observations and theory have been shown for stars with birth masses between 1.3 and 8 M

, which comprise a convective core, enshrouded by a radiative envelope (possibly with internal convective shells from partial ionization zones or a thin outer convective envelope for

 M

). In these radiative envelopes, the transport of chemical elements on a macroscopic scale is ascribed to convective core overshooting (e.g., Viallet et al. 2015), rotation (e.g., Maeder 2009), or internal gravity waves (IGWs, e.g., Rogers & McElwaine 2017), whereas the transport of chemical elements on a microscopic scale is the result of atomic diffusion (Michaud et al. 2015). In stellar evolution codes, the description of macroscopic mixing introduces additional free parameters, whereas mixing from atomic diffusion can be derived from first principles. So far, the theory of element transport has been mainly evaluated by measurements of surface abundances. Asteroseismology constitutes a novel technique to empirically assess the conditions deep inside the interior (Aerts et al. 2010) of a star, as well as its evolutionary history (e.g., Bowman et al. 2019). The unprecedented high-quality data from the space-based CoRoT (Auvergne et al. 2009), Kepler  (Borucki et al. 2010), and TESS (Ricker et al. 2015) missions allow for scrutiny of the current stellar evolution models of the stars’ interiors by means of gravito-inertial asteroseismology (Aerts et al. 2018). The current state-of-the-art stellar models and pulsation codes are not capable of reproducing the observed oscillation frequencies of gravity (g) modes in γ Doradus (γ Dor; see Kurtz et al. 2014; Saio et al. 2015; Schmid & Aerts 2016; Van Reeth et al. 2016) and slowly pulsating B-type (see Pápics et al. 2014; Moravveji et al. 2015; Szewczuk & Daszyńska-Daszkiewicz 2018; Aerts et al. 2019b) stars within the uncertainties of the data. Hence, additional physics is required in order to improve both the current stellar models and the prediction of the g-mode frequencies from these equilibrium models. Studies have already demonstrated the potential of g-modes to distinguish between different near-core mixing profiles (Pedersen et al. 2018) and the temperature gradient close to the convective core interface (Michielsen et al. 2019). The work of Aerts et al. (2018) has evaluated a hierarchy of input physics when modeling g-modes across a wide mass range. In the current work, we investigate to what extent the process of atomic diffusion can improve the theoretically predicted oscillation frequencies in two slowly rotating γ Dor stars.


It is well known that the accretion on to compact objects may influence the nearby ambient around SMBHs in the centre of galaxies (e.g. Salpeter 1964; Fabian 1999; Barai 2008; Germain, Barai & Martel 2009). Together with the outflow phenomena, it is believed to play a major role in the feedback processes invoked by modern cosmological models (i.e. Λ-Cold Dark Matter) to explain the possible relationship between the SMBH and its host galaxy (e.g. Magorrian et al. 1998; Gebhardt et al. 2000) as well as in the self-regulating growth of the SMBH. The problem of accretion on to an SMBH has been studied via hydrodynamical simulations (e.g. Ciotti & Ostriker 2001; Di Matteo, Springel & Hernquist 2005; Li et al. 2007; Ostriker et al. 2010; Novak, Ostriker & Ciotti 2011). In numerical studies of galaxy formation, spatial resolution permits resolving scales from the kpc to the pc, while the sub-parsec scales of the Bondi radius are not resolved. This is why a prescribed sub-grid physics is employed to solve this lack of resolution. With sufficiently high X-ray luminosities, the falling material will have the correct opacity, developing outflows that originate at sub-parsec scales. Therefore, calculations of the processes involving accretion on to SMBH have become of primary importance (e.g. Proga, Stone & Kallman 2000; Proga 2000, 2003; Proga & Kallman 2004; Proga 2007; Ostriker et al. 2010). Numerical calculations of the accretion of matter on to SMBHs, including the radiative-outflow component, have been mostly performed using Eulerian finite-difference methods (Mościbrodzka & Proga 2013) [see also the overviews by Edgar (2004) and Foglizzo et al. (2005) and references therein for earlier work], while only a few calculations have been reported using smoothed particle hydrodynamics (SPH) techniques (Barai 2008; Barai, Proga & Nagamine 2011, 2012; Nagamine, Barai & Proga 2012), where results for the accretion rates, outflow rates, thermal instabilities, and impact of the thermal, mechanical, and X-ray feedbacks have been obtained for evolutions up to 5 Myr and scales from 0.1 to 200 pc.


In addition, the Abell 901/902 field has deep and extensive photometry in the UV (Galex, Gray et al. 2009), optical (COMBO-17 survey, Wolf et al. 2003), near-infrared (Spitzer 24 μm, Bell et al. 2007), and X-ray (XMM-Newton, Gilmour et al. 2007) wavelength range. Out of the four main substructures that embody Abell 901/902, only the two most massive (A901a and A901b) show significant X-ray emission, but this may come from a very bright AGN close to the cluster center in A901a (Gilmour et al. 2007). The evolution of the cluster members’ colors, morphologies, and star-formation activity has been studied over the years, and redder stellar populations, lower star-formation rates, and indications of interactions within the cluster population of galaxies were reported (Wolf et al. 2009; Gallazzi et al. 2009). More recently, the emission-line OMEGA-OSIRIS survey provided similar results (e.g., Chies-Santos et al. 2015; Rodríguez del Pino et al. 2017; Weinzirl et al. 2017; Roman-Oliveira et al. 2019). Our group carried out a kinematic analysis of a subsample of cluster galaxies using slit spectra taken by VIMOS at the Very Large Telescope (VLT) with the HR-blue grism (R ∼ 2000) to search for indications of ram-pressure stripping (Bösch et al. 2013a) and study the slope and scatter of the TFR (Bösch et al. 2013b). Galaxies within three times the velocity dispersion (3σ) of each substructure are considered to be cluster members (Bösch et al. 2013a). We retrieved a sample of 45 cluster galaxies from Bösch et al. (2013b) characterized by their high-quality rotation curves, their disk morphology, and stellar masses above log(M*) = 9.5. This sample is used in Sect. 4 to explore the evolution of the TFR between clusters at different redshifts. The distribution of the main parameters (M* and Vmax) and their mean properties are shown in Fig. 1 and listed in Table 3. However, the sizes and exact coordinates of these galaxies within the Abell 901/902 cluster complex are not provided in the publications mentioned above, and we therefore excluded this sample from the analysis that requires them.


After the disruption phase, the star is tidally stretched into a very long thin stream and the evolution of the stream structure in the transverse and longitudinal directions are decoupled (Kochanek 1994). Thus, the system enters the free-fall phase where each stream segment follows its own geodesic like a test particle (Coughlin et al. 2016). Then, after passing the apocentres of the highly eccentric orbits, the bound debris falls back towards the BH at a rate given by the distribution of specific energy (Evans & Kochanek 1989; Phinney 1989). Due to relativistic apsidal precession, the bound debris, after passing the pericentre, collides violently with the still in-falling stream (see Fig. 1). It has been shown that shocks at the self-intersection point is the main cause of orbital energy dissipation and the subsequent formation of an accretion disc (Rees 1988; Kochanek 1994; Hayasaki, Stone & Loeb 2013; Guillochon, Manukian & Ramirez-Ruiz 2014; Shiokawa et al. 2015; Bonnerot et al. 2016). However, the aftermath of the self-intersection is an extremely complex problem, which depends on the interplay among magnetohydrodynamics, radiation, and general relativity in 3D. No numerical simulations to date have been able to provide a deterministic model for TDEs with realistic star-to-BH mass ratio and high eccentricity (see Stone et al. 2018a, for a review). Many simulations consider either an intermediate-mass BH (e.g. Guillochon et al. 2014, Evans, Laguna & Eracleous 2015; Shiokawa et al. 2015; Sa̧dowski et al. 2016) or the disruption of a low-eccentricity (initially bound) star (e.g. Bonnerot et al. 2016; Hayasaki, Stone & Loeb 2016). It is unclear how to extrapolate the simulation results to realistic configurations and provide an answer to the following questions: How long does it take for the bound gas to form a circular accretion disc (if at all)? How much radiative energy is released from the system? What fraction of the radiation is emitted in the optical, UV, or X-ray bands?


The number of objects in a specific volume such as a sphere is called counts-in-cells (CIC) (Hubble 1936; Zwicky 1957; Balian & Schaeffer 1989). We know that in small scales, the distribution of CIC or equivalently one-point probability of the matter density field is not Gaussian and follows approximately a lognormal distribution (Coles & Jones 1991; Ueda & Yokoyama 1996). The nearly lognormal behaviour of the cosmic matter density field is a feature of evolving perturbations from the linear Gaussian inflationary initial conditions (Guth 1981; Linde 1982) to the late time non-linear and non-Gaussian distribution. Accordingly, it is informative to investigate the shape of the probability distribution of the matter density field and its evolution (Lam & Sheth 2008; Bernardeau, Pichon & Codis 2014; Uhlemann et al. 2016; Ivanov, Kaurov & Sibiryakov 2019; Mandal & Nadkarni-Ghosh 2020; Repp & Szapudi 2020b). It is worth mentioning that other interesting ideas such as an Edgeworth expansion, skewness, and kurtosis analysis are argued in this field of study (Colombi 1994; Gaztanaga, Fosalba & Elizalde 2000; Shin et al. 2017; Klypin et al. 2018; Einasto et al. 2021). On large scales, the CIC contains the same information as the two-point correlation function. But there is more information encoded in the lognormal shape of the CIC distribution on small scale. Accordingly, the cosmological dependence of the CIC statistics is interesting to be explored in mildly and strongly non-linear regimes from an observational and theoretical point of view. Uhlemann et al. (2020) showed that the measured CIC statistics are sensitive to the cosmological parameters and neutrino mass. Repp & Szapudi (2020a) used the CIC to break the degeneracy between σ8 and galaxy bias. Also, it is employed to study the primordial non-Gaussianity in LSS by measuring the fNL parameter (Friedrich et al. 2020). Recently, Jamieson & Loverde (2020) introduced an approach to use a position-dependent one-point distribution of matter density as a cosmological observable. Besides all this progress, there are some limitations. The results depend on the size and shape of the cell, where for large smoothing scales the distribution is Gaussian whereas, for small scales, the distribution is approximately lognormal. So for each cell size, one should calculate the CIC distribution, which is a computationally expensive procedure. Finally, we conclude that although the CIC is a computationally costly process, it is advantageous to explore different regimes and compare the linear and non-linear scales.


When comparing the results obtained with our computational approach with the previously published decay rates, we find an overall good agreement. This is illustrated in Figs 2–5, where our calculations are compared with the experimental data reported by Salih et al. (1985), Crespo López-Urrutia et al. (1994), Mullman et al. (1998a,b) and those obtained theoretically by Raassen et al. (1998). More precisely, as shown in Fig. 2, we obtain a mean ratio of 1.036 ± 0.205 when comparing our transition probabilities with those of Salih et al. (1985), who combined lifetime values obtained by TR-LIF with branching fractions measured on spectra recorded with the 1-m Fourier-transform spectrometer at the Kitt Peak National Observatory, to deduce the decay rates for 41 transitions depopulating the 3d74p z5F, z5D and z5G levels. Fig. 3 shows a slightly larger scatter between our calculations and the transition probabilities published by Crespo López-Urrutia et al. (1994). Here the mean ratio gAThiswork/gACrespo is equal to 1.098 ± 0.493. However, it is worth noting that the gA-values obtained by the latter authors were deduced from the combination of branching ratio measurements with available experimental lifetimes for the 3d74p z5F, z5D, z5G levels (Pinnington, Lutz & Carriveau 1973; Pinnington et al. 1974; Salih et al. 1985) but also with estimated lifetimes for the z3G, z3F and z3D levels from the measurement of total intensity of all lines of each of these levels under the assumption of almost equal population. The branching fractions were found using intensity measurements with a special hollow electrode radio frequency discharge and using a phase method with a modified wall-stabilized arc in a spectrointerferometric arrangement. Mullman et al. (1998a) reported 28 oscillator strengths for ultraviolet Co ii lines deduced from laser-induced fluorescence lifetimes and branching fraction measurements using a high-resolution grating spectrometer and an optically thin hollow cathode discharge. As illustrated in Fig. 4 , our gf-values were found to agree in general within 20–30 per cent with the results obtained by Mullman et al. (1998a). More particularly, the mean ratio gfThiswork/gfMullman was found to be equal to 1.339 ± 0.552 when using all the common lines, and to 1.238 ± 0.411 when using the strongest transitions for which log gf > −1. Finally, Fig. 5 shows the comparison between our computed oscillator strengths and those published by Raassen et al. (1998) who used the theoretical method of orthogonal operators to determine the log gf-values for (3d8+3d74s)–3d74p transitions in Co ii. In this case, the two sets of data generally agree within about 20 per cent, this percentage difference being reduced to 12 per cent when considering the most intense transitions with log gf > −1. We also note that our oscillator strengths are on average larger than those obtained by Raassen et al. This could be due to the fact that these latter authors included explicitly a less extended set of interacting configurations in their model.


As scattered light imaging is sensitive to the stellar irradiation, it allows one to search for misalignments between various disk regions. While studying the morphology of the innermost disk region is challenging due to its very small radial extent, often marginally resolvable by optical interferometry (Lazareff et al. 2017), scattered light imaging of the outer disk can indirectly reveal the presence of a misaligned inner disk. In this scenario, depending on the misalignment angle, the outer disk image will show narrow shadow lanes (e.g., Pinilla et al. 2015; Stolker et al. 2016; Benisty et al. 2017; Casassus et al. 2018), broad extended shadows (Benisty et al. 2018) or low-amplitude azimuthal variations (Debes et al. 2017; Poteet et al. 2018). In some cases, studies of the CO line kinematics support a misalignment between inner and outer disk regions (Loomis et al. 2017; Pérez et al. 2018). The exact origin of such a misalignment is still unclear. In the case of T Tauri stars, if the stellar magnetic field is inclined, it can warp the innermost edge of the disk, which would then rotate at the stellar period (AA Tau; Bouvier et al. 2007). Alternatively, inner and outer disk regions can have different orientations if the primordial envelope had a different angular momentum vector orientation at the time of the inner/outer disk formation (Bate 2018). Other scenarios involve the presence of a massive companion/planet that is inclined with respect to the disk. If the companion is massive enough, the disk can break into two separate inner and outer disk regions, that can then precess differently and result in a significant misalignment between each other (e.g., Nixon et al. 2012; Facchini et al. 2013; Nealon et al. 2018; Zhu 2019). A clear example of such a scenario is the disk around HD 142527, in which an M-star companion was detected (Biller et al. 2012), likely on an inclined and eccentric orbit (Lacour et al. 2016; Claudi et al. 2019). Dedicated hydrodynamical simulations successfully reproduce most of the observed features in this disk (eccentric cavity, spiral arms, misaligned inner disk and shadows; Price et al. 2018).


In the previous section, we discussed how SNe Ia with blueshifted Na i D have broader light curves but this may be driven by their preference for late-type host galaxies and their differing environments. One of the main aims of this study was to investigate, for the first time, if there is a connection between the presence of broad high-velocity Ca ii features in SNe Ia and the presence of narrow blueshifted Na i D features. As previously discussed, high-velocity Ca ii features are ubiquitous in SNe Ia and we confirm this here finding that the vast majority of the sample require a high-velocity Ca ii component. We also identify high-velocity Si ii features in 12 SNe Ia in our sample, although these features are not clearly ‘detached’ from the photospheric component. The reason that high-velocity features are interesting to investigate in connection with blueshifted Na i D features is that there are suggestions that the high-velocity Ca ii features may be at least partially due to ejecta–CSM interaction (e.g. Mazzali et al. 2005; Tanaka et al. 2006). Therefore, if a link between these quantities was identified, it would provide evidence that blueshifted Na i D features are due to CSM also rather than contamination. We remind the reader that the two probes do explore different distances from the SN, with Ca ii originating at significantly shorter distances than Na i D. However, when we examine the strength of the high-velocity Ca ii components (parametrized through the ${\rm Ca\, {\small{\rm II}}}~R_{\textrm {HVF}}$ of Childress et al. 2013a) compared to the blueshifted${\rm Na\, {\small{I}}}~\text{D}_{2}$ pEQW (15), we do not identify any clear trend between them. In particular, we also find that a number of SNe Ia with no Na i D absorption at all have very high ${\rm Ca\, {\small{\rm II}}}~R_{\textrm {HVF}}$ values, which is difficult to interpret in the context of a common CSM origin for both strong blueshifted Na i D features and strong high-velocity Ca ii components, as with this interpretation of their origin a strong signature would be expected in both probes rather than singularly. We also find no correlation between the pEQW of the high-velocity Ca ii features and the pEQW of the blueshifted Na i D features.


CMEs are known for large-scale expulsion of magnetized plasma structures from closed magnetic field regions on the Sun. They were first detected in the coronagraphic images taken in 1971 by NASA’s OSO-7 spacecraft (Tousey 1973). However, some definite inferences for the solar wind (Eddington 1910; Birkeland 1916; Biermann 1951) as well as CMEs from the Sun (Chapman & Ferraro 1931; Eddy 1974) were made decades before their formal discovery. Following OSO-7, a series of spacecraft (Skylab, Helios, P78-1 Solwind, SOHO, Coriolis, and STEREO, etc.) have observed thousands of CMEs leading to a vast literature (Munro et al. 1979; Howard et al. 1985; Gosling 1993; Hundhausen 1999; Gopalswamy et al. 2000; Schwenn 2006; Vourlidas et al. 2010; Chen 2011; Wang et al. 2011; Webb & Howard 2012; Mishra & Srivastava 2013; Mishra et al. 2017; Harrison et al. 2018). CMEs have been observed to occur often having spatial and temporal relation with solar flares, eruptive prominences (Munro et al. 1979; Webb & Hundhausen 1987; Zhang et al. 2001; Gopalswamy et al. 2003) and with helmet streamer disruptions (Dryer 1996). Unlike CMEs from the Sun, to observe stellar CMEs are challenging because the close stellar environment cannot be spatially resolved. Although stellar CMEs have not yet been directly detected in Thomson-scattered optical light from other stars, it is believed that the extreme X-ray flares observed on stars may be in conjunction with extreme stellar CMEs (Houdebine, Foing & Rodono 1990; Wheatley 1998; Leitzinger et al. 2011; Aarnio, Matt & Stassun 2012; Osten & Wolk 2015; Vida et al. 2016). Indeed, the stellar X-ray flare, helmet streamers, and prominences observed on T Tauri Stars have shown similarities with those observed on the Sun (Haisch, Antunes & Schmitt 1995; Massi et al. 2008). The CMEs and flares themselves may not be causally related, they both seem to be involved with the reconfiguration of complex magnetic field lines within the corona caused by the same underlying physical processes, e.g. magnetic reconnection (Priest & Forbes 2002; Compagnino, Romano & Zuccarello 2017). But, even for the sun, it has been noted that not all flares are accompanied by CMEs and not all CMEs by flares (Munro et al. 1979; Harrison 1995; Yashiro et al. 2008b; Wang & Zhang 2008).


We consider time-varying dynamical effects, breaking the assumption of a steady state, to be the most probable reason for this unexpected result. We do see how local phase-space substructures can bias our result for individual stellar samples, most clearly for those of area cell B8. However, explaining the steep gravitational potential close to the Galactic mid-plane, inferred for almost all stellar samples, requires a phase-space structure that spans the whole spatial volume that is studied in this work. Indeed, spatially large time-varying phase-space structures are present in the Galaxy, for example in the form of phase-space spirals and ridges (Gaia Collaboration 2018c; Antoja et al. 2018), and Galactic plane mirror asymmetries (Bennett & Bovy 2019, especially prominent for heights |z|≳400 pc). In order to produce a steep gravitational potential at low |z|, there could be a breathing mode in the stellar disk (Widrow et al. 2014; Monari et al. 2016) which is currently in its most compressed state. Such a configuration would not be detectable by comparing the mean vertical velocities above and below the mid-plane, because the breathing oscillation would be at a turning point between contraction and expansion. Mass estimates close to the mid-plane and under the steady state assumption would be biased towards more massive results, as the stellar disk would have a smaller scale height and larger vertical velocities. In order to explain our results, such a breathing mode would have to be large enough for the stellar number density in the mid-plane to oscillate with a relative amplitude of ∼5%. Monari et al. (2016 see for example Fig. 4) have shown that a local breathing mode could be created by a spiral arm that passes close enough to the Sun, inducing a net motion away from (towards) the Galactic mid-plane for stars on the outside (inside) of the spiral arm. Furthermore, such a close passage of a spiral arm is indicated by some dynamical models of the horizontal motions within the Galactic disk (for example Siebert et al. 2012). The dynamics of the Galactic disk are very complex and probably contains a combination of breathing and bending modes created by the last impact of the Sagittarius dwarf galaxy (for example Laporte et al. 2019); it is very plausible to think that the famous phase-space spirals in the z–w plane are a local manifestation of these larger scale perturbations. The phase-space spiral structure could have an effect on our analysis, especially for the stellar samples with higher Zlim.. On a larger scale, the bending and breathing modes of the Galaxy have been shown to affect dynamical mass measurements of the Galactic disk, especially at greater heights (Banik et al. 2017; Haines et al. 2019).


One has to be sure to rule out cases where inorganic chemistry can mimic the presence of life (“false positives”). Potential abiotic ozone production on Venus- and Mars-like planets has been discussed by Schindler & Kasting (2000, and references therein). While this is based on photolysis of e.g., CO2 and H2O and is thus limited in extent, a sustainable production of abiotic O3 which could build up to a detectable level has been suggested by Domagal-Goldman & Meadows (2010) for a planet within the habitable zone of AD Leonis with a specific atmospheric composition. Indeed, other studies confirm that abiotic buildup of ozone is possible (e.g., Hu et al. 2012; Tian et al. 2014); however, detectable levels are unlikely if liquid water is abundant, as e.g. rainout of oxidized species would keep atmospheric O2 and O3 low (Segura et al. 2007), unless the CO2 concentration is high and both H2 and CH4 emissions are low (Hu et al. 2012). False-positive detection of molecules such as CH4 and O3 is discussed by von Paris et al. (2011). Seager et al. (2013) present a biosignature gas classification. Since abiotic processes cannot be ruled out for individual molecules (e.g. for O3), searches for biosignature molecules should search for multiple biosignature species simultaneously. It has been suggested that the simultaneous presence of O2 and CH4 can be used as an indication for life (Sagan et al. 1993, and references therein). Similarly, Selsis et al. (2002) suggest a so-called “triple signature”, where the combined detection of O3, CO2 and H2O would indicate biological activity. Domagal-Goldman & Meadows (2010) suggest to simultaneously search for the signature of O2, CH4, and C2H6. Of course, care has to be taken to avoid combinations of biosignature molecules which can be generated abiotically together (see e.g. Tian et al. 2014). The detectability of biosignature molecules is discussed, e.g. by von Paris et al. (2011) and Hedelt et al. (2013). In particular, the simulation of the instrumental response to simulated spectra for currently planned or proposed exoplanet characterization missions has shown that the amount of information the retrieval process can provide on the atmospheric composition may not be sufficient (von Paris et al. 2013).


At the disc age t ≈ 1.5 Myr, the decay of 26Al has sufficiently advanced to not melt forming planetesimals and dust from the inner disc has enriched the outer disc (Ciesla 2011). At rh = 30 au, we get τ ≈ 0.1 Myr and t0 ≈ 0.5 Myr because ρ(1 au)/ρ(30 au) = 170 and 1800 in the MMSN and Nice models, respectively (Zsom et al. 2010). The number of fractals is still larger than that of pebbles of similar sizes:
(3)
\begin{equation}
N_{\rm F} / N_0 \gtrsim \exp [-(t - t_0)/\tau ] \gtrsim N_{\rm P} / N_0 \approx \phi _{\rm F} / \phi _{\rm P}
\end{equation}
with ϕF ≈ 10−5, the others being restructured into cm-sized pebbles (Weidling et al. 2009; Zsom et al. 2010). Any further pebble growth would require so longer times at so high relative speeds (Davidsson et al. 2016) to destroy or convert into pebbles all the remaining fractals. The input of dust from the inner disc triggers a streaming instability in the outer disc (Youdin & Goodman 2005; Johansen et al. 2007), lasting ≈0.1 Myr and concentrating pebbles and fractals sticking to pebbles into filaments where the comet nucleus collapses by gravity at speeds 1 m s−1 into a randomly packed (Onoda & Liniger 1990; Song, Wang & Makse 2008) aggregate of cm-sized pebbles, with the fractals stored in the voids among the pebbles (Fulle et al. 2016b). The voids fill (40 ± 5) per cent of the nucleus volume (Onoda & Liniger 1990; Song, Wang & Makse 2008). This scenario is confirmed by the pebbles observed in the pristine terrain at the final Philae landing site, which have a narrow differential size distribution (Fig. 2) peaked at diameters of $6^{+4}_{-2}$ mm (Poulet et al. 2016). For polydisperse spheres, the void volume occupies a lower percentage of the total, e.g. 32 per cent for a log-normal size distribution with a standard deviation of 0.3 (Baranau & Tallarek 2014). These facts allow us to model the 67P nucleus as composed of pebbles of the same size, with a void volume filling (37 ± 5) per cent of the total nucleus volume. A random packing of spheres does not result in the densest possible configuration, i.e. small pebbles will not always occupy available void spaces, because access to these voids is not necessarily available during the formation of the cometary nucleus.


Given their potentially profound impact on both the stellar and gas properties, galaxy mergers are often invoked to explain the presence of metals and low ionization species in the CGM at large impact parameters (e.g. Farina et al. 2013, 2014; Johnson, Chen & Mulchaey 2015b). Indeed, merger-induced tidal torques can give rise to observed stellar tidal features extending to many tens of kpc (e.g. Hernández-Toledo et al. 2006; Patton et al. 2011, 2013; Casteels et al. 2014). Although some gas asymmetries coexist with asymmetries in the stellar profiles of interacting galaxies, tidally induced asymmetries can persist even longer in H i gas (e.g. Lelli, Verheijen & Fraternali 2014a,b; Scott et al. 2014). Such tidal debris can potentially diffuse into the CGM contributing a significant gas and metal mass. In addition to morphological disturbances, galaxy mergers can trigger vigorous galactic outflows associated with feedback from the enhanced star formation (e.g. Martin 2005; Rupke, Veilleux & Sanders 2005a; Strickland & Heckman 2009; Hayward & Hopkins 2017) and AGN activity (e.g. Rupke, Veilleux & Sanders 2005b; Veilleux et al. 2013; Zschaechner et al. 2016; Woo, Son & Bae 2017) which can populate the CGM with metals while giving rise to multiphase absorbers (e.g. Borthakur et al. 2013; Bird et al. 2015; Heckman & Borthakur 2016; Bordoloi et al. 2017; Heckman et al. 2017). Besides, merger-induced shocks and feedback can increase the CGM's internal energy; numerical simulations of galaxy mergers show that CGM gas can be significantly heated (to X-ray emitting temperatures) through shocks and feedback processes (e.g. Cox et al. 2004, 2006b; Sinha & Holley-Bockelmann 2009). Furthermore, studies of galaxies in dense environments (higher merger probability) show different CGM properties when compared to a matched isolated galaxy sample: The CGM of galaxies in groups show distinct kinematics (Pointon et al. 2017) and ionic covering fractions (Johnson, Chen & Mulchaey 2015a; Burchett et al. 2016). Despite the possibly significant influence of galaxy mergers on the CGM, the details of the interplay between galaxy mergers and the CGM remain relatively unexplored and we are currently lacking clear and quantitative predictions of how the CGM will be affected during the merger process. Current observations of the impact of galaxy mergers on the CGM are limited to a few case studies (e.g. Keeney et al. 2011; Johnson et al. 2014). A systematic survey targeting the CGM of kinematic galaxy pairs (i.e. COS-Pairs: Bordoloi et al. in preparation) is needed to place observational constraints on the effect of mergers on the CGM.


On the same SSA22 field, Nestor et al. (2011) and Nestor et al. (2013) show nine LBGs and 20 Lyman-α emitters (LAEs) with LyC detection out of a sample of 41 LBGs and 91 LAEs (all spectroscopically confirmed). They started from a different narrowband image centred at ~3640 Å, which is deeper than that used by Iwata et al. (2009), at ~3590 Å. A careful analysis of their LBG detections, however, shows that even in this case the LyC emission for many z ~ 3 sources is offset by 0.4–1.0 arcsec. The observed ratio between the 900 and 1500 Å rest-frame emission is difficult to reconcile with that expected by standard stellar populations (Vanzella et al. 2012a). The HST images in I814W filter available for a few of them show the presence of clearly separated galaxies, sometimes fainter at 1500 Å than in the ionizing continuum (i.e. their C16 object), with a resulting escape fraction well exceeding 1000% if estimated in the LyC position. For the majority of them, no HST imaging is available but even ground-based images often show the presence of slightly offset emission in LyC, w.r.t. the non-ionizing continuum. Similar conclusions can be reached for the Mostardi et al. (2013) sample where they adopt the same analysis as in Nestor et al. (2013). At z ~ 2.8, they found four LyC emitters out of 49 LBG galaxies and seven LyC emitters out of 91 LAEs. In this case the lack of high spatial resolution data from HST for the majority of the sample prevents any detailed analysis about possible contamination by interlopers/foregrounds. These conclusions have been strengthened by recent observations by Siana et al. (2015), who found no convincing detection in their deep HST imaging with WFC3-UVIS of five LyC emitters extracted from the sample of Nestor et al. (2011), or by Mostardi et al. (2015), who only found one robust LyC emitter after a reanalysis of a sample of 16 galaxies by Mostardi et al. (2013). More interestingly, the only robust candidate LyC emitter by Mostardi et al. (2015), the galaxy MD5b, has an observed ratio FUV/FLyC = 4.0 ± 2.0, equivalent to a relative escape fraction of 75%, when assuming complete transmission of the IGM. Instead, if a mean value of ⟨ exp(−τIGM) ⟩  = 0.4 at z ~ 3.1 is adopted, following Inoue et al. (2014), the relative escape fraction of MD5b turns out to be 188%. Imposing the constraint of a physical value for the relative escape fraction of \hbox{$f^{\rm rel}_{\rm esc}<100\%$}fescrel100%, the LoS of MD5b must be very transparent, exp(−τIGM) > 0.75, which corresponds to a probability 10-4, according to Inoue et al. (2014). This could be an indication that this galaxy is also a low-z contaminant, similar to the other cases studied by Mostardi et al. (2015).


There are a plethora of data available in the form of spectra, astrometric, and photometric information, as well as multiwavelength maps with the advent of large-scale spectroscopic (Apache Point Observatory Galactic Evolution Experiment/APOGEE: Eisenstein et al. 2011, RAdial Velocity Experiment/RAVE: Steinmetz et al. 2006, Gaia-ESO: Gilmore et al. 2012, Large Sky Area Multi-Object Fiber Spectroscopic Telescope/LAMOST: Cui et al. 2012, Galactic Archaeology with HERMES/GALAH: De Silva et al. 2015, Abundances and Radial velocity Galactic Origins Survey/ARGOS: Ness et al. 2012), astrometric (Hipparcos: Perryman et al. 1997, Gaia: Gaia Collaboration 2016), and photometric surveys (Two-Micron All Sky Survey/2MASS: Skrutskie et al. 2006, Sloan Digital Sky Survey/SDSS: Stoughton et al. 2002, Vista Variables in the Vía Láctea/VVV: Minniti et al. 2010, the SkyMapper Southern Survey : Wolf et al. 2018). These surveys have enabled the chemo-dynamic characterization of stellar populations in the Milky way that constitute different Milky Way components like thin disc, thick disc, halo, bulge, etc. For example, star count observations in the solar neighbourhood (Yoshii 1982; Gilmore & Reid 1983) led to the discovery of the thick disc, followed by its characterization as the old α-enhanced population in the double sequence exhibited by the solar neighbourhood stars in the [α/Fe] versus [Fe/H] plane (Fuhrmann 1998; Bensby, Feltzing & Lundström 2003; Reddy, Lambert & Allende Prieto 2006; Adibekyan et al. 2012; Haywood et al. 2013). At present, data from large-scale spectroscopic surveys (Anders et al. 2014; Hayden et al. 2015; Weinberg et al. 2019) have led to the discovery of this trend at different galactocentric radius, R, and average height, |Z|, across the Galaxy shedding light on the disc formation and evolution scenarios. In addition, many age determination methods have been developed that uses these survey data to provide valuable information about the star formation histories and age metallicity relation of disc stellar populations (Casagrande et al. 2011; Bedell et al. 2018; Lin et al. 2020; Nissen et al. 2020). Secular processes such as radial migration (Sellwood & Binney 2002; Schönrich & Binney 2009; Minchev & Famaey 2010), which leads to the mixing of stars across the Galaxy, are also being explored using a combination of accurate phase space information from Gaia (Gaia Collaboration 2018) and chemistry and age information of stars from large-scale spectroscopic surveys (Buder et al. 2019). The discovery of streams and dynamically different stellar populations in the Milky Way halo, considered to be the result of past accretion/merger events (Belokurov et al. 2018; Helmi et al. 2018; Ibata, Malhan & Martin 2019; Myeong et al. 2019) using the Gaia data and their further exploration with chemistry from large-scale spectroscopic surveys (Buder et al. in preparation) is another example. Multiple components in the Bulge metallicity distribution function discovered by multiple individual and large-scale spectroscopic observations, are being studied in detail to understand the origin of the Bulge and its connection with the Milky Way bar and Galaxy evolution (Ness et al. 2013; Rojas-Arriagada et al. 2017, 2020). There are many upcoming surveys [4-metre Multi-Object Spectroscopic Telescope/4MOST: de Jong et al. (2019), Sloan Digital Sky Survey/SDSS-V: Kollmeier et al. (2017), WEAVE: Dalton et al. (2018)] that will further improve our understanding of the formation and evolution of the Milky Way and its components.


Figure 1 shows our synthetic color–magnitude diagrams (CMDs) for the two RCs at four different metallicity regimes, which are almost identical to those presented in Figure 1 of Paper I, but here (

) CMDs are added in the right panels. We recall that in our models, the fRC and bRC are produced by G1 and G2, respectively, where G1 follows the standard helium-enrichment parameter (i.e.,

), while G2 is substantially enhanced in helium abundance (Y = 0.406). Following Paper I, we have also adopted a 0.2 dex difference in metallicity between G2 and G1, and assumed 12 and 10 Gyrs for the ages of G1 and G2, respectively, with the same population ratio for the two RCs (Nataf et al. 2010; Paper I and references therein). It is evident from these models that in the metal-rich population like the bulge, highly helium-enhanced stars

 are not placed on the very blue HB as in the metal-poor GCs, but are instead placed on the bRC. We refer the reader to Section 2 of Paper I for a detailed description of the RC features of our models at four different metallicity regimes in Figure 1. Here, we note from the (

) CMDs that the variation of the overall RC features on metallicity is similar to that in (

) CMDs. Panel (f) in (

) CMD can also naturally reproduce the observed double RC feature, i.e., ∼0.5 mag difference with almost negligible color difference between the two RCs, as is the case in panel (b) in (

) CMD. Hereafter, we refer to these models in panels (b) and (f) constructed at

 as “

,” to distinguish them from the models with different input parameters presented below. The CMDs for these reference models, down to the MS luminosity level, are further presented in Figure 2. This figure confirms that, in the position and width of the lower red-giant-branch (RGB) and main-sequence turn-off (MSTO), our models are not inconsistent with the observed CMDs of bulge population by Clarkson et al. (2008, 2011) and Brown et al. (2010).


The Large Binocular Telescope (LBT) consists of two 8.4Â m aperture optical telescopes on a single ALT-AZ mount installed on Mount Graham in southeastern Arizona (at an elevation of 3192Â m) and operated by an international collaboration among institutions in the United States, Italy, and Germany (Hill et al. 2014; Veillet et al. 2014). Both telescopes are equipped with deformable secondary mirrors which are driven with the LBT's adaptive optics (AO) system to correct atmospheric turbulence at 1Â kHz (Esposito et al. 2010; Bailey et al. 2014). Each deformable mirror uses 672 actuators that routinely correct 400 modes and provide Strehl ratios exceeding 80%, 95%, and 99% at 1.6âÎ¼m, 3.8âÎ¼m, and 10âÎ¼m, respectively (Esposito et al. 2012; Skemer et al. 2014). The LBTI is an interferometric instrument designed to coherently combine the beams from the two 8.4Â m primary mirrors of the LBT for high-angular resolution imaging at infrared wavelengths (1.5â13âÎ¼m; Hinz et al. 2012). It is developed and operated by the University of Arizona and based on the heritage of the Bracewell Infrared Nulling Cryostat on the MMT Hinz et al. (2000). The overall LBTI system architecture and performance will be presented in full detail in a forthcoming publication (P. M. Hinz et al., in preparation). In brief, the LBTI consists of a universal beam combiner (UBC) located at the bent center Gregorian focal station and a cryogenic Nulling Infrared Camera (NIC). The UBC provides a combined focal plane for the two LBT apertures while the precise overlapping of the beams is done in the NIC cryostat. Nulling interferometry, a technique proposed 36Â yr ago to image extra-solar planets (Bracewell 1978), is used to suppress the stellar light and improve the dynamic range of the observations. The basic principle is to combine the beams in phase opposition in order to strongly reduce the on-axis stellar light while transmitting the flux of off-axis sources located at angular spacings which are odd multiples of 0.5Î»/B (where B = 14.4Â m is the distance between the telescope centers and Î» is the wavelength of observation). Beam combination is done in the pupil plane on a 50/50 beamsplitter which can be translated to equalize the pathlengths between the two sides of the interferometer. One output of the interferometer is reflected on a short-pass dichroic and focused on the Nulling Optimized Mid-Infrared Camera (NOMIC) (Hoffmann et al. 2014). NOMIC uses a 1024 Ã 1024 Raytheon Aquarius detector split into two columns of eight contiguous channels. The optics provides a field of view (FOV) of 12Â arcsec with a plate-scale of 0.018Â arcsec. Tip/tilt and phase variations between the LBT apertures are measured using a fast-readout (1âHz) K-band PICNIC detector (PHASECam) which receives the near-infrared light from both outputs of the interferometer. Closed-loop correction uses a fast pathlength corrector installed in the UBC (see more details in DefrÃ¨re et al. 2014).


This paper is the fourth in a series. In our first work (Merlin et al. 2018) we presented an accurate and conservative technique to single out passive galaxies at high redshift by means of spectral energy distribution (SED) fitting with a probabilistic approach. We selected 30 z > 3 candidates in the GOODS-S field. Passive galaxy candidates, while being relatively easy to select from photometric surveys once the technique is established, need to be confirmed by other means. This is usually achieved through spectroscopic observations. However, spectroscopy becomes particularly difficult and time consuming at z > 3, where only few candidates have been confirmed so far (Glazebrook et al. 2017; Schreiber et al. 2018a; Tanaka et al. 2019; Valentino et al. 2020; Forrest et al. 2020a,b; Saracco et al. 2020; D’Eugenio et al. 2020). In our second work (Santini et al. 2019, S19 hereafter), we used a complementary approach and looked for evidence of the lack of star formation as seen in the sub-millimetre regime to confirm the passive classification of the high-z candidates selected in GOODS-S. At that time, we could confirm 35% of the targets on an individual basis adopting conservative assumptions, and we validated the sample as a whole in a statistical sense. In our third work (Merlin et al. 2019, M19 hereafter), we extended the search for passive galaxies to the entire CANDELS sample and selected 102 z > 3 candidates over the five fields. In the present work, we first confirm the passive nature of these candidates, adopting the method presented in S19 and taking advantage of the richer ALMA archive, which includes observations that were still proprietary at the time of our previous work. We then analyse the emergence and mass growth of this peculiar class of galaxies by means of two powerful statistical tools: the stellar mass function (SMF) and the stellar mass density (SMD). Very few studies so far have pushed the analysis of the SMF of passive galaxies at z > 3 (Muzzin et al. 2013; Davidzon et al. 2017; Ichikawa & Matsuoka 2017; Girelli et al. 2019) because of the difficulty in assembling statistically meaningful samples of candidates at such high redshift.


Before leaving this section, in Fig. 8 we display the spatial dependence of the self-consistent neutron and proton density profiles for the optimal solutions in spherical WS cells with average baryon densities nb = 0.0475 fm-3, 0.065 fm-3, and 0.076 fm-3. It is observed that in denser matter the size of the WS cell decreases, as we discussed previously, and that the amount of free neutrons in the gas increases, as expected. It can be seen that the nuclear surface is progressively washed out with increasing average baryon density as the nucleon distributions become more uniform. At high nb the density profile inside the WS cell extends towards the edge of the cell, pointing out that the WS approximation may be close to its limits of validity (Negele & Vautherin 1973; Chamel et al. 2007; Baldo et al. 2007; Pastore et al. 2011; Gögelein & Müther 2007; Newton & Stone 2009). Although the proton number Z is similar for the three average baryon densities of Fig. 8, the local distribution of the protons is very different in the three cases. In Fig. 8c the proton density profile extends more than 3 fm farther from the origin than in Fig. 8a, while the central value of the proton density has decreased by more than a factor 2, hinting at the fact that the neutrons have a strong drag effect on the protons. Figure 9 presents the nucleon density profiles obtained for cylindrical and planar geometries at the same average density nb = 0.076 fm-3 as in Fig. 8c. From Figs. 8c (droplets),  9a (rods), and 9b (slabs) we see that the size of the WS cells decreases with decreasing dimensionality, i.e. Rc,droplet>Rc,rod>Rc,slab. At high average densities near the crust-core transition, nucleons inside the WS cell can arrange themselves in such a way that the region of higher density is concentrated at the edge of the cell, leaving the uniform region of lower density in the inner part of the cell. This distribution of nucleons corresponds to the cylindrical tube and spherical bubble configurations. In Figs. 9c and d, we plot the neutron and proton density profiles of the optimal solution for tubes and bubbles at nb = 0.076 fm-3. At equal average density, the size of the cells containing tubes and bubbles is larger than the size of the cells accommodating rods and droplets, respectively, as can be appreciated by comparing Fig. 9a for rods with Fig. 9c for tubes, and Fig. 8c for droplets with Fig. 9d for bubbles. As a consequence of this fact and of the effectively larger value of the integration factors 2πr and 4πr2 when the densities are accumulated near the edge of the cell, the total number of nucleons and the atomic number in the tube and bubble cells is about 1.5−2 times larger than in their rod and droplet counterparts. The proton fraction xp = Z/A is, however, practically the same for all geometries.


Recent theoretical models clearly demonstrate the role of expanding H I shells for the formation of molecular clouds (e.g., Hennebelle et al. 2008; Heitsch et al. 2009; Inoue & Inutsuka 2009). In particular, these models highlight the importance of multiple compressions for the formation of magnetized filamentary molecular clouds (e.g., Inutsuka et al. 2015; Iwasaki et al. 2019). The typical timescale of such compressions is estimated in the Galactic disk to be on average ~1 Myr (McKee & Ostriker 1977; Inutsuka et al. 2015). Thus, the formation of molecular clouds may last from a few million years to ~10 Myr or more (see, e.g., Kobayashi et al. 2017). These successive compressions may continuously alter the density, velocity, and magnetic field structures of the clouds, and also have a strong impact on the formation of new generations of filaments and consequently that of stars. While the first generation of stars form and impact their (local) surroundings (through outflow, jets, winds, and ionizing radiation), new cold matter is continuously assembled replenishing the sites of star formation (i.e., filaments and hubs). This matter replenishment may be channeled from within the cloud itself through molecular filaments toward dense ridge-like main filaments (Schneider et al. 2010; Palmeirim et al. 2013) or toward hubs (Myers 2009; Peretto et al. 2013, 2014; Treviño-Morales et al. 2019). Matter can also be brought into the system (the cloud) by a new event of external collision (e.g., Fukui et al. 2018b). Arzoumanian et al. (2018) identified, in position-velocity (PV) diagrams, extended structures with mean line-of-sight (LOS) velocities offset with respect to, and connected to the velocity of, a filament. They suggested a multi-interaction scenario where sheet-like extended structures interact, in space and time, with a star-forming filament, and are responsible for its compression or disruption. Arzoumanian et al. (2018) also identified a bent velocity structure in the PV space. They showed that such a V- or Λ-shaped velocity structure can result from the filament formation process by shock compression as proposed by the theoretical model of Inoue et al. (2018). In this model, a filament is formed due to convergence of a flow of matter generated by the bending of the ambient magnetic field structure induced by an interstellar shock compression (see also Inoue & Fukui 2013; Vaidya et al. 2013). This velocity structure has also been observed toward another filament, the Musca filament (Bonne et al. 2020). More recently, in a theoretical study, Abe et al. (2021) proposed a classification of filament formation mechanisms resulting from the variation in the relative importance between the shock velocity, the turbulence, and the magnetic field strength (see also the theoretical study by Chen et al. 2020a).


The above finds an explanation within the context of the two-phases formation scenario of ETGs (Oser et al. 2010). According to this scenario, in the early (z ≳ 2) dissipative phase driven by wet major mergers (e.g. Hopkins et al. 2008) and/or violent disc instability (e.g. Barro et al. 2013; Dekel & Burkert 2014; Zolotov et al. 2015; Tacchella et al. 2016), the proto-ellipticals are compact objects that form stars in situ in a very intense regime until this process is stopped abruptly by gas shock heated in massive haloes, and/or rapid gas exhaustion and Supernova/AGN feedback. As the compact quiescent galaxy ages and reddens (red nugget), during the second non-dissipative phase (z ≲ 1−2), more mass is assembled by the accretion of ex situ stars through merging with other galaxies, which are also mostly quiescent. Dry minor or intermediate mergers contribute little to the mass growth but promote substantial size growth (the accreted stars tend to be deposited mostly in the external regions), making spheroidal galaxies less compact and likely also less concentrated (Bezanson et al. 2009; Naab, Johansson & Ostriker 2009; Oser et al. 2010; Trujillo, Ferreras & de La Rosa 2011; Bluck et al. 2012; Johansson, Naab & Ostriker 2012; Hilz, Naab & Ostriker 2013; Shankar et al. 2013; van Dokkum et al. 2015; Wellons et al. 2016; Faisst et al. 2017; Furlong et al. 2017; Hill et al. 2017; Genel et al. 2018, among others). Dry mergers can also be major, though they are less frequent and relevant only to the most massive galaxies (e.g. Bundy et al. 2009; López-Sanjuan et al. 2012; Rodríguez-Puebla et al. 2017). These mergers increase substantially the mass, while the size increases approximately proportional to the mass increase (e.g. Nipoti, Londrillo & Ciotti 2003; Johansson et al. 2012; Nipoti et al. 2012; Hilz et al. 2013) in a such way that the shift in the mass–size relation is small, affecting in a lesser degree the compactness and concentration of the merged galaxies. Although the second phase of ETG formation, driven by dry mergers, is a reliable explanation for the growth in size and the puffing-up of massive ETGs, there is still an intense debate as to whether or not this mechanism is enough to describe observational inferences (e.g. López-Sanjuan et al. 2012; Newman et al. 2012; Nipoti et al. 2012; Sonnenfeld, Nipoti & Treu 2014; Man, Zirm & Toft 2016; Frigo & Balcells 2017, see for a discussion Zanisi et al. 2021 and more references therein). An alternative or complementary mechanism suggested for the apparent strong growth in size of massive ETGs is quasar feedback, which removes huge amounts of cold gas from the central regions, inducing an expansion of the stellar distribution (Fan et al. 2008, but see Trujillo et al. 2011).


To highlight the evidence for CO2 in the transmission spectrum, in Fig. 18 we show three atmo model atmospheres: our best-fitting model from the free-chemistry retrieval; a model with all of the same parameters as the best fit, except the CO2 abundance, which is set to zero; and a third model with both CO and CO2 abundances set to zero. The strong absorption feature centred on the 4.5 $\, \mu$m Spitzer channel disappears in the latter two models. With only Spitzer photometry, however, the contribution of CO to the 4.5 $\, \mu$m point complicates the interpretation of the C/O ratio. Theoretical models have found that CO should be the dominant carbon-bearing molecule for hydrogen-dominated atmospheres above 1000 K (e.g. Lodders & Fegley 2002; Heng & Lyons 2016), and CO has been detected at high resolution in hot Jupiter atmospheres (e.g. Snellen et al. 2010). In our equilibrium chemistry retrieval, CO is at least 100× more abundant than CO2 (see Fig. 12). However, at 4.5 $\, \mu$m the CO2 opacity is much stronger and dominates over the CO contribution even though CO has much higher VMR concentrations. In the free-chemistry retrieval, the CO VMR is not constrained by the data – only an upper limit to the CO is found, as very high values affect the mean molecular weight, and the data are consistent with no CO contribution. The lack of a CO feature in the WFC3 data further pushes the free-chemistry retrieval to prefer CO2 over CO. With CO constrained through chemistry in one retrieval and unconstrained in the free case, the C/O ratios obtained are vastly different. In the chemical-equilibrium case, a supersolar C/O is found (see Fig. 13) while in the free case a subsolar C/O ratio is found (Fig. 14). This finding highlights the extreme sensitivity and degeneracies of measuring the C/O ratio with a free-chemistry retrieval model, as all major molecular species have to be well constrained by the data. For a hot Jupiter such as WASP-127b, we consider a scenario with all of the carbon found in CO2 and little to none in CO to be thermochemically implausible, as no obvious non-equilibrium mechanism would deplete CO by many orders of magnitude while enhancing CO2. This situation is unlike CH4, where dynamical mixing and vertical quenching can dramatically enhance CH4 (e.g. Cooper & Showman 2006; Moses et al. 2011; Tsai et al. 2017; Drummond et al. 2018a, b). With only one photometric data point at 4.5 $\, \mu$m, it is currently impossible to fully disentangle the contribution of both CO and CO2 in a model-independent way. Further transmission spectroscopy observations of WASP-127b at high resolution with the JWST will clarify which is the dominant carbon-bearing molecule in WASP-127b’s atmosphere, and allow stronger constraints to be placed on its carbon-to-oxygen ratio.


In the last decade, several projects have focused on collecting the deepest images of clusters and groups of galaxies. Among the most recent examples, we can mention the Frontier Fields initiative (Lotz et al. 2017), the Hyper Suprime-Cam Subaru Strategic Program (Aihara et al. 2018a, 2018b, 2019), the Fornax Deep Survey (Iodice et al. 2016), or the upcoming Vera C. Rubin Observatory (Ivezic et al. 2008). In addition, technical development offers a new and barely explored perspective: a panchromatic, more detailed view of the universe through the use of narrowband filter systems, such as those from the J-PLUS and J-PAS surveys (Benitez et al. 2014; Cenarro et al. 2019; Bonoli et al. 2021). In this work we intend to show how the combination of these two characteristics, high-quality data and information at different wavelengths, can provide strong clues on the clusters’ formation and evolution through the analysis of the ICL. It is known that the ICL presents different morphologies, substructures, and ICL fractions depending on the wavelength used (Tang et al. 2018). Whereas the ICL fraction measured in single bands can be useful for establishing qualitative relations (e. g., evolution with redshift or halo mass), a panchromatic view of the ICL can give insights into its stellar populations or the dynamical stage of the cluster (e.g., Jiménez-Teja et al. 2019). With this aim, we use the recently acquired data from the Reionization Lensing Cluster Survey (RELICS; Coe et al. 2019), a Hubble Space Telescope (HST) Treasure program that has observed 41 very massive, strong-lensing clusters in three optical (ACS) and four infrared (WFC3) bands. In this work we present the potential of the RELICS data for ICL purposes, focused on the cluster WHL J013719.8–08284 (WHL0137 hereafter). Future work will apply the CICLE algorithm, which is free of a priori assumptions, extensively to the whole RELICS sample with two main aims: (1) analyze the optical and infrared ICL fractions to extract information about the stellar populations of the diffuse light, and (2) infer the dynamical stage of the clusters.


With the release of Gaia DR2 (Gaia Collaboration et al. 2018; Katz et al. 2019), the proper motions of billions of stars are now available to the astronomical community. Combining with radial velocities from large spectroscopic surveys, like the Sloan Digital Sky Survey (Eisenstein et al. 2011; Blanton et al. 2017), Gaia-ESO survey (Gilmore et al. 2012; Randich et al. 2013), and LAMOST Galactic spectroscopic survey (Deng et al. 2012; Zhao et al. 2012), the wealth of 6D information of billions of stars have challenged and even overthrown many aspects of our understanding of the Milky Way (MW). The discovery of snail shells in the phase-space distribution of MW disk stars (Antoja et al. 2018) has inspired debates about their origin: whether they are generated by the passage of a dwarf galaxy (probably the Sagittarius dwarf galaxy) through the MW disk (Binney & Schönrich 2018) or are the echo of the MW bar buckling (Khoperskov et al. 2019). Meanwhile, major accretion events begin to unveil themselves when the stellar distribution in various energy–momentum spaces (e.g., Myeong et al. 2019) is investigated. These major accretion events injected most of the materials from the progenitor dwarf galaxies into our MW, including globular clusters (GCs). As GCs are one of the oldest objects in our Galaxy, identifying and studying accreted GCs help us trace back the accretion history of our Galaxy. Though details of major accretion events, e.g., the number of accretion events and the GCs associated with each event, are still under debate (e.g., Helmi et al. 2018; Massari et al. 2019; Myeong et al. 2019), it is widely accepted that a substantial number of halo stars and GCs were accreted (e.g., Ostdiek et al. 2019). Along the same line, more and more substructures, e.g., stellar streams, are identified inside the MW (e.g., Malhan et al. 2018; Ibata et al. 2019b). An increasing number of stellar streams are suggested to be related to the debris of (inner-halo) GCs (e.g., Ibata et al. 2019a). Aside from these GC destruction events under the influence of Galactic potential, the dynamical relaxation of GCs (e.g., Weinberg 1994; Vesperini & Heggie 1997) also ejects member stars into the field. It would be of great interest to find such GC-ejected stars in order to estimate the mass loss from GCs to better understand the formation and evolution of our MW. To help achieve this goal, another characteristic of GCs is very helpful.


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).