It is widely accepted that an SN Ia is a thermonuclear explosion resulting from a binary system, of which one star is necessarily a degenerate carbon-oxygen (

) white dwarf (WD) (Hoyle & Fowler 1960) near the Chandrasekhar mass (

). Current research considers various progenitor configurations and final outcomes. Depending on whether or not both stars are WDs, the progenitor system is called double-degenerate (DD) or single-degenerate (SD). In addition to progenitor configuration, proposed scenarios are distinguishable by the ignition mechanism and other characteristics. In the case of a DD progenitor system, a dynamical merger or a violent collision between the WDs is capable of releasing enough heat to trigger an ignition. This process can end up as a SN Ia, a highly magnetized WD (MWD), or an accretion-induced collapse (AIC; Iben & Tutukov 1984; Webbink 1984; Benz et al. 1990; Rasio & Shapiro 1994; Segretain et al. 1997; Yoon et al. 2007; Lorén-Aguilar et al. 2009; Wang et al. 2009a, 2009b; Isern et al. 2011; Pakmor et al. 2011). Another class of SNe Ia scenarios is the double-detonation of a sub-

 WD with accretion from a helium (

) companion. A detonation in the surface helium layer causes a secondary detonation in the core (Weaver & Woosley 1980; Nomoto 1982a; Livne 1990; Woosley & Weaver 1994; Hoeflich & Khokhlov 1996; Kromer et al. 2010; Woosley & Kasen 2011). Finally, there is the

 explosion scenario, where the WD progenitor accretes material from a companion star and nuclear surface burning to C/O leads to an increase of the WD mass. With increasing WD mass the electron gas in the central region becomes increasingly relativistic, which leads to faster compressional heat release, the rising of the central temperatures, and the triggering of a central C/O deflagration front when the mass of the progenitor approaches

. (Hoyle & Fowler 1960; Sugimoto & Nomoto 1980; Nomoto 1982b; Hoeflich & Stein 2002; Piersanti et al. 2003). It is likely that the dynamical merger,

 explosion, and double-detonation channels all contribute to the SN Ia population because of the “stellar amnesia” effect (Hoeflich (2006), and references therein). This can happen in either a SD system, where the donor star is a main-sequence star, a red giant, etc., or in a DD system with another WD being the donor (Whelan & Iben 1973; Piersanti et al. 2003).


Several well-studied TeV blazars show rich spectral behavior in X-rays, which may represent the general behavior of the synchrotron peak of all AGN jets. The X-ray spectra are usually curved (Massaro et al. 2004) and can only locally be fitted by a power law. The spectral variation with flux can be complex (Zhang et al. 2002; Cui 2004). Generally, the spectrum hardens when the flux increases (e.g., Gliozzi et al. 2006; Xue et al. 2006; Tramacere et al. 2009), but photon indices can saturate at higher fluxes (Xue & Cui 2005; Giebels et al. 2007). The synchrotron peak usually moves to higher frequencies with increasing flux during outbursts (e.g., Pian et al. 1998), but no correlation between the break energy and the flux exists when a broken power law is adopted to fit the X-ray spectra (Xue & Cui 2005; Giebels et al. 2007; Garson et al. 2010). A cooling break in the spectrum of emitting particles cannot explain these features (Wierzcholska & Wagner 2016), and some special particle acceleration processes may be involved (Madejski & Sikora 2016). There are also energy-dependent lags between the variations of different energy bands. In some flares, soft bands lag behind hard bands (e.g., Zhang et al. 2002), while lags in the opposite direction can also happen (e.g., Ravasio et al. 2004; Sato et al. 2008). Hysteresis in the HR (hardness ratio)–flux diagram is often used as a diagnostic of lags. Clockwise loops (e.g., Acciari et al. 2009; Kapanadze et al. 2016) in the HR–flux plane are a sign of soft lags while counterclockwise loops (e.g., Tramacere et al. 2009) are a sign of hard lags. The same source can exhibit both clockwise and counterclockwise loops; the observed patterns are further complicated by the superposition of flares at different timescales (Cui 2004). The above knowledge of TeV blazars in the X-ray regime comes from studies focusing on timescales of hours to weeks. We will extend this kind of analysis to much smaller timescales in this paper.


AGN While—starting from the very early works (e.g., Seldner and Peebles 1978; Longair and Seldner 1979; Hill and Lilly 1991; Peacock and Nicholson 1991; Allington-Smith et al. 1993; Zirbel 1997)—virtually all the studies presented in the literature converge at indicating that radio-AGN preferentially reside within overdense structures, the three (or rather five if one also includes cross-correlation studies) methods presented in Sect. 4 provide different information on the large-scale structure behaviour of these objects. To summarize them in a few words, we might say that the method based on clustering returns more information on the very large/cosmological (i.e., at Mpc level and beyond) scales traced by radio sources and also on the dark matter content of the regions that host them. On the other hand, very different results are obtained if one searches for structures around known radio-AGN or if one pinpoints radio-AGN within known structures. Indeed, in the first case one finds that virtually all radio-AGN are surrounded by over-densities (e.g., Venemans et al. 2007; Mayo et al. 2012; Galametz et al. 2012; Castignani et al. 2014; Wylezalek et al. 2013; Rigby et al. 2014), while the second method shows that only about 20–30% of them inhabit rich (group- and cluster-like) structures (e.g., Best et al. 2007; Magliocchetti and Brüggen 2007; Lin and Mohr 2007; Croft et al. 2007; Magliocchetti et al. 2018b; Croston et al. 2019). The reason for this discrepancy is not known, but it is likely related to the different redshift ranges probed by the two methods (much more local sources are considered in the second one), and/or—under the assumption of a strong correlation between radio luminosity and environmental density (e.g., Bardelli et al. 2010; Magliocchetti et al. 2018b; Croston et al. 2019; Mo et al. 2020, but see further in this section for different points of view)—to the fact that generally the first method images much brighter radio sources than the second one. In any case, we note that these findings also have implications for the life-time of the radio-AGN phenomenon, and it is therefore of no surprise if works based on the different methods illustrated above find different values, ranging from ∼60\documentclass[12pt]{minimal}
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				\begin{document}$$\sim 60$$\end{document} Myr up to a few Gyr (e.g., Lin and Mohr 2007; Smolčić et al. 2011; Hatch et al. 2014; Magliocchetti et al. 2017). We also note that recent studies based on direct LOFAR observations which—we remind—sample lower frequencies and therefore older emission, would tend to better agree with the high-end values provided above for the radio-active phase of an AGN (τ>200\documentclass[12pt]{minimal}
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				\begin{document}$$\tau > 200$$\end{document} Myr – Heesen et al. 2018).


Large-scale magnetic fields with strength of the order of 1–10 μG have been observed in disk galaxies (e.g., Beck et al. 1996; Fletcher 2010; Beck 2012; Beck & Wielebinski 2013; Van Eck et al. 2015). The origin of these fields can be explained through mean-field dynamo theory (Ruzmaikin et al. 1988; Beck et al. 1996; Brandenburg & Subramanian 2005a; Kulsrud & Zweibel 2008). The conservation of magnetic helicity is one of the key constraints in these models, and also leads to the suppression of the α-effect. The operation of the mean-field dynamo automatically leads to the growth of magnetic helicity of opposite signs between the large-scale and small-scale magnetic fields (Pouquet et al. 1976; Gruzinov & Diamond 1994; Blackman & Field 2002). To avoid catastrophic suppression of the dynamo action (α-quenching), the magnetic helicity due to the small-scale magnetic field should be removed from the system (Blackman & Field 2000, 2001; Kleeorin et al. 2000). Mechanisms suggested to produce these small-scale magnetic helicity fluxes are: advection of magnetic fields by an outflow from the disk through the galactic fountain or wind (Shukurov et al. 2006; Sur et al. 2007; Chamandy et al. 2014), magnetic helicity flux from anisotropy of the turbulence produced by differential rotation (Vishniac & Cho 2001; Subramanian & Brandenburg 2004, 2006; Sur et al. 2007; Vishniac & Shapovalov 2014), and through diffusive flux (Kleeorin et al. 2000, 2002; Brandenburg et al. 2009; Mitra et al. 2010; Chamandy et al. 2014). The outflow of magnetic helicity from the disk through dynamo operation leads to the formation of a corona (Blackman & Field 2000). According to Taylor's hypothesis, an infinitely conducting corona would resistively relax to force-free field configurations under the constraint of global magnetic helicity conservation (Woltjer 1960; Taylor 1974; Finn & Antonsen 1983; Berger & Field 1984; Mangalam & Krishan 2000). In this paper, we include advective and diffusive fluxes in a simple semi-analytic model of a galactic dynamo that transfers magnetic helicity outside the disk and consequently builds up a force-free corona in course of time. We first solve the time-dependent dynamo equations by expressing them as separable in variables r and z. The radial part of the dynamo equation is solved using an eigenvector expansion constructed using the steady-state solutions of the dynamo equation. The eigenvalues of the z part of the solution are obtained by solving a fourth-order algebraic equation, which primarily depends upon the turbulence parameters and the magnetic helicity fluxes. Once the dynamo solutions are written out as parametric functions of these parameters, the evolution of the mean magnetic field is computed numerically by simultaneously solving the dynamical equations for α-quenching and the growth of large-scale coronal magnetic helicity. Since the large-scale magnetic field lines cross the boundary between the galactic disk and the corona, the magnetic helicity of the large-scale magnetic field in the disk volume is not well defined. Hence we use the concept of gauge-invariant relative helicity (Finn & Antonsen 1983; Berger & Field 1984; Berger 1985) to estimate the large-scale magnetic helicity in the disk and the corona. Here the gauge-invariant relative helicity for the cylindrical geometry is calculated using the prescription given in Low (2006, 2011). We then investigate the dependence of the saturated mean magnetic field strength and its geometry on the magnetic helicity fluxes within the disk and the corresponding evolution of the force-free field in the corona.

Kleeorin et al. 2000
Kleeorin et al. 2000


Top left: the revised, CO(J = 1 → 0)-based Mgas from VLASPECS confirm that z = 2–3 galaxies detected in the ASPECS survey (green circles; tentative detections are marked with a plus sign) closely follow the “star formation law” (i.e., Mgas–SFR relation) at high redshift. CO-detected main-sequence galaxies at similar redshifts from the PHIBBS1/2 surveys (typically based on CO J = 3 → 2, but using a metallicity-dependent conversion factor; Tacconi et al. 2018) and local galaxies from the xCOLD GASS CO(J = 1 → 0) survey (Saintonge et al. 2017) are shown for comparison. Bottom left: same as the top left panel, but plotting the depletion time tdep against Mgas. All samples cover a similar range in tdep, but the average tdep for the (higher Mgas) high-z samples appear lower. Top right: the r31 brightness temperature ratio of VLASPECS galaxies (green circles) is similar to that of strongly lensed z ∼ 3 Lyman-break galaxies (red triangles; Riechers et al. 2010), z > 2 main-sequence galaxies from the PHIBSS survey (gray crosses; Bolatto et al. 2015), and z > 2 dusty star-forming galaxies (DSFGs; blue squares; compilation from Sharon et al. 2016; including data from Danielson et al. 2011; Ivison et al. 2011; Riechers et al. 2011a, 2011b, 2013; Thomson et al. 2012; Fu et al. 2013; Sharon et al. 2013, 2015; other DSFGs shown as light gray squares are from Nayyeri et al. 2017; Dannerbauer et al. 2019; Harrington et al. 2019; Leung et al. 2019; Sharon et al. 2019) and clustered DSFGs (dark gray squares; Bussmann et al. 2015; Gómez-Guijarro et al. 2019), but ∼2 times higher on average than BzK-selected main-sequence galaxies at z ∼ 1.5 (magenta crosses; Daddi et al. 2015). Nearby galaxy samples from the xCOLD GASS survey (Lamperti et al. 2020) and two studies of infrared-luminous galaxies (Yao et al. 2003; Papadopoulos et al. 2012) are shown for comparison. Dashed lines and shaded regions indicate mean/median values and spread for high-z samples with >2 galaxies or clusters, with the same color coding as the symbols. Dashed–dotted lines indicate mean values for the low-z samples. Bottom right: same as the top right panel, but shown as binned histograms in r31 (excluding upper limits) and across the full redshift range, and only including samples for which mean/median values are indicated in the top right panels.


Several searches for high-frequency signals were performed in the past for WR stars, notably in the context of searches for compact companions (e.g. Marchenko et al. 1994). However, there were few cases of reported and confirmed periodicities. Focusing on our sample, the following detections were published. Blecha, Schaller & Maeder (1992) claimed a detection of pulsations with a 627-s period and a 5-mmag peak-to-peak amplitude in WR 40. However, at the corresponding frequency of 138 d−1, the TESS high-cadence data (sector 10) show no signs of such a signal, confirming previous negative reports (Gosset et al. 1994; Marchenko et al. 1994; Martinez et al. 1994; Schneider et al. 1994), including that by the discovery team itself (Bratschi & Blecha 1996). Other low-frequency detections for that star (e.g. Antokhin et al. 1995) certainly correspond to red-noise stochastic variability. Another photometric campaign detected a 6.828 d−1 signal in WR 66 (Antokhin et al. 1995), but with strong daily aliasing. It was subsequently confirmed in an independent, less aliased dataset (largest peak at 5.815 d−1: Rauw et al. 1996). These values are close (but not identical) to the frequency of the largest TESS peak, or its daily alias. To assess the compatibility between datasets, we have simulated a signal composed of the three main frequencies detected by TESS but sampled as in Rauw et al. (1996). The resulting periodogram appears similar to the one reported in the literature, even if the passbands are different6: the old and new datasets therefore appear fully compatible. Note also that the presence of several frequencies casts further doubt on the hypothesis of the literature signal being the orbital period of a compact companion (Antokhin et al. 1995). Finally, a 25-min signal with 2.6-mmag amplitude was reported by Bratschi & Blecha (1996) for WR 78 but considered as a transient event, as it was observed only during one night. Because WR 78 was not observed with a 2-min cadence, we cannot check for the presence of such a frequency in the TESS data.


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


Theoretical quantum chemical calculations help in narrowing down candidates for much more expensive laboratory experiments. Considering the high cost, time consumption and other constraints faced in laboratory, theoretical computational study can propose selected PAHs for which laboratory spectroscopy can most usefully be performed. Density Functional Theory (DFT) has been used rigorously to calculate the harmonic frequencies and intensities of vibrational modes of PAHs in various forms including size, composition and charge states (Langhoff 1996; Bauschlicher & Langhoff 1997; Bauschlicher et al. 1997; Langhoff et al. 1998; Hudgins, Bauschlicher & Allamandola 2001; Hudgins, Bauschlicher & Sandford 2004; Pathak & Rastogi 2005, 2006, 2007; Pathak & Sarre 2008; Candian, Sarre & Tielens 2014). In this work, DFT in combination with a B3LYP functional and a 6–311G** basis set has been used to optimize the molecular structures of PAHs. The optimized geometry is used to obtain the vibrational frequencies of various modes at the same level of theory. Theoretical calculations tend to overestimate the frequency compared to experiments (Langhoff 1996). The use of a larger basis set, e.g. 6–311G**, generally reduces the overestimation compared to smaller basis sets (Langhoff 1996). Use of a larger basis set compared to a smaller one also shows good agreement with experiment. However, the use of a large basis set does not support use of a single scaling factor for all of the vibrational modes (Langhoff 1996). In order to evaluate the mode-dependent scaling factors, calibration calculations were made for selected PAHs, both neutral and ionized. On comparing the theoretical frequencies with matrix isolated spectroscopic experimental data (Hudgins & Allamandola 1995a,b; Hudgins & Sandford 1998a,b), three different scaling factors have been determined. The scaling factors obtained are 0.974 for the C–H out-of-plane (oop) mode, 0.972 for the C–H in-plane and C-C stretching modes and 0.965 for the C–H stretching mode. Gaussian line shapes of 30 cm− 1 FWHM are used to plot the computationally obtained spectra. Our sample includes deuteronated pyrene (DC16H$_{10}^+$), deuteronated perylene (DC20H$_{12}^+$) and deuteronated coronene (DC24H$_{12}^+$). Isomers of DC16H$_{10}^+$ and DC20H$_{12}^+$ have also been included. The data presented here were produced using gamess quantum chemistry suite of programs (Schmidt et al. 1993).


The extragalactic sky from any direction and at all frequencies is filled with radiation from discrete sources and from a diffuse (or unresolved) component known as the cosmic background. This pervasive radiation, discovered only in relatively recent times, is one of the most fundamental observables from the Universe, as it carries crucial information on the integrated radiation emitted over the entire cosmic history. The first extragalactic background to be detected was the cosmic X-ray background (CXB; Giacconi et al. 1962), a few years before the discovery of the cosmic microwave background (CMB; Penzias & Wilson 1965), which is much brighter in terms of energy density, and is truly diffuse. The extragalactic γ-ray background (EGB) was first detected by the SAS2 satellite in the 1970's (Fichtel et al. 1977), and for a long time its nature was poorly understood. The latest Fermi Large Area Telescope (Fermi-LAT) survey data are now providing strong evidence towards an origin mostly due to integrated radiation from blazars and radio galaxies (e.g. Inoue 2014; Ajello et al. 2015; Fornasa & Sánchez-Conde 2015). Blazars are a special type of extragalactic sources showing extreme observational properties, such as rapid and large amplitude variability, superluminal motion, and strong non-thermal emission across the entire electromagnetic spectrum. These sources are thought to be active galactic nuclei (AGN) that host a jet pointing almost directly to the observer, within which relativistic particles move and radiate by losing their energy in a magnetic field (Blandford & Rees 1978; Urry & Padovani 1995). Among extragalactic objects blazars are known to accelerate particles to the highest observed energies and therefore are considered as prime candidates for multimessenger astronomy. Padovani & Resconi (2014), on the basis of a joint positional and energetic diagnostic, have suggested a possible association between blazars (BL Lacs) and some neutrino events reported by the IceCube collaboration (IceCube Collaboration 2014). It has also been suggested that blazars could be sites where ultra-high energy cosmic rays are generated (e.g. Zhang, Zhao & Cao 2014), although a firm association has so far been elusive despite the continuous improvement of the available data (P. Auger Collaboration 2014).


We initiated the H0LiCOW (H0 Lenses in COSMOGRAIL's Wellspring) program with the aim of measuring the Hubble constant with better than 3.5 per cent precision and accuracy (in most background cosmological models), through a sample of five time-delay lenses. We obtain the key ingredients to each of the lenses through observational follow-ups and novel analysis techniques. In particular, we have high-quality lensed quasar light curves, primarily obtained via optical monitoring by the COSMOGRAIL (COSmological MOnitoring of GRAvItational Lenses; e.g. Courbin et al. 2005; Vuissoz et al. 2008; Courbin et al. 2011; Tewes et al. 2013b) and Kochanek et al. (2006) teams but also via radio-wavelength monitoring (Fassnacht et al. 2002). COSMOGRAIL has been monitoring more than 20 lensed quasars for more than a decade. The unprecedented quality of the light curves combined with new curve-shifting algorithms (Tewes, Courbin & Meylan 2013a) lead to time delays with typically ∼3 per cent accuracy (Fassnacht et al. 2002; Courbin et al. 2011; Tewes et al. 2013b). In addition, we obtain HST imaging that reveal the ‘Einstein ring’ of the lens systems in high resolution, and develop state-of-the-art lens modelling techniques (Suyu et al. 2009; Suyu & Halkola 2010; Suyu et al. 2012b) and kinematic modelling methods (Auger et al. 2010; Sonnenfeld et al. 2012) to obtain the lens mass distribution with a few percent uncertainty (e.g. Suyu et al. 2013, 2014). We further obtain wide-field imaging and spectroscopy to characterize the environment of the field, as well as the spectroscopy of the lens galaxy to obtain the stellar velocity dispersion. The exquisite follow-up data set that we have acquired allow us not only to constrain cosmology but also to study lens galaxy and source properties for understanding galaxy evolution, including the dark matter distribution in galaxies, the stellar initial mass function of galaxies and the co-evolution between supermassive black holes and their host galaxies.


Figure 2 shows solar wind plasma and magnetic field measurements for a CIR that occurred between July 26 and 27, 2003 (days of year 207–208). Following Chotoo et al. (2000), Richardson et al. (1993), we marked four regions in the plot: the slow wind region (S), the compressed slow wind region (S′), the compressed fast wind region (F′), and the fast wind itself (F). Throughout four regions, the mean charge states of iron measured by ACE/SWICS lies around 11+, consistent with typical values in the solar wind (Lepri et al. 2001). The stream interface (S′-F′) is indicated by the vertical line in Fig. 2 and is characterized by a drop of the O7+/O6+ abundance ratio measured with SWICS in the bulk solar wind (Wimmer-Schweingruber et al. 1997, 1999). The leading (S-S′) and trailing edge (F′-F) of the CIR were determined by the total pressure (Jian et al. 2006). Bučík et al. (2009) found that CIR boundaries can be well defined when the total pressure exceeds 50 pPa (indicated by the horizontal dashed line in Fig. 2), which is slightly higher than that in the background solar wind, which typically is 20−30 pPa, according to Jian et al. (2006). The total pressure P was obtained from the sum of plasma and magnetic field pressure, that is, \hbox{$P=n_{\rm p}v^{2}_{\rm th}m+B^2/2\mu_0$}P=npvth2m+B2/2μ0, where np and vth are the proton density and thermal speed, respectively, and B is the magnitude of the magnetic field. Because SOHO has no magnetometer, we used magnetic field data from ACE/MAG (which is also around L1). Comparing plasma parameters (bulk speed, thermal speed, and proton density) measured by PM with those of SWEPAM, we see that the physical conditions at SOHO and ACE were almost the same, and that the time difference between passages of the CIR boundaries is less than ten minutes. The CIR shown in Fig. 2 was bounded by a reverse shock (vertical line separating F′ from F). We clearly see that the suprathermal He++ intensity peaks inside the decelerated and compressed fast-wind region (F′), close to the reverse shock. In contrast, suprathermal particles are very rare in the S and S′ regions. After passage of the reverse shock, suprathermal particles continue to be observable for more than one day. They are commonly believed to be the sunward particles accelerated by the reverse shock far beyond the Earth orbit. In other words, the observer saw the duration of the CIR particle event, which was longer than that of the CIR compression region itself. The background level shown in green was estimated using the method described above. The signal-to-noise ratio (S/N) in the F and F′ regions is higher than 100, confirming that our observations are due to real He++ particles.


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


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


In active galactic nuclei (AGNs), the gaseous accretion disc around the SMBH may facilitate binary formation and mergers of stellar-mass compact objects (McKernan et al. 2014; Bellovary et al. 2016; Bartos et al. 2017; Stone, Metzger & Haiman 2017; Tagawa, Haiman & Kocsis 2020a). In this scenario, BHs form in situ in the vicinity of a GN and sink to the inner region due to mass segregation or they are delivered to these regions by infalling globular clusters (Morris 1993; Miralda-Escudé & Gould 2000; Freitag, Amaro-Seoane & Kalogera 2006; Hopman & Alexander 2006; O’Leary et al. 2009; Antonini 2014), then get captured in the disc by hydrodynamic drag as they cross the disc (e.g. Goldreich, Lithwick & Sari 2002; Bartos et al. 2017; Yang et al. 2019b; Tagawa et al. 2020a). Alternatively, some BHs may have formed in the disc itself (Levin 2007; Stone et al. 2017). Once in the disc, BHs get transported to the inner regions by exchanging angular momentum with the surrounding gas (Goldreich & Tremaine 1979). In certain regions, the BHs open an annular gap in the accretion disc and accumulate in a narrow range of radii, the so-called migration traps (Bellovary et al. 2016; Secunda et al. 2019, 2020, 2021). Bellovary et al. (2016) argue that migration traps may be expected to be close to the SMBH from ∼20 to ∼300 Schwarzschild radii (rS = 2GMSMBH/c2) from the central SMBH of mass MSMBH.6 However, they may exist in slim discs near the innermost stable circular orbit (ISCO; Peng & Chen 2021) or near the boundary of a gap region if a gap opens due to a heavy stellar-mass BH or an intermediate-mass BH (McKernan et al. 2014). Dynamical encounters frequently happen in migration traps leading to the formation and subsequent merger of binary black holes (BBHs) on short time-scales (Secunda et al. 2019, 2020; Yang et al. 2019a), where the binary separation is efficiently reduced by gas dynamical friction (Escala et al. 2004; Kim & Kim 2007; Baruteau, Cuadra & Lin 2011) to the point where GW emission drives the binaries together. Alternatively, BBHs may also form and merge in the disc outside migration traps (Tagawa et al. 2020a). Because of the deep potential barrier of the SMBH, the merger remnant BH remains near the migration trap and may undergo subsequent mergers with additional BHs, which leads to high BH masses, characteristic spin properties, and possibly non-zero eccentricity identifiable via GW observations (Yang et al. 2019a; Secunda et al. 2020; Tagawa et al. 2020b, 2021a,b; Samsing et al. 2022).


Ultraviolet observations of the hot Jupiter HD 209458 b have found up to a 15% occultation in the wings of hydrogen Lyα, with effective Doppler shifts of up to ±150 km s−1, significantly larger than the 5% occultation observed at optical (Vidal-Madjar et al. 2003, 2008; Ben-Jaffel 2007; Ehrenreich et al. 2008). The high occultation and large velocity are indicative of a fast and extended component of the atmosphere, interpreted as an escaping planetary wind. Similar outflows have been reported for another hot and one warm Jupiter, HD 189733 b (Lecavelier Des Etangs et al. 2010; Bourrier et al. 2013) and 55 Cnc b (Ehrenreich et al. 2012
)5

5
Along with a nondetection for a super Earth, 55 Cnc e, placing an upper limit on its mass loss.
, and for one hot Neptunian planet, GJ 435 b (Kulow et al. 2014; Ehrenreich et al. 2015; Bourrier et al. 2016; Lavie et al. 2017). Interestingly, the outflow from GJ 435 b is asymmetric both temporally and spectrally,6

6
Redshifted occultation of (0.7 ± 3.6)% pretransit and (8.0 ± 3.1)% posttransit. Blueshifted occultation of (17.6 ± 5.2)% pretransit and (47.2 ± 4.1)% posttransit (Ehrenreich et al. 2015).
 suggesting a cometary tail-like outflow moving rapidly away from the star. Tentative detections indicate that metals may be present in these escaping winds, including oxygen (Vidal-Madjar et al. 2004; Ben-Jaffel & Sona Hosseini 2010), magnesium (Vidal-Madjar et al. 2013), and carbon and silicon (Linsky et al. 2010; Loyd et al. 2017). Additionally, hydrogen Hα absorption has been seen in HD 189733 b’s transmission spectra (Jensen et al. 2012), but its relation to hydrodynamic escape is still uncertain (Barnes et al. 2016). Recently, the outflow from Wasp-107 b was detected in the 1083 nm line of excited neutral helium (Spake et al. 2018). This line, predicted for exoplanet atmospheres by Seager & Sasselov (2000), and in their outflows by Oklopčić & Hirata (2018), provides an opportunity for ground-based observations.


In MS, the tidal tails host the formation of overdensities similar to TDGs (about 3 in each tail are visible in Fig. 3). Their associated phantom DM further favours their growth, while no such structure is visible in the stellar nor gaseous component of the NA model. The formation of TDGs in simulations is sensitive to the resolution (Wetzstein, Naab & Burkert 2007) and the truncation of the DM halo (Bournaud et al. 2003). By conducting our comparisons at the same resolution in Newton and MOND, and by testing the formation of substructures with much more extended haloes (Appendix C), we ensure that the differences we detect have a physical origin. Observations of the Antennae galaxies report only one TDG candidate, at the tip of the southern tail (Mirabel, Dottori & Lutz 1992), but the exact nature of this structure is still questioned (Hibbard et al. 2001, see also Bournaud et al. 2004). It could be either an unbound object or a forming TDG still out of equilibrium. For the models we consider, the Newtonian framework does not allow for the formation of TDGs, while the MOND does. However we note that, in the absence of efficient shielding from the rest of the galaxy, star-forming regions in the tidal tails are more sensitive to ultraviolet radiation of extragalactic origin. A stronger radiation, e.g. at higher redshift or in a denser galactic environment, could potentially prevent the formation of TDGs and thus reduce the differences (in the young stellar component) between Newtonian and Milgromian cases in this context. Our simulations show however that the old stellar component is likely to remain more clumpy in MOND, as long as the gaseous contribution to the local gravitational potential is negligible over the stellar one. Leaving this issue aside, with the specific models considered here, the Milgromian runs tend to slightly overproduce TDGs given the absence of unambiguously defined ones in the Antennae, whilst the Newtonian runs might potentially slightly underproduce them if the observed TDG candidate turns out to be real. However, the uniqueness of our initial conditions has not been established and it is possible that other sets of parameters could reproduce the same morphology with a different number of TDGs. A much larger simulation sample including more interacting systems would be necessary to reach a clear conclusion on this particular topic.


To classify the bursts in our models, we use the remaining mass in the envelope to define the boundary between the embedded and optically visible phases. Namely, we assume that the optically visible Class II begins when less than 10% of the initial core mass is left in the envelope. The boundary between the deeply embedded Class 0 phase and the partly embedded Class I phase is defined as the time when 50% of the initial core mass is left in the envelope. Our adopted classification scheme is based on physical properties of a young stellar object, such as envelope and disk masses (e.g., Robitaille et al. 2006; Dunham et al. 2010, 2014), rather than on observational signatures, such as submillimeter luminosities or effective temperatures (e.g., André et al. 1993; Chen et al. 1995). Classifications relying upon physical properties are usually referred in the literature as “stages”, whereas those using observational signatures are called “classes”. For simplicity here we use the term “class” to refer to both the physical stages and observational classes. Our adopted definition of physical stages was extensively investigated in Dunham et al. (2010). They found that there is not always a one-to-one correspondence between physical stage defined by the envelope mass and observational class defined by the submillimeter luminosity or effective temperature due to the effects of geometry and extinction. In reality the exact point at which to set the class boundaries is somewhat uncertain, which could shift the duration of the embedded phase in our models by a factor of order unity in either direction. We disentangle the disk and infalling envelope on our numerical grid using the algorithm described in Vorobyov (2011), which is based on the disk-to-envelope transition density of

 g cm−2 and the velocity field in the infalling envelope. Varying the value of

 by a factor of 5 results in changes of the estimated onset time of different phases by only a few per cent.


Other important result we reported in Section 3.3 is the reversing behaviour of red and blue galaxies with respect to velocity and groupcentric distances segregation, with redshift. Regarding velocity segregation, the preceding paragraph provides a qualitative scenario. Now, to explain the spatial segregation, we should notice that our analyses in Sections 3.2 and 3.3 take into account galaxies within 2R/R200. One can reasonably assume that such objects at lower redshifts correspond to a mixture of descendants of galaxies at higher redshifts in the same radii and of infalling objects from outer radii. Thus, both survival and replenishment of galaxies should be expected over the time, and two important factors come into play: (i) the accretion rate of galaxies; and (ii) the orbital dependence of galaxy properties (e.g. Biviano & Katgert 2004; Iannuzzi & Dolag 2012). Indeed, regarding velocity segregation, it has also been interpreted as red and blue galaxies having different kinds of orbits, with the orbits of blue galaxies being more anisotropic than the red ones (e.g. Biviano & Katgert 2004). Recently, Biviano et al. (2016) verified that the anisotropy profile of z ∼ 1 clusters is nearly isotropic near the cluster centre, and increasingly elongated with radius. This result is consistent with a halo evolution through an initial phase of fast collapse and a subsequent slow phase of inside-out growth by accrection of field material (e.g. Lapi & Cavaliere 2009). Since the accretion rate of galaxies from the field is higher at higher redshifts (e.g. McGee et al. 2009), our sample at z ∼ 0.8 is expected to be more affected by recent infalls, which had less time to go deeper into the group potential. This could explain the development of a more marked difference between the mean groupcentric distance of red and blue galaxies (see Fig. 12). After ∼3 Gyr, part of these infalling galaxies may reach the R  2R200 region, at z ∼ 0.4, mixing with virialized and backsplash objects, and thus presenting a less pronounced radial segregation between red and blue galaxies.


The standard photometric analysis (see Dalessandro et al. 2008a, 2008b) has been performed on the “flc” images, which are corrected for flat field, bias, dark counts, and charge transfer efficiency. These images have been further corrected for “Pixel-Area-Map”10

10
For more details see the ACS Data Handbook.
 with standard IRAF procedures. By using the DAOPHOT II ALLSTAR and ALLFRAME packages (Stetson 1987), we performed an accurate photometric analysis of each image. First of all, we modeled the point-spread function (PSF) by using a sample of ∼200 bright but not saturated stars. The model has been chosen on the basis of a χ2 test and, in every image, the best fit is provided by a Moffat function (Moffat 1969). Then we performed a source detection analysis, setting a 3σ detection limit, where σ is the standard deviation of the measured background. Once a list of stars was obtained, we performed a PSF-fitting in each image. In the resulting catalog we included only stars present at least in half the images for each filter. For each star, we homogenized the magnitudes estimated in different images, and their weighted mean and standard deviation have been finally adopted as the star mean magnitude and its related photometric error (see Ferraro et al. 1991, 1992). However, in order to perform variability studies, for each source we also kept the homogenized magnitude measured in each frame in both filters. Then, instrumental magnitudes have been calibrated to the VEGAMAG system, cross-correlating11

11
We used CataXcorr, a code that is specifically developed to perform accurate astrometric solutions. It has been developed by P. Montegriffo at INAF–Osservatorio Astronomico di Bologna. This package is available at http://davide2.bo.astro.it/paolo/Main/CataPack.html, and has been successfully used in a large number of papers by our group in the past ten years.
 our catalog with that by Anderson et al. (2008), using the ∼7600 stars in common.


Understanding how, when, and where galaxies quench their star formation is one of the most muddled, outstanding problems in galaxy formation. Different models for galaxy formation and evolution often make very different assumptions and/or predictions. Among them, semi-analytic galaxy formation models (SAMs; e.g., White & Frenk 1991; Kang et al. 2005; Bower et al. 2006; Croton et al. 2006; Bower et al. 2008; Somerville et al. 2008; Parry et al. 2009; Guo et al. 2011; Lu et al. 2011, 2014; Gonzalez-Perez et al. 2014; Lee et al. 2014; Henriques et al. 2015; Ruiz et al. 2015; Somerville et al. 2015) and hydrodynamical simulations (e.g., Katz et al. 1992; Springel et al. 2001, 2005; Springel & Hernquist 2003; Kereš et al. 2009; Angulo et al. 2012; Vogelsberger et al. 2014a, 2014b; Schaye et al. 2015) are two powerful tools to trace galaxy formation and evolution in cosmological volumes. SAMs are phenomenological models that use an approximate/empirical formula to describe all baryonic processes relevant to galaxy formation, such as gas accretion, heating and cooling, star formation, feedback from stars and AGN, mergers, and stripping due to tides and ram pressure. Because of their different locations within host halos, centrals and satellites in SAMs are assumed to undergo different quenching processes (see, e.g., Henriques et al. 2017). For example, the stripping of hot and cold gas associated with galaxies is assumed to only act on satellites. In addition, the efficiency of radio AGN feedback is assumed to depend on the associated hot gas mass, which may be very different between centrals and satellites. Hydrodynamical simulations, on the other hand, evolve the dark matter and baryonic components in a self-consistent way, though some assumptions have also to be adopted to model subgrid physics (see, e.g., Springel & Hernquist 2003). More importantly, centrals and satellites are not treated differently a priori, and their differences, if any, result directly from a complicated interaction between the baryonic content of a galaxy and its environment, while the (subgrid) modeling of star formation and feedback processes carry no knowledge of this environment.


The lack of detection of supersymmetric particles at Large Hadron Collider led alternative candidates for dark matter to rapidly gaining attention. Apart from other particles, modifications of the gravitational action also offer a new avenue to account for the dark matter. Among many theories, MOG has been successfully tested with galaxies and cluster of galaxies showing the capability to explain the rotation curves of spiral galaxies, the gravitational lensing, the Sunyaev–Zeldovich effect, and the X-ray emission in galaxy clusters without resorting to any dark matter component (Brownstein & Moffat 2006; Moffat & Toth 2013; Moffat & Rahvar 2013, 2014; Moffat 2016; Banerjee et al. 2017; De Martino & De Laurentis 2017; Lopez Armengol & Romero 2017). Nevertheless, a recent study of the dynamics of dwarf spheroidals orbiting around the Milky Way has shown some inconsistencies with previous results (Haghi & Amiri 2016). Since dwarfs are supposed to be dominated by dark matter, any theory that aims to replace it with a modification of the gravitational potential must also be able to account for the dynamics of these galaxies. Here, we have investigated the dynamics of stars in Antlia II in the framework of MOG theory. Antlia II is a recently discovered low-surface-brightness dwarf galaxy being ∼100 more diffuse than ultra diffuse galaxies. It has a very wide core ∼3 kpc, and it is supposed to be strongly dominated by dark matter (Broadhurst et al. 2019; Torrealba et al. 2019). Due to its own nature, it represents an ideal candidate to test alternative theories of gravity such as MOG. Therefore, we have predicted the dispersion velocity profile by solving the spherically symmetric Jeans equation, and assuming that the dynamics of stars is determined by the modified potential well in equation (2) arising in MOG weak field limit, and the stellar density profile is well described by the Plummer model in equation (5). Finally, we have projected the solution of Jeans equation along the line of sight to compare it with the data.


Observations are now probing galaxies in the middle of the reionization epoch, when the gas in the intergalactic medium was transformed from its initially neutral state into a hot, ionized plasma (e.g. McLure et al. 2011; Finkelstein et al. 2012; Bouwens et al. 2014). Most likely stars in galaxies are responsible for this transformation, although this heavily depends on the fraction of ionizing photons produced by the stars that make it into the intergalactic medium, the so-called escape fraction fesc. The escape fraction is a key parameter in studies of the contribution of the observed galaxy population to reionization (e.g. Bouwens et al. 2012; Robertson et al. 2013), semi-analytic modelling of reionization (e.g. Choudhury, Haehnelt & Regan 2009; Pritchard, Loeb & Wyithe 2010; Santos et al. 2010; Mesinger, Furlanetto & Cen 2011; Raskutti et al. 2012; Mitra, Ferrara & Choudhury 2013; Shull et al. 2012) and numerical simulations of reionization (e.g. Iliev et al. 2006; Trac & Cen 2007; Ciardi et al. 2012). A large effort is going into determining the escape fraction observationally. Except for two objects (Leitet et al. 2011, 2013), in the local Universe no ionizing radiation has been detected directly (Leitherer et al. 1995; Deharveng et al. 2001), although some objects show indirect evidence of photon leakage (Heckman et al. 2011; Zastrow et al. 2011). The lack of detections may be partly due to selection bias (Bergvall et al. 2013), but the objects from which radiation is detected have very low escape fractions, fesc  4 per cent. At z ∼ 1, no objects with leaking ionizing photons have been detected (Bridge et al. 2010; Siana et al. 2010), but at z ∼ 3, the highest redshift at which the opacity of the intergalactic medium for ionizing photons is approximately less than unity, ionizing photons have been detected in ∼10 per cent of the observed objects (Nestor et al. 2013). Attempts to constrain the escape fraction with numerical simulations find ranges between fesc  10 per cent (Razoumov & Sommer-Larsen 2006, 2007; Gnedin, Kravtsov & Chen 2008; Paardekooper et al. 2011; Kim et al. 2013) and fesc > 80 per cent (Wise & Cen 2009; Razoumov & Sommer-Larsen 2010), with likely a strong mass and redshift dependence (Yajima, Choi & Nagamine 2010; Wise et al. 2014). Due to the opacity of the intergalactic medium, we need to mostly rely on numerical simulations to learn about the escape fraction during the epoch of reionization.


Since the errors of the LIGO-estimated rates are dominated by Poisson statistics (Abbott et al. 2020a,b), we approximate the PDF for the expected number of detections $\mathcal {N}=\mathcal {R}VT$ (from the surveyed space–time volume VT) by $\mathrm{d}P/\mathrm{d}\mathcal {N}\propto \mathcal {N}^{k-1/2}\mathrm{e}^{-\mathcal {N}}/k!$, where k = 1 for each of the relevant cases ($\mathcal {R}_{190814}$, $\mathcal {R}_{170817}$, and $\mathcal {R}_{190425}$), and the factor of $\mathcal {N}^{-1/2}$ is from Jeffrey’s prior (Abbott et al. 2020a). From the median values of $\bar{\mathcal {R}}_{190814}=7\rm \, Gpc^{-3}\, yr^{-1}$ (Abbott et al. 2020a), $\bar{\mathcal {R}}_{\rm 170817}=760\rm \, Gpc^{-3}\, yr^{-1}$, and $\bar{\mathcal {R}}_{\rm 190425}=460\rm \, Gpc^{-3}\, yr^{-1}$ (Abbott et al. 2020b), we obtain the effective surveyed space–time volumes $VT=1.2/\bar{\mathcal {R}}$ for each of these three events (‘1.2’ is the median of $\mathrm{d}P/\mathrm{d}\mathcal {N}$). We consider both GW170817 and GW190425 as bNS mergers, because the component masses of GW190425 are not far from those of GW170817 and the nature of the merging objects makes little practical difference in our model. Thus, the PDF of the total bNS merger rate from the sum of the two is given by a convolution of the two individual PDFs
(1)$$\begin{eqnarray*}
{\mathrm{d}P\over \mathrm{d}\mathcal {R}_{\rm bns}} = \int _0^{\mathcal {R}_{\rm bns}} \mathrm{d}\mathcal {R}_1 {\mathrm{d}P\over \mathrm{d}\mathcal {R}_1} \left.{\mathrm{d}P\over \mathrm{d}\mathcal {R}_2}\right|_{\mathcal {R}_{\rm bns}-\mathcal {R}_1},
\end{eqnarray*}$$where we have written $\mathcal {R}_{1} = \mathcal {R}_{170817}$, $\mathcal {R}_{2} = \mathcal {R}_{190425}$ for brevity. We then calculate the PDF for the inverse of the total bNS merger rate $\mathrm{d}P/\mathrm{d}\mathcal {R}_{\rm bns}^{-1}=\mathcal {R}_{\rm bns}^2\mathrm{d}P/\mathrm{d}\mathcal {R}_{\rm bns}$. Finally, the PDF of the rate ratio $\beta =\mathcal {R}_{190814}/\mathcal {R}_{\rm bns}$ is given by
(2)$$\begin{eqnarray*}
{\mathrm{d}P\over \mathrm{d}\beta } = \int _0^\infty {\mathrm{d}\mathcal {R}_{3}\over \mathcal {R}_3} {\mathrm{d}P\over \mathrm{d}\mathcal {R}_{3}} \left.{\mathrm{d}P\over \mathrm{d}\mathcal {R}_{\rm bns}^{-1}}\right|_{\beta /\mathcal {R}_3},
\end{eqnarray*}$$where we have written $\mathcal {R}_{3} = \mathcal {R}_{190814}$ for brevity. We find the 90 per cent confidence interval for the rate ratio to be in the range $0.064\, \rm {per\, cent}\lt \beta \lt 2.8\, \rm {per\, cent}$.


MSH 11-61A (also known as G290.1-0.8) is a mixed morphology SNR detected from radio to soft X-rays (up to ~3 keV) that was formed by the core collapse of a massive progenitor star (mass ≳25 M⊙;  Filipović et al. 2005; Reynoso et al. 2006; García et al. 2012; Kamitsukasa et al. 2015; Auchettl et al. 2015a). Following these authors, the distance to the SNR is in the range 6−11 kpc; the most recently determined values converge towards 7 ± 1 kpc. We adopt a distance of 7 kpc throughout the paper1. The INTEGRAL source IGR J11014-6103 is located close to MSH 11-61A and is powered by PSR J1101-6101 (Pavan et al. 2011, hereafter Paper I; Tomsick et al. 2012; Pavan et al. 2014, hereafter Paper II; Halpern et al. 2014). The pulsar shows spin-down parameters typical for pulsars of its age: a period of P = 62.8 ms and a pulse period derivative Ṗ = (8.56 ± 0.51) × 10-15 s s-1. The estimated spin-down energy is Ė = 1.36 × 1036 erg s-1 and the surface dipolar magnetic field is 7.4 × 1011 G (Halpern et al. 2014). Previous Chandra observations aimed at the INTEGRAL source showed that PSR J1101-6101 simultaneously powers several outflows: an X-ray and radio PWN, shaped in a narrow cone elongated towards the parent SNR, and an X-ray jet and counter-jet, both oriented nearly perpendicular to the PWN axis (Tomsick et al. 2012; Paper II). The main jet extends for nearly 5′ in the sky, which corresponds to a projected length of ~11 pc, and showed a remarkable helicoidal pattern (see Paper II). Already in the data set analysed in Paper II, indications for a spatial deviation from the helical pattern of the main jet were noticed at a distance of ~50″ from the pulsar. At this position the surface brightness of the jet was low, forming what looked like a gap, but its brightness profile was compatible with expectations of Doppler-deboosting in the jet-helix model. The spatial deviation was therefore not considered significant at the time because the data were hampered by the presence of CCD chip gaps, resulting in only 50% effective exposure in that region. The counter-jet was detected at 3.7σ in the Chandra image and its flux was estimated to be ~5% that of the main jet. The conical shape of the PWN in IGR J11014-6103 was ascribed to the supersonic motion of PSR J1101-6101 in the ISM (Tomsick et al. 2012).


We have rigorously developed the embedded gravitational lensing theory for point mass lenses in a series of recent papers (Chen et al. 2010, 2011, 2015; Kantowski et al. 2010, 2012, 2013) including the embedded lens equation, time delays, lensing magnifications, shears, etc. We successfully extended the lowest-order embedded point mass lens theory to arbitrary spherically symmetric distributed lenses in Kantowski et al. (2013). The gravitational correctness of the theory follows from its origin in Einstein’s gravity. The embedded lens theory is based on the Swiss cheese cosmologies (Einstein & Straus 1945; Schücking 1954; Kantowski 1969). The idea of embedding (or Swiss cheese) is to remove a co-moving sphere of homogeneous dust from the background Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology and replace it with the gravity field of a spherical inhomogeneity, maintaining the Einstein equations. In a Swiss cheese cosmology the total mass of the inhomogeneity (up to a small curvature factor) is the same as that of the removed homogeneous dust sphere. For a galaxy cluster, embedding requires the overdense cluster to be surrounded by large underdense regions often modeled as vacuum. For a cosmic void, embedding requires the underdense interior to be “compensated” by an overdense bounding ridge, i.e., a compensated void (Sato & Maeda 1983; Bertschinger 1985; Thompson & Vishniac 1987; Martínez-González et al. 1990; Amendola et al. 1999; Lavaux & Wandelt 2012). A low-density region without a compensating overdense boundary, or with an overdense boundary not containing enough mass to compensate the interior mass deficit, has a negative net mass (with respect to the homogeneous background) and is known as an “uncompensated” or “undercompensated” void (Fillmore & Goldreich 1984; Bertschinger 1985; Sheth & van de Weygaert 2004; Das & Spergel 2009).3

3
This dichotomy between compensated and uncompensated voids is slightly different from one based on the classification of the small initial perturbations from which voids are thought to be formed. The initial perturbation can be compensated or uncompensated, which leads to different void growth scenarios (Bertschinger 1985), but if the evolved void formed from either perturbation is surrounded by an overdense shell that “largely” compensates the underdense region (i.e., the majority of the void mass is swept into the boundary shell in the snowplowing fashion when the void is growing), we still call it compensated because the small mass deficit originating in the initial perturbation is unimportant for gravitational lensing.
 Similarly, an overcompensated void has positive net mass with respect to the homogeneous FLRW background. Numerical or theoretical models of over-or undercompensated voids do commonly exist (e.g., Sheth & van de Weygaert 2004; Cai et al. 2010, 2014; Ceccarelli et al. 2013; Hamaus et al. 2014). We focus on compensated void models in this paper, given that uncompensated void models do not satisfy Einstein’s equations. The critical difference between an embedded lens and a traditional lens lies in the fact that embedding effectively reduces the gravitational potential’s range, i.e., partially shields the lensing potential because the lens mass is made a contributor to the mean mass density of the universe and not simply superimposed upon it. At lowest order, this implies that the repulsive bending caused by the removed homogeneous dust sphere must be accounted for when computing the bending angle caused by the lens mass inhomogeneity and legitimizes the prior practice of treating negative density perturbations as repulsive and positive perturbations as attractive. In this paper we investigate the gravitational lensing of cosmic voids using the lowest-order embedded lens theory (Kantowski et al. 2013). We introduce the embedded lens theory in Section 2, build the simplest possible lens model for a void in Section 3, and study the lensing of the CMB by individual cosmic voids in Section 4. Steps we outline can be followed for many void models of current interest.


In a collisional thick-target model, the HXRs are produced by collisional bremsstrahlung during the passage of non-thermal electrons through denser plasma regions, in which the electrons are stopped completely by Coulomb collisions (Brown 1971; Brown et al. 2009; Kontar et al. 2011). Using the electron distribution parameters derived from RHESSI spectroscopy, the power delivered by non-thermal electrons above low-energy cutoff (ELC) can be calculated by the expression
2

where ELC is the low-energy cutoff, Fe is the total number of electrons per second above ELC in units of 1035 electrons s−1, and δ is the electron spectral index (Fletcher et al. 2013). An accurate determination of the low-energy cutoff to non-thermal electron distributions is crucial for the calculation of power and consequently non-thermal energy in solar flares (Sui et al. 2005; Veronig et al. 2005). In general flares are thought to have low-energy cutoffs close to or in the region where the emission is dominated by thermal bremsstrahlung (Ireland et al. 2013). We further emphasize that in flares with multiple HXR sub-peaks during the impulsive phase (like the present one), the determination of ELC is rather illusive during the peak emission as it is difficult to distinguish the signals of flare accelerated electrons against dominant thermal bremsstrahlung. This often results in the overestimation of ELC during HXR peak phases. For this event, we find that ELC varies in the range of 20–32 keV with relatively higher values (∼32 keV) during the second peak (see Figure 13(d)). Therefore, in order to get an estimation of power (and consequently energy) of the non-thermal electrons, we have taken ELC as 25 keV, which is the average of ELC over the flare time interval. The estimated non-thermal electron flux (Fe) above 25 keV is plotted in Figure 14(b). In Figure 14(c), we have plotted the power (Pnth) and energy (Enth) contained in non-thermal electron beams. The plots of Fe and Pnth clearly indicate noticeable enhancement in the particle rate and consequently the power of flare-accelerated electrons during the two HXR peaks.


During the past decade, significant information has been gathered on the chemical compositions of post-asymptotic giant branch (AGB) stars in the Milky Way. This has led to the discovery of a class of post-AGB stars that have C/O > 1 and display extreme enrichment in the abundances of the elements heavier than Fe produced by slow neutron captures (the s-process, Van Winckel & Reyniers 2000; Reyniers & Van Winckel 2003; Reyniers et al. 2004). Since AGB stars can become C rich and have been confirmed both theoretically and observationally as the main stellar site for the s-process (see, e.g., Busso et al. 2001), it is natural to interpret these post-AGB observations as the signature of the nucleosynthesis and mixing events that occurred during the preceeding AGB phase. These events are currently identified as (i) the mixing of protons into the radiative He-rich intershell leading to the formation of a thin region rich in the main neutron source 13C (the 13C “pocket”); (ii) proton-ingestion episodes (PIEs) inside the convective thermal pulses (TPs); and (iii) the third dredge-up (TDU), which carries C and s-process elements from the He-rich intershell to the convective envelope and to the stellar surface. Since the details of all these processes are very uncertain (see discussion in, e.g., Busso et al. 1999; Herwig 2005; Campbell & Lattanzio 2008), observations of post-AGB stars provide strong constraints. Recent observations of the chemical composition of four low-metallicity ([Fe/H] from −1.15 to −1.34), s-process-rich, C-rich post-AGB stars in the Large (J050632, J052043, and J053250) and Small (J004441) Magellanic Clouds (LMC and SMC, respectively) have provided a challenge to AGB s-process models (De Smedt et al. 2012, 2014; van Aarle et al. 2013)1. Since we know the distance of these stars, it is possible to determine from the observed luminosity that their initial stellar mass was in the range 1–1.5 M⊙. Stellar AGB models in this range of mass and metallicity can produce the high observed abundances of the s-process elements, such as Zr and La (1  [Zr/Fe]  2 and 1  [La/Fe]  3), together with [Pb/La] ≃ 1, if a deep TDU is assumed after a last TP. Instead, negative [Pb/La] values are observed as upper limits (De Smedt et al. 2014). Here we test different possible modifications of the current AGB s-process scenario to explain the neutron-capture abundance pattern observed in the MC post-AGB stars.


Figure 11 shows that the distribution of the spectral index α (see Table A.1) is bimodal suggesting the existence of two populations (disc-bearing and discless stars) with approximately the same number of sources. We verified that the bimodality of the distribution of spectral indices is not an artefact caused by the different number of points and wavelength range of the photometric data available for each star to compute the spectral indices. A similar result was also observed for the Chamaeleon I star-forming region (see Fig. 11 of Luhman et al. 2008). Previous studies suggested that the early disappearence of circumstellar discs could be related to environmental effects imposed by the presence of massive stars that produce strong UV radiation, stellar winds, and supernova explosions (see e.g. Walter et al. 1994; Martin et al. 1998). However, we see no dependency of the spectral index on the position of the stars in our sample and any nearby OB star surrounding the Lupus clouds to support this scenario. As shown in Fig. 10 we note the existence of only a few stars older than 10 Myr in our sample which could be potential contaminants (as expected based on the performance of our classifier, see Table 1). Thus, the hypothesis of contamination by older field stars does not explain the bimodality of spectral indices in our sample given that the two populations have the same number of stars, similar ages and are younger than the potential contaminants from the Sco-Cen association. Alternatively, we investigated the dependency of the spectral indices on the age and colour of the stars. Figure 12 shows that the age distribution of the Class II and Class III stars in Lupus overlap. The median age of Class III stars inferred from the Baraffe et al. (2015) and Siess et al. (2000) stellar models is about 3 Myr which yields a rough estimate of the typical disc lifetime in the Lupus association. However, it should also be noted from Fig. 12 that we observe an excess of Class III stars at cooler temperatures (red colours) suggesting that the survival time of circumstellar discs may also depend on other stellar parameters. For example, Galli et al. (2015) used an empirical disc evolution model to determine the lifetime of circumstellar discs in Lupus in terms of the mass of the star. According to their model the average lifetime of a circumstellar disc around a star with 0.1 M⊙ is of the order of 1 Myr which could explain the early disapperance of circumstellar discs for some stars in our sample.


The top-down dynamical approach consists in producing ab initio simulations of Milky Way-like galaxies in a cosmological context. This approach can be useful to understand some general features of galaxy formation (e.g. Minchev et al. 2014). However, it is not flexible enough to produce an acceptable model for the wide range of extremely detailed data soon to be available for our own Galaxy. On the other side, the bottom-up approach for dynamical modelling consists in starting from the actual Galactic data, rather than from simulations, in order to construct a model of the Galaxy. To avoid the redundancy and computational waste of representing the orbits of every single particle in the model, one can use a phase-space distribution function (DF) to represent each population of constituent particles (typically, various stellar populations and dark matter; see e.g. Binney & Piffl 2015; Piffl, Penoyre & Binney 2015). The model-building generally starts from the assumptions of dynamical equilibrium and axisymmetry. These assumptions allow us to make use of Jeans’ theorem constraining the DF to depend only on three integrals of motion, which can typically be chosen to be the radial, azimuthal, and vertical action variables. However, one should remember, especially when modelling the stellar populations of the Galactic disc, that the Galaxy is obviously not axisymmetric, as it harbours a central bar as well as spiral arms. Such perturbations can obviously be treated through perturbation theory, whose foundations in the case of flat 2D discs have been laid down by Kalnajs (1971). For instance, following up on the work of Binney & Lacey (1988) who derived the orbit-averaged Fokker–Planck equation for a 2D stellar disc, recent investigations (e.g. Fouvry, Binney & Pichon 2015) have focused on the long-term secular evolution of such a flat disc by means of diffusion through action space at resonances, producing ridges in action space. Here, we are rather interested in the present-day perturbed DF in the action-angle space of the unperturbed Hamiltonian, in the presence of a 3D spiral arm perturber, which could be fitted to a snapshot of the Galaxy taken by current and upcoming large surveys. Our philosophy is thus closer to that of McMillan (2013), except that the shape of the perturbed DF will be computed directly from the linearized Boltzmann equation. Moreover, in this paper, we will first concentrate only on the response away from the main resonances, the extremely interesting effects expected at resonances, as well as the effect of resonance overlaps of multiple perturbers (e.g. Quillen 2003; Minchev & Famaey 2010), being the subject of further analytical work.


The collision velocity dependence of the coefficient of restitution between particles was observed in experiments (Bridges et al. 1996; Higa et al. 1996) and is discussed in the literature (e.g., Ramírez et al. 1999; Zhang & Vu-Quoc 2002). However, the experiments by Heißelmann et al. (2010), used in the present paper to support our assumption of a constant coefficient of restitution, do not see a variation of the coefficient of restitution between particles at low collision velocities (≤ 1 cm s−1). This discrepancy in results might originate in the nature of the collisions studied in these different experiments: Bridges et al. (1996) and Higa et al. (1996) performed collisions of a particle with a flat surface, while Heißelmann et al. (2010) observed particle-particle collisions in a free-floating environment. The latter is an experimental environment very similar to NanoRocks. In such inter-particle collisions in free-floating environments, other physical effects lead to a different behavior of the energy dissipation during collisions. In particular, the damping behavior of a large plate or surface is expected to differ from that of a same-sized particle, so that the velocity dependence of the coefficient of restitution might be an effect of the experimental setup in Bridges et al. (1996) and Higa et al. (1996). Colwell et al. (2016) and Brisset et al. (2018) studied collisions between a round cm-sized particle and a flat surface of fine grains. They also observed an increase of the coefficient of restitution with decreasing collision velocity. While the composition of the target surface was different than in Bridges et al. (1996) and Higa et al. (1996) (fine granular material vs. solid ice), the similar behavior of the coefficient of restitution supports the fact that particle-surface collisions are very different from particle-particle collisions, and coefficients of restitution are only velocity dependent for collisions with particles with very different sizes (a much larger particle can be approximated as a target surface).


Molecular line ratio diagnostics are often used to investigate the physics and chemistry of the ISM in all of these environments. For example, as the gas chemistry located in the central, nuclear regions of galaxies is believed to be dominated by X-rays produced by the AGN, in so-called X-ray dominated regions (XDRs), the molecular content of the ISM surrounding such nuclei will greatly differ from that in starburst regions (Usero et al. 2004; García-Burillo et al. 2010). Hence, line ratios of specific molecules have been proposed as indicators of certain energetic or physical processes, for example HCN/HCO+ as a tracer of AGNs (Loenen et al. 2007), HCN/HNC as a mechanical heating tracer (Hacar et al. 2020), and HCN/CO as a density tracer (Leroy et al. 2017). In particular, the “submillimeter-HCN diagram”, first proposed in Izumi et al. (2013) and later expanded upon in Izumi et al. (2016), is a very notable example of the use of molecular line ratios as a probe of AGN-galaxies; this diagram makes use of two line ratios, HCN(4−3)/HCO+(4−3) and HCN(4−3)/CS(7−6), where all of the molecules involved are considered tracers of dense gas. Izumi et al. (2016) observed a clear trend that AGNs, including the Seyfert composite galaxy NGC 1068, tend to show higher HCN/HCO+ and/or HCN/CS than in SB galaxies as long as the observations were at high enough spatial resolutions to separate energetically discrete regions. Izumi et al. (2016) propose a scenario where it is the high temperature that is responsible for the HCN enhancement, whereby neutral-neutral reactions with high reaction barriers are enhanced (Harada et al. 2010), thus leading to the possible enhancement of HCN and the depletion of HCO+ via newly available formation and destruction paths, respectively. However, while of course higher gas temperatures are expected in AGN-dominated regions, these are not unique to these environments, as starburst regions and/or regions where outflows dominate can also harbour high enough temperatures for such enhancement to occur. Additionally, the higher temperatures could increase HCN excitation, relative to HCO+ and CS, without necessarily changing their relative abundances (Imanishi et al. 2018a). Finally, infrared radiative pumping is also a possible explanation of the HCN intensity enhancement relative to HCO+ and CS. Infrared pumping is a result of the emission of 14 μm infrared photons due to the presence of hot dust around AGN. These photons vibrationally excite HCN to the ν2 = 1 state. Upon de-exciting from this state back to the vibrational ground state, ν = 0, the HCN line intensities are thus pumped to higher fluxes (Imanishi et al. 2018a). However, we note that it is also not unlikely that the 12 μm infrared photons can similarly vibrationally excite HCO+, thus nullifying the extent of this effect (Imanishi et al. 2016).


If we consider for the bulk density the value 4500 kg m−3, which is one of the highest measured in the asteroid population out of those asteroids with good quality of data (see Carry 2012), it will strengthen the hypothesis that Psyche could be an exposed metal core of a differentiated asteroid (Elkins-Tanton et al. 2017). According to the models of asteroid differentiation, the process that led to the formation of Psyche happened very early. Considering Psyche's current diameter, Deff = 226 km (Shepard et al. 2017), the Psyche parent body (PPB) was supposed to be ∼500 km in diameter and have suffered severe ‘hit-and-run’ impact events capable of removing all crust and mantle, exposing the core (Elkins-Tanton et al. 2016). In addition, Psyche should have ∼40 per cent macroporosity, if we assume that it is made of blocks of iron/nickel with a density around 7500 kg m−3. In that case, the core itself was possibly destroyed and re-accumulated, implying a severe collisional history. When an asteroid is disrupted catastrophically, with a remaining mass ≤50 per cent of the initial one, after a collision with another body, an asteroid family is formed. If the collision happened in the Main Belt, a family of asteroid fragments should be in the region of Psyche; however, no family related to Psyche has been found yet (Davis, Farinella & Marzari 1999). One possibility to solve this issue is that the potential Psyche asteroid family was created at an early time, e.g. within the first 500 Myr of Solar system history (Davis et al. 1999). This would allow the family fragments to be ground down by collisional evolution and be unobservable today. The same models show that, even in this case, today there should be several surviving fragments having diameters around 20 km and above the detection limit. There is a lack of primordial asteroid families in the Main Belt (Brož et al. 2013; Spoto, Milani & Knežević 2015), very likely due to the classical methods that are used to identify them. The hierarchical clustering method (HCM) is not sensitive enough to find old and dispersed families, as it searches for asteroids forming compact groups in orbital element space (semi-major axis, eccentricity and inclination). A new approach has been proposed and implemented with success (Walsh et al. 2013; Delbo’ et al. 2017), as it is able to distinguish very old families, having eccentricities and inclinations dispersed in space. Therefore the possibility of the absence of a Psyche family could be due to searching biases. However, this may be an unlikely hypothesis, because A-type asteroids that could represent mantle material (almost pure olivine) from differentiated bodies do not exist extensively in the orbital space related to Psyche, but instead are distributed randomly in the Main Belt (Davis et al. 1999; DeMeo et al. 2015). In order to study this puzzling small body further, NASA is sending a new Discovery Mission to Psyche. The main goal is to get insight into whether it is a core of a parent body and understand the procedures of differentiation, making all the above questions more valid than ever. The alternative theory is that Psyche is a planetesimal that bears primitive unmelted material (Elkins-Tanton et al. 2016).


Here, we report Li–Be–B and Al–Mg isotopic compositions of seven CAIs from Sayh al Uhaymir (SaU) 290 (CH) and one CAI from Isheyevo (CH/CB) chondrites, which are one of the most pristine (unmetamorphosed) meteorites in our collections (e.g., Bischoff et al. 1993; Weisberg et al. 2001; Krot et al. 2002). The CH and CH/CB (hereafter: CH–CB) chondrites and their components are characterized by enrichments in 15N (up to 1,100‰; Murty et al. 2007; Ivanova et al. 2008; Briani et al. 2009; Bonal et al. 2010), which is similar to the characteristics of comets (Füri & Marty 2015). In addition, Van Kooten et al. (2016) and Olsen et al. (2016) proposed that Mg and Cr isotopic compositions of bulk CH–CB chondrites require significant amounts (20%–50%) of primordial molecular cloud matter in their precursor material. Hence, CH–CB chondrites may have accreted a significant amount of outer solar system materials. Most CAIs in CH–CB chondrites also have a unique absence of excess 26Mg derived from the decay of the short-lived radionuclide 26Al (Kimura et al. 1993; Weber et al. 1995; Krot et al. 2008a), which is unlikely attributed to thermal metamorphism and/or aqueous alteration in the parent bodies (Kimura et al. 1993; Krot et al. 2002; Krot et al. 2008b; Zhang & Hsu 2009). Thus, CH–CB CAIs may also have distinctive information about the origin of 10Be in the solar protoplanetary disk. However, because of their small sizes, it is difficult to measure B isotopic compositions of CAIs in CM, CO, and CH–CB chondrites using a conventional mass spectrometer. To overcome this problem, we have developed a protocol for high accuracy and high spatial resolution measurement techniques using a NanoSIMS 50 (Fukuda et al. 2018). Based on a newly obtained data set in this study, together with the data of previous studies, we will discuss the origin of 10Be in the early solar system and its implications for the astronomical setting of CAI formation in the solar protoplanetary disk.


Another way of obtaining information about the nucleosynthesis processes involved in producing carbon is to compare it with other elements that are characterised by a well-known source of production, as in the case of oxygen. In Fig. 5, we show the variation of [C/O] as a function of [Fe/H], which serves as a first-order approximation to the evolution with time. To calculate the [C/O] ratios, two oxygen abundance indicators are used independently. At subsolar metallicities, the abundance ratios with both oxygen indicators are mostly negative and show an increasing trend towards higher metallicity. This is explained by the fact that oxygen is entirely produced by SNe Type II from massive progenitors, which started to release theiryields at earlier ages in the Galaxy and, hence, at lower metallicities (e.g. Woosley & Weaver 1995). The massive stars producing carbon at low metallicities might be less massive than those producing oxygen (i.e. having a longer life), explaining a delayed contribution of carbon, hence, the negative [C/O] ratios. Alternatively, this could be explained by increasing O/C yields for more massive progenitors of SNeII. Once metallicity starts to increase, low- and intermediate-mass stars release carbon and massive stars start to eject more carbon than oxygen (Carigi et al. 2005). The [C/O] ratio seems to have a constant rise towards higher metallicities when using the forbidden oxygen line. However, in the case when the O I 6158 Å line is employed, we do observe that the maximum in [C/O] takes places close to solar metallicity to then become flat or decrease. This suggests that low-mass stars mostly contribute to carbon around solar metallicity, whereas at super-solar metallicities, massive stars produce carbon together with oxygen, thereby flattening or even decreasing the [C/O] ratio. This trend is in agreement with the metallicity dependent yields from Carigi et al. (2005), which provide higher carbon as [Fe/H] increases from massive stars (i.e. also increasing the O production) but lower carbon from low and intermediate mass stars as [Fe/H] increases (i.e. less production of C). The turning point of increased relative production of carbon from massive stars takes place at A(O) ~ 8.7 dex (see Fig. 2 of Carigi et al. 2005) which equals to [O/H] ~ 0.0 dex. This observed behaviour of [C/O] is in contrast to the steady increase of [C/O] up to [Fe/H] ~ 0.3 dex found, for example, by Franchini et al. (2021). Nevertheless, the general trend we find when using the [O I ] 6300 Å line is similar to the reported by Franchini et al. (2021), who use also that oxygen indicator. All thick-disk stars present negative [C/O] ratios and when using the oxygen line at 6158 Å thin-disk stars with [Fe/H] ≲ –0.2 have [C/O]  0 as well. Thick-disk stars and low-metallicity thin-disk stars at the same metallicity have similar [C/O] ratios, meaning that the balance between different production sites for oxygen and carbon is the same among both populations, despite [C/Fe] and [O/Fe] being systematically higher for thick-disk stars at a given metallicity.


The recent detection of gravitational-wave (GW) emission from a merging neutron star binary (Abbott et al. 2017d) and merging black hole binaries (BHBs; Abbott et al. 2016a, 2016b, 2017a, 2017b, 2017c; The LIGO Scientific Collaboration & The Virgo Collaboration 2018) by the Laser Interferometer Gravitational-Wave Observatory (LIGO)/Virgo have ushered in an exciting new era of GW astrophysics. The astrophysical origin of the detected mergers is currently under debate, with numerous explanations proposed. These explanations can be very roughly divided into two main categories: mergers due to isolated binary evolution (e.g., Belczynski et al. 2016; de Mink & Mandel 2016; Mandel & de Mink 2016; Marchant et al. 2016), and mergers due to dynamical interactions (e.g., Portegies Zwart & McMillan 2000; Wen 2003; O’Leary et al. 2006, 2009, 2016; Antonini & Perets 2012; Kocsis & Levin 2012; Antonini et al. 2014; Antonini & Rasio 2016; Rodriguez et al. 2016; VanLandingham et al. 2016; Askar et al. 2017; Arca-Sedda & Gualandris 2018; Fragione & Kocsis 2018; Hoang et al. 2018; Randall & Xianyu 2018; Arca-Sedda & Capuzzo-Dolcetta 2019). Orbital eccentricity has been explored as a way to distinguish between these merger channels in both the LIGO/Virgo and Laser Interferometer Space Antenna (LISA) frequency bands. In contrast to mergers from isolated binary evolution, merging binaries from dynamical channels have been shown to have measurable eccentricities when they enter the LISA and/or LIGO/Virgo band, and can potentially be used as a way to distinguish between channels (e.g., O’Leary et al. 2009; Cholis et al. 2016; Gondán et al. 2018; Lower et al. 2018; Randall & Xianyu 2018; Rodriguez et al. 2018; Samsing 2018; Zevin et al. 2019). Unlike LIGO/Virgo, which can only detect merging BHBs in the final inspiral phase before merger, LISA will be able to detect eccentric stellar-mass BHBs for long timescales before they merge in the LIGO/Virgo band (e.g., O’Leary et al. 2006; Breivik et al. 2016; Nishizawa et al. 2016; Chen & Amaro-Seoane 2017; Nishizawa et al. 2017; D’Orazio & Samsing 2018; Kremer et al. 2019; Samsing & D’Orazio 2018). This provides us with invaluable insight into the dynamical evolution of eccentric binaries leading up to the merger, which has important implications about the astrophysical context in which merging binaries evolve.


Since its discovery more than five decades ago (Cheung et al. 1968), ammonia (NH3) has been a most valuable molecule for investigating the physical properties of molecular clouds (e.g., Ho & Townes 1983). While thermally excited transitions in the centimeter-wavelength inversion transitions of ammonia are regarded as a reliable thermometer of molecular clouds (e.g., Walmsley & Ungerechts 1983; Danby et al. 1988), ammonia masers have attracted attention since the first detection of maser action in the (J, K) = (3,3) metastable (J = K) line toward the massive star-forming region W33 (Wilson et al. 1982). Subsequent observations have led to the detection of new metastable ammonia masers, including 15NH3 (3,3) (Mauersberger et al. 1986), NH3 (1,1) (Gaume et al. 1996), NH3 (2,2) (Mills et al. 2018), NH3 (5,5) (Cesaroni et al. 1992), NH3 (6,6) (Beuther et al. 2007), NH3 (7,7), NH3 (9,9), and NH3 (12,12) (Henkel et al. 2013). These have led to the discovery of metastable maser lines in 22 different regions (Mauersberger et al. 1986, 1987; Wilson & Henkel 1988; Wilson et al. 1990; Pratap et al. 1991; Cesaroni et al. 1992; Wilson & Schilke 1993; Mangum & Wootten 1994; Kraemer & Jackson 1995; Zhang & Ho 1995; Zhang et al. 1999; Walsh et al. 2007; Hunter et al. 2008; Galván-Madrid et al. 2009; Brogan et al. 2011; Urquhart et al. 2011; Walsh et al. 2011; Wang et al. 2012; Henkel et al. 2013; Hoffman & Joyce 2014; McEwen et al. 2016; Mills et al. 2018; Hogge et al. 2019; Mei et al. 2020; Towner et al. 2021). Compared with the metastable ammonia masers, detected non-metastable (J > K) ammonia maser transitions are more numerous. The first highly excited non-metastable ammonia maser was detected by Madden et al. (1986) in the (J, K) = (9,6) and (6,3) lines. Thereafter, many other NH3 non-metastable inversion transition lines have been identified as masers, including the (5,3), (5,4), (6,1), (6,2), (6,4), (6,5), (7,3), (7,4), (7,5) (7,6), (8,3), (8,4), (8,5), (8,6), (9,3), (9,4), (9,5), (9,7), (9,8), (10,7), (10,8), (10,9), and (11,9) transitions (e.g., Mauersberger et al. 1987, 1988; Walsh et al. 2007; Henkel et al. 2013; Mei et al. 2020). Except for the NH3 (3,3) masersproposed to be associated with four supernova remnants (McEwen et al. 2016), almost all the other ammonia masers are detected in high-mass star-forming regions (HMSFRs). However, while many HMSFRs host water (H2O), hydroxyl (OH), or methanol (CH3OH) masers, ammonia masers are quite rare in these sources, and the role that the environment of a young high-mass star plays in their excitation remains unclear. Therefore, dedicated searches for ammonia masers in HMSFRs are indispensable in regard to their overall incidence and association with different environments, which can provide additional constraints on the pumping mechanism of ammonia masers.


However, most Herschel sources are not SMGs; they are, instead, less luminous dusty star-forming galaxies at lower redshifts (z  2; Casey et al. 2012, 2014). To select Herschel sources that are likely to be SMGs, we chose only the subsample that satisfies the following criteria: (1) flux density peak at 350 μm (

 and S500 S350; i.e., “350 μm peakers”), (2) S500 > 20 mJy, and (3) >3σ detections in all three SPIRE bands. Criterion 1 is essentially a photometric redshift selection because emission from dusts at T = 35 K would peak at 350 μm if redshifted to z ∼ 2.5. This is confirmed by the blind carbon monoxide (CO J = 1–0) survey of a subsample of the brightest 350 μm peakers (S350 ≥ 115 mJy), which has shown a strikingly similar redshift distribution as 850 μm selected SMGs (zCO = 2.5 ± 0.8; Harris et al. 2012). But note that most of these bright sources are strongly lensed and they do not overlap with our sample. Criterion 2 is introduced to ensure that the Rayleigh–Jeans extrapolation would give S850 > 3 mJy, the classic definition of an SMG, given a typical power-law slope of 3.5 for a modified blackbody with a frequency-dependent absorption cross section (

). Criterion 3 ensures that all of the sources we considered are statistically significant. This is necessary because the image depth varies substantially from field to field, ranging from σ500 = 15 mJy beam−1 for the large HeLMS and HerS fields (confusion noise included; Oliver et al. 2012; Viero et al. 2014) to confusion limited with σ500 = 6.8 mJy beam−1 for the deeper HerMES fields (Nguyen et al. 2010). Given the range of observed far-IR SEDs at z = 2 from Casey et al. (2012), our color selection and the high threshold on the 500 μm flux density ensure that ∼95% of our sample would be classified as SMGs if they were observed at 870 μm. Nevertheless, we should keep in mind that the Herschel-selected SMGs are a subsample of SMGs and they likely cover a smaller range of dust temperatures than 870 μm selected SMGs (e.g., Hwang et al. 2010; Magnelli et al. 2012). Only 70,823 Herschel sources remained after this selection. The average surface density of 92 deg−2 is five times lower than the observed 870 μm source count above S870 ≳ 3 mJy (∼500 deg−2; Coppin et al. 2006; Weiß et al. 2009). This is not surprising given that almost half of the total Herschel area is only 10%–20% complete at S500 = 20 mJy. Note that this incompleteness in the Herschel catalogs is not a concern for compiling a sample of SMG−QSO pairs.


We measured the apparent axial ratio on the IF814W-band data, which correspond to the rest-frame V band for galaxies at z ∼ 0.4 and the rest-frame B band for those at z ∼ 0.8. Such differences in the rest-frame wavelength could cause some biases in the morphological analysis due to the color differences between bulge and disk, the blue star-forming regions/clumps, the dust extinction effect, and so on (e.g., Windhorst et al. 2002; Huertas-Company et al. 2009; Wuyts et al. 2012; Vika et al. 2013; Murata et al. 2014; Mager et al. 2018). In order to check the effects of the morphological K-correction, we used publicly available HST/ACS VF606W-band data over a 0.05 deg2 region in the COSMOS field from the CANDELS survey (Grogin et al. 2011; Koekemoer et al. 2011). With the VF606W-band data, we can measure the apparent axial ratio of galaxies at 0.2  z  0.6 in the rest-frame B band and investigate to what extent the difference in the rest-frame wavelength affects the measurements. There are 92 main-sequence and 51 passively evolving galaxies with VF606W  25 at 0.2  z  0.6 in the region, and we measured the apparent axial ratio of these galaxies on the VF606W-band data in the same way. In Figure 17, we compare the apparent axial ratios b/a measured on the VF606W-band data with those measured on the IF814W-band data. The differences between the VF606W and IF814W bands are also summarized in Table 4. The apparent axial ratios measured on the VF606W- and IF814W-band data agree well with each other for both main-sequence and passively evolving populations. The average values of (b/a)F606W − (b/a)F814W are −0.006 and −0.007 for main-sequence and passively evolving galaxies, respectively. These systematic offsets from zero are slightly larger than the averages of the measurement errors but much smaller than the dispersion around the mean value. When we use only bright subsamples with VF606W  22, the results do not significantly change, although the average offsets and measurement errors become slightly smaller. Since these systematic offsets are much smaller than the bin width of 0.1 in the distribution of b/a we used, the morphological K-correction does not significantly affect the distribution of the apparent axial ratio.


Shortly after the ignition of the Sun, the solar system contained a colossal cloud of dust and gas known as the protoplanetary disk. Within just a few million years, trillions of submillimeter-scale solids formed from this disk and coalesced to create a spectrum of planetary bodies that included asteroids, comets, and ultimately the planets that we recognize today. The mechanisms by which these early solids formed and evolved in the disk as well as the processes by which they interacted with each other and the remaining gas and dust governed the chemical and physical properties adopted by these bodies. As such, these early processes played pivotal roles in establishing the long-term thermochemical evolutions of the different planetary bodies found throughout our solar system. Aggregates of these early solids, as well as fragments of the first planetary bodies that formed in the solar system, exist on Earth today in the form of meteorites. Through novel high-resolution and high-sensitivity techniques, these samples have recently provided several new insights into the evolution of the protoplanetary disk and the formation of the first solids. For instance, a number of measurements have revealed that the stable isotopic compositions of all meteorites fall into two distinct families (Warren 2011; Scott et al. 2018; Kruijer et al. 2019; Kleine et al. 2020; Bermingham et al. 2020). This dichotomy has been used to argue that these extraterrestrial rocks each originate from one of two reservoirs of material that existed in the protoplanetary disk that were spatially separated by a large feature (possibly Jupiter; Kruijer et al. 2017; Brasser & Mojzsis 2020; Lichtenberg et al. 2021) that hindered the exchange of material between these regions. This restricted motion prevented disk-wide mixing and compositional homogenization, allowing the distinct composition of each reservoir to form and be retained over much of the disk’s lifetime. One key observation supporting this dichotomy is the ε94Mo and ε95Mo values (where ε denotes normalized isotopic concentration in parts per 10,000) of iron meteorites (fragments of the metallic cores of melted asteroids), rocky achondrites (fragments of the mantles and crusts of melted asteroids), and chondrites (fragments of unmelted asteroids), which together form two parallel lines when plotted against each other (Budde et al. 2016; Kruijer et al. 2017; Budde et al. 2019). Additionally, the isotopic compositions of a suite of other elements (including ε48Ca, ε50Ti, ε54Cr, ε62Ni, ε100Ru, and △17O values, where △ denotes the normalized non-mass-dependent isotopic concentration in parts per 1000) all form pairs of clusters when plotted against each other, further supporting the existence of separated reservoirs composed of material with isotopically distinct compositions in the protoplanetary disk (Warren 2011; Fischer-Godde & Kleine 2017; Bermingham et al. 2018; Schiller et al. 2018; Nanne et al. 2019; Worsham et al. 2019). In all of these cases, the same meteorite groups systematically share similar isotopic signatures and fall into the same families. As such, all meteorites can be primarily categorized as either noncarbonaceous (NC) or carbonaceous (CC) based on their isotopic compositions (named after the type of chondrite found within each family; Budde et al. 2016).