Studying the dynamical properties of rotating neutron stars is a domain which brings out various interesting features when one assumes a perfect fluid. It is known that the centrifugal force of a rotating star counters gravitational force and hence one can expect massive stars to be fast rotors, at least in the initial stages of the stellar evolution. As a result of rotation a star may experience damping due to unstable oscillations such as the r-modes. The r-modes are one of many pulsating modes that exist in neutron stars and are characterized by the Coriolis force acting as the restoring force (Andersson 1998). The r-modes are unstable to emission of gravitational radiation (GR) by the Chandrashekhar-Friedman-Schutz (CFS) mechanism (Chandrasekhar 1970; Friedman & Schutz 1978). It was shown in Andersson (1998) that the r-modes are unstable for all rotating perfect fluid stars irrespective of their frequency. Dissipative effects such as shear and bulk viscosities work towards suppressing GR driven instabilities and has been studied by various authors over the past few years (Lindblom, Owen & Morsink 1998; Jones 2001; Lindblom & Owen 2002; van Dalen & Dieperink 2004; Drago, Lavagno & Pagliara 2005; Nayyar & Owen 2006; Jaikumar, Rupak & Steiner 2008; Jha, Mishra & Sreekanth 2010; Ofengeim et al. 2019) under various considerations. If the GR time-scale is shorter than the damping time-scale due to such dissipative processes, then the r-mode will be unstable and a rapidly rotating neutron star could lose a significant fraction of its rotational energy through GR. At higher temperatures (T > 109 K), the dominant dissipation is due to bulk viscosity, which arises due to density and pressure perturbations, a consequence of the star being driven out of equilibrium by oscillations. The system tries to restore equilibrium through various internal processes. In the case of r-modes, since the typical frequencies are of the order of the rotational frequencies of the stars, the reactions that dominate are the weak processes. Within these weak processes, although the modified Urca processes involving leptons are important, it has been shown that non-leptonic processes involving hyperons contribute more significantly towards bulk viscosity at temperatures lower than a few times 109 K (Lindblom & Owen 2002). Our goal here is to investigate the same using a chiral model calibrated to reproduce the desired nuclear matter properties, in particular the density content of the nuclear symmetry energy at both low and high densities.


By using the RADEX2 dense cloud models developed by Aalto et al. (2015) to reproduce the HCN(3–2)/(1–0) line luminosity ratios in the outflow of Mrk 231, we can attempt to find a combination of XHCN, XCN, Tkin, and nH2 solutions that can also fit the CN/HCN and CN spin doublet line ratios (Table 2). We assume that the HCN and CN line emissions arise from the same dense cloud population, while the low-J CO line emission is due to a different, more diffuse phase of the outflow. We recall that in these models (see also Aalto et al. 2015), the dense clouds can be either self-gravitating virialised clouds, which implies that their internal velocity dispersion (Δvsg) is locked to their mass (Mvir) and size (R) through Δvsg = (GMvir/G)1/2, or unbound clouds, for which Δv ≫ Δvsg. We explored CN and HCN abundances in the range between 10−8 and 10−6. We find that depending on whether the clouds are self-gravitating or unbound, the models produce very different values for the absolute CN and HCN abundances, hence XCN and XHCN remain quantitatively unconstrained for the outflow with current data. However, all possible solutions that fit the observed line ratios consistently require XCN >  XHCN, with a CN abundance that is at least a factor of three higher than the HCN abundance. Gas densities for this outflow phase (traced by the CN and HCN emissions) are nH2 ∼ 105 − 106 cm−3, with temperatures not much higher than Tkin ∼ 20 K. Because CN is a well-known PDR tracer (see also Sect. 1), these results strongly suggest that the whole dense cloud population in outflow is affected by UV radiation. We should mention that high CN abundances may also be due to cosmic rays (e.g. see work done on the Galactic centre by Harada et al. 2015), which are known to permeate the outflow of Mrk 231, as inferred by González-Alfonso et al. (2018) based on the high OH+ abundance. However, it is not clear whether a cosmic-ray chemistry would also explain XCN >  XHCN.


We have presented the principles and framework for calculating the radio signal from a PSR in an EMRB. We restrict our study to the extreme mass ratio of EMRB systems and so do not consider PSRs in stellar-mass BH binaries with finite mass ratios (e.g. Blanchet 2014; Liu et al. 2014). We account for both relativistic and astrophysical effects and the convolution between the two. This includes gravitational and relativistic time dilation and energy shift, gravitational light bending, complex orbital dynamics induced by spin couplings, temporal variation and distortion of the pulse profile due to spin axis precession and relativistic aberration, second-order pulses due to gravitational bending, and dispersions (temporal and spatial) induced by the material along the line of sight. We have demonstrated that within our framework we are able to determine the time–frequency behaviour accounting for all these effects. The framework also applies for any orbital configuration, e.g. we are not restricted to orbital motion in the equatorial plane or beaming confined to the orbital plane. The methods used are entirely covariant and general relativistic, rather than working under any post-Newtonian approximation and so are inherently more accurate. Indeed, the post-Newtonian method is an explicitly weak-field method, and the validity of its application to strong-field dynamical regimes is unclear (Will 2011). Whilst working explicitly in the Kerr metric means that we are unable to independently probe either alternative gravitational theories or extensions to Kerr (e.g. Kerr space–time with an arbitrary mass quadrupole; see Bini et al. 2009), our framework provides the basis for a theoretical timing model that can then be compared with observations for tests of strong field GR. We approximate the PSR body as a perfect sphere. However, due to the spin of the PSR the true shape is more oblate. This will ultimately influence the pitch angle of the ray with the neutron star surface. This effect is considered to be minor, but the method could easily be extended to account for this oblateness (see Nättilä & Pihajoki 2018). We neglect the effects of hydrodynamic drag due to the plasma that surrounds that BH since at compact radii (≲ 104rg) the gravitational and relativistic effects dominate (Psaltis 2012). We also do not take account of any potential Newtonian perturbations on the motion of the pulsar (e.g. Merritt et al. 2011) due to the presence of other masses (e.g. stars, other compact objects etc.) since these factors are likely negligible for the orbital periods considered in this work (≲0.3 yr; Liu et al. 2012). Indeed, the potential for external perturbations to hamper tests of strong-field GR necessitates that an ideal PSR–EMRB systems should have orbital periods on the order of 0.1 yr (or better), or else observations should be taken close to periapsis (see discussion in Psaltis, Wex & Kramer 2016). These are precisely the regions where the space–time curvature and orbital acceleration is greatest, further stressing the importance of a strong-field timing model. We also neglect any influence of gravitational radiation on the orbit or the ray trajectory. The neglect of gravitational radiation is justified since in the extreme mass ratio limit, the time-scale for orbital decay due to gravitational wave emission is (Misner, Thorne & Wheeler 1973)
(45)
\begin{eqnarray*}
\tau _{\mathrm{ GW}} \sim \frac{5 r^4}{96mM(m+M)} f(e)^{-1} \ ,
\end{eqnarray*}
where M is the mass of the BH, m the pulsar mass, and r the orbital separation. The eccentricity function is
(46)
\begin{eqnarray*}
f(e) = (1-e^2)^{-7/2} \left(1 + \frac{73}{24} e^2 + \frac{37}{96} e^4\right) \ .
\end{eqnarray*}
If we take the PSR orbital period P to be Keplerian, then for a pulsar with mass $1.4 \, \mathrm{M}_{\odot }$ on an eccentric (e = 0.8), P = 0.1 yr orbit around a BH with mass $4.3 \times 10^6 \, \mathrm{M}_{\odot }$(47)
\begin{eqnarray*}
\frac{\tau _{\mathrm{ GW}}}{P} \sim 10^9 \gt \gt 1 \ ,
\end{eqnarray*}
and so the effects of gravitational radiation can be neglected. Even for smaller radii and more eccentric orbits the space–time is well approximated as stationary (e.g. τGW/P  ∼ 105 for e = 0.9, r = 100 M). Whilst the effects of gravitational radiation are then not important for a single orbit, for observations over longer periods of time the effect of gravitational emission on the orbit and hence the timing solution will need to be considered. The PSR may also emit a gravitational wave burst during passage through periastron (Berry & Gair 2013a,b). The influence of this gravitational radiation on both the PSR trajectory and the photon ToA is highly non-trivial and not considered here.


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


The temperature gradient of the 3-equation model is comparable to results of different TCM approaches (Xiong & Deng 2001; Li & Yang 2007) for the base of the solar convective envelope. Both Zhang & Li (2012; their Figs. 6 and 7) and Xiong & Deng (2001; their Fig. 8) find a temperature gradient that transitions gradually from the adiabatic to the radiative value. They also find a Deardorff layer with a degree of sub-adiabaticity at the formal Schwarzschild boundary comparable to our findings. From the convective flux as presented in Xiong (1986) one also would expect a similar temperature gradient in the overshooting zone. Furthermore, the shape of the model temperature gradient is also in qualitative agreement with the discussion in Viallet et al. (2015). They argue that under the physical conditions in convective cores, in regions of overshooting efficient chemical mixing and a gradually transitioning temperature gradient are expected. In the 3-equation non-local model, the extent of the nearly adiabatic overshooting zone is controlled by the shape of the negative convective flux in the overshooting zone. For smaller (more negative) values of the convective flux (i.e. more efficient buoyancy braking) the temperature gradient is expected to be closer to the adiabatic value, while for larger (less negative) values it will be closer to the radiative temperature gradient. In Eq. (1) the negative convective flux and the dissipation term act as sink terms in the overshooting zone. Hence, the behaviour of the dissipation term will impact also on the convective flux and in turn on the value of the temperature gradient in the overshooting zone. In computations with the 1-equation non-local version of the theory, the negative convective flux is the dominant sink term for the TKE and the actual dissipation term is negligible (Fig. 8 of Paper I). This leads to more negative values of the convective flux and thus to a mostly adiabatic temperature gradient in the overshooting zone. We discuss this in more detail in Sect. 5.1 (we also refer to Fig. 10).


In the last few years, several experiments have reported upper limits on the power spectrum of 21-cm fluctuations during reionization (Parsons et al. 2014; Patil et al. 2017; Barry et al. 2019; Mertens et al. 2020; The HERA Collaboration 2021b) and the earlier cosmic-dawn era (Eastwood et al. 2019; Gehlot et al. 2019, 2020; Garsden et al. 2021; Yoshiura et al. 2021). Scenarios in which the bulk IGM is still colder than the cosmic microwave background (CMB) during reionization give rise to the strongest fluctuations and so will be the first models to be tested as upper limits continue to improve (e.g. Parsons et al. 2014; Pober et al. 2015; Greig, Mesinger & Pober 2016). Similarly, stronger-than-expected 21-cm signals can arise if the cosmic radio background has contributions other than the CMB (Feng & Holder 2018), e.g. synchrotron emission from accreting black holes (Ewall-Wice et al. 2018), star-forming galaxies (Mirocha & Furlanetto 2019), or from decaying particles (Fraser et al. 2018; Pospelov et al. 2018). Indeed, constraints from MWA, HERA, and LoFAR disfavour models with negligible X-ray heating at z ∼ 8–9 or very strong radio backgrounds (Ghara et al. 2020, 2021; Mondal et al. 2020; Greig et al. 2021a, b; The HERA Collaboration 2021a). Of course, the recent report of an absorption signal in the sky-averaged spectrum at z ∼ 17 from EDGES (Bowman et al. 2018) requires an even colder IGM (Barkana 2018; Boddy et al. 2018; Fialkov, Barkana & Cohen 2018; Kovetz et al. 2018; Muñoz & Loeb 2018) or a brighter background (Ewall-Wice et al. 2018; Feng & Holder 2018; Fialkov & Barkana 2019; Mirocha & Furlanetto 2019) than models in ΛCDM cosmologies generally predict. However, the most stringent power spectrum upper limits from The HERA Collaboration (2021b) are derived at sufficiently low redshifts relative to EDGES (z ≲ 10 versus z ≃ 18) that they cannot yet directly address the EDGES controversy (Hills et al. 2018; Bradley et al. 2019; Singh & Subrahmanyan 2019; Sims & Pober 2020; Tauscher, Rapetti & Burns 2020; Singh et al. 2021).


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.


The standard single-frequency detection methods for point sources in the CMB and far IR are based on wavelet techniques (Vielva et al. 2003; Barnard et al. 2004; González-Nuevo et al. 2006) or on the matched filter (or MF hereafter, Tegmark & de Oliveira-Costa 1998; Herranz et al. 2002; Barreiro et al. 2003; López-Caniego et al. 2006, see also Herranz & Vielva 2010 for a review.). Wavelets are well suited for the detection of compact sources due to their good position-scale determination properties, whereas the MF is the optimal linear detector-estimator because it provides the maximum signal-to-noise (S/N) amplification for a source with a known shape (usually the point-spread function, or PSF hereafter, of the telescope) embedded in statistically homogeneous and spatially correlated noise. By default, these techniques are applicable only to single-frequency sky images: even for multiwavelength observatories such as the Herschel Space Observatory (Pilbratt et al. 2010) or Planck (Tauber et al. 2010), the standard detection pipelines have produced individual source catalogs for each frequency band (see e.g., Planck Collaboration VII 2011; Planck Collaboration XXVIII 2014; Planck Collaboration XXVI 2016; Maddox et al. 2018). The next logical step is to boost the signal of faint sources by combining the different bands into a single detection, that is, “multifrequency detection”. Most of the blind component separation algorithms that are used for diffuse components in microwave and far IR astronomy can not deal with the high diversity of spectral behaviors associated to the different populations of extragalactic compact sources (see for example Leach et al. 2008). However, over the last few years a number of multifrequency compact source detection techniques have been proposed in the literature (Herranz & Sanz 2008; Herranz et al. 2009; Lanz et al. 2010, 2013; Planck Collaboration Int. LIV 2018). A review on the topic can be found in Herranz et al. (2012). In particular, if the spatial profile and the spectral energy distribution (SED) of the sources are known, and if the cross-power spectrum is known, or can be estimated from the data, the optimal linear detection method is the matched multifilter (or MMF hereafter, Herranz et al. 2002). Lanz et al. (2010) also showed that the MMF can be generalized for the case where the SED of the sources is not known. This generalization outperforms the single-frequency MF in terms of S/N and can be used to infer the spectral index of synchrotron-dominated radio sources, as shown in Lanz et al. (2013). However, in this paper we will incorporate a specific SED to the MMF in order to derive a photometric redshift estimation of dusty galaxies and high-redshift star forming galaxies detected in the IR part of the spectrum1. We will do so by applying the multifrequency MMF filter to the first and second data releases of the Herschel Astrophysical Terahertz Large Area Survey (the Herschel-ATLAS or H-ATLAS, Eales et al. 2010), the largest single key project carried out in open time with the Herschel Space Observatory. We restrict our multifrequency analysis to the three wavelength bands covered by the SPIRE instrument aboard Herschel (Griffin et al. 2010), centered around 250, 350 and 500 μm. As discussed in Hopwood et al. (2010), Lapi et al. (2011), González-Nuevo et al. (2012), Pearson et al. (2013) and Donevski et al. (2018), the SPIRE bands are ideal for capturing the peak in the SED corresponding to dust emission of star-forming galaxies at z ∼ 2, that is redshifted from its rest-frame wavelength around 70–100 μm to the SPIRE wavelengths: This is the redshift range where galaxies have formed most of their stars. At higher redshifts, dusty star-forming galaxies (DSFGs) occupy the most massive halos and are among the most luminous objects found at z ≳ 4 (Michałowski et al. 2014; Oteo et al. 2016; Ikarashi et al. 2017). These high-redshift DSFGs have markedly red colors as seen by SPIRE, with rising flux densities from 250 to 500 μm (the so-called “500 μm-risers”), and have received a great deal of attention in the recent years (see for example Ivison et al. 2016; Negrello et al. 2017; Strandet et al. 2017). The DSFGs, and particularly the 500 μm risers uncovered by Herschel, are providing much insight into the early star forming history of the universe. However, sensitivity and limited angular resolution severely constrain the power of this type of objects as astrophysical probes. The sensitivity of SPIRE allows for the direct detection of only the brightest, and thus rarest objects, at the bright end of the luminosity function. By means of our multifrequency MMF technique, we intend to enhance the detectability and statistical significance of very faint red objects in the H-ATLAS source catalog and so expand the list of reliable 500 μm-riser candidates.


The evolution of galaxies sensitively depends on the stellar initial mass function (IMF). The understanding of the IMF has changed rapidly in the past decade. Despite a direct conflict (Kroupa et al. 2013) with the theoretical expectation that the IMF should vary as the star-forming environment alters (e.g. ambient gas temperature, metallicity, density, and pressure dependence, as argued by Adams & Fatuzzo 1996; Larson 1998; Elmegreen 2004; Dib et al. 2007; Papadopoulos 2010) the observed IMFs of star clusters in the local Universe are consistent with no variation (Kroupa 2001, 2002; Bastian et al. 2010; Offner et al. 2014; Hopkins 2018). Thus, the universal and invariant canonical IMF assumption was widely applied. The more recent observations, which are able to probe physical regimes further from the solar and Galactic neighbourhood, have been consistently suggesting a variation of the galaxy-wide IMF (gwIMF1). For the distribution of low-mass stars, a bottom-heavy IMF (excess in the number of low-mass stars) in the inner regions of massive metal-rich elliptical galaxies is indicated by the galaxy mass-to-light ratio (Li et al. 2017), spectral analysis of stellar-mass sensitive features (Vazdekis et al. 1997, 2003; Cenarro et al. 2003; van Dokkum & Conroy 2010; Conroy & van Dokkum 2012; Ferreras et al. 2013; Martín-Navarro et al. 2015; La Barbera et al. 2017; Parikh et al. 2018) and lensing studies (Auger et al. 2010; Oldham & Auger 2018)2. For the distribution of massive stars, independent evidence strongly indicates a systematically varying IMF (galaxy photometry: Hoversten & Glazebrook 2008; Meurer et al. 2009; Lee et al. 2009; Gunawardhana et al. 2011, metal abundance of galaxy clusters: Renzini & Andreon 2014; Urban et al. 2017, isotope abundance: Romano et al. 2017; Zhang et al. 2018), being top-heavy (more massive stars than predicted when assuming the canonical IMF) when the SFR is high and/or when the metallicity is low, as summarized by Kroupa et al. (2013), Yan et al. (2017), and Jeřábková et al. (2018). We note that the IMF can be bottom-heavy and top-heavy at the same time (see Jeřábková et al. 2018).


We then allow the synthetic single or binary system to evolve until present time, adopting for our reference model a thin disc age of 10 Gyr (Cojocaru et al. 2014) and a thick disc age of 12 Gyr. This is motivated by the findings of Feltzing & Bensby (2009), who presented a sample of very likely thick disc candidates with ages, on average, well above 10 Gyr and of Ak et al. (2013), who found that thick disc cataclysmic variables have ages up to 13 Gyr. If the synthetic star is single and has time to become a white dwarf, it evolves following the cooling tracks detailed in the following section. If that is the case, the mass of the white dwarf is obtained from the initial-to-final mass relation (IFMR) according to the prescription from Hurley, Tout & Pols (2002). If the object is member of a binary system and the primary star has time to become a white dwarf, then the pair can evolve through two different scenarios. In the first scenario, the binary evolves without mass transfer interactions as a detached system and the primary star evolves into a white dwarf that subsequently cools down following the cooling sequences described in the next section. In this case, the mass of the white dwarf is also calculated from the IMFR of Hurley et al. (2002). The second scenario involves mass transfer episodes and the evolution of the binary is obtained following the prescriptions of the bse package (Hurley et al. 2002), following the parameter assumptions detailed in Camacho et al. (2014). If the system evolves though the common envelope phase, we use the α-formalism as described in Tout et al. (1997), with αCE being the efficiency in converting orbital energy into kinetic energy to eject the envelope (assumed to be 0.3 in our reference model). This implementation also takes into account the αint parameter (assumed to be 0.0 in our reference model), first presented in Han, Podsiadlowski & Eggleton (1995), describing the fraction of the internal energy (thermal, radiation and recombination energy) used to eject the envelope. As described in Camacho et al. (2014), the αint parameter is used to include the effects of the internal energy in the binding energy parameter λ, which is thus not taken as a constant, but computed using a specific algorithm (Claeys et al. 2014) in bse. In the current version of the code, provided that a positive value is used, the parameter αint represents the fraction of recombination energy that contributes to eject the envelope. It is important to note that the thermal energy of the envelope is always taken into account (using the virial theorem) even if αint is set to zero. For a more detailed discussion on how this is implemented in the latest version of BSE and important comments on the correct use of BSE and the notations used in the code itself, we direct the reader to Zorotovic, Schreiber & Parsons (2014a), mentioning that the notations αint or αrec are, in our case, equivalent.


As mentioned in Section 1, once the sample of matching halos between the twin N-body simulations is established, we can study the halo−LSS correlations. We employ the Hessian matrix method used in many previous articles (e.g., Hahn et al. 2007a, 2007b; Zhang et al. 2009; Kang & Wang 2015) to define the matrix as:
4

H

ij

=

∂

2

ρ

s

x

∂

x

j

∂

x

i

.

This method is based on the smoothed density field

ρ

s

x

 at the halo position (based on a more accurate and improved algorithm by Wang et al. 2020), which can be given by the Cloud-in-Cell (CIC) technique (MacNeice 1995). The smoothing length Rs is the only parameter of the CIC, which can be regarded as the typical scale of a halo LSS environment identified by the Hessian matrix method. Many previous works (e.g., Aragón-Calvo et al. 2007; Hahn et al. 2007a; Zhang et al. 2009; Codis et al. 2012; Hoffman et al. 2012; Libeskind et al. 2013; Trowland et al. 2013, but see also Libeskind et al. 2014) used a constant smoothing length. To determine which Rs value should be chosen, we test some LSS properties (e.g., the environment and eigenvectors) of matching halos for three fixed Rs: 2.5,  5, and  10 h−1 Mpc. We find that the halo−LSS correlation, as well as other main conclusions we make below, become stronger as Rs decreases, which is a reasonable result according to our previous discussions. Consequently Rs = 2.5 h−1 Mpc is chosen hereafter. The three eigenvalues of the Hessian matrix are marked as λ1, λ2, and λ3, with corresponding eigenvectors e1, e2, and e3. Eigenvalues λi can be used to define the LSS environment of dark matter halos according to the number of positive eigenvalues (Zel’Dovich 1970; Hahn et al. 2007a, 2007b; Libeskind et al. 2018; Zhang & Yang 2019); i.e.,

1.
void: 0  λ1 λ2 λ3

2.
wall: λ1  0  λ2 λ3

3.
filament: λ1 λ2  0  λ3

4.
cluster: λ1 λ2 λ3  0

and the eigenvectors ei stand for the three compressed directions of the smoothed density field. The e3 vector indicates the least compressed direction, which is a robust and universal definition of the LSS. In this work, we will focus on the alignment of halo spin and shape with the e3 vector; i.e.,

cos

θ

3

=
a
·

e

3

, where a is the halo spin or major-axis vector.

Many previous works
used a constant smoothing length.


Furthermore, Duvall et al. (1993) noticed an inversion of the sense of asymmetry between spectrometric and photometric measurements, with line profiles in the velocity spectrum featuring more power in their low-frequency wing than in their high-frequency wing and vice-versa for line profiles in the intensity spectrum. Since intensity perturbations were expected to be proportional to velocity perturbations, one would have expected the asymmetries to be the same. Many hypotheses were posited to explain this puzzling result. Duvall et al. (1993) suggested that it was due to non-adiabatic effects lifting the proportionality relationship between the two kinds of perturbations (fluid displacement and temperature) but this hypothesis was later contradicted by Rast & Bogdan (1998). Non-adiabaticity was brought up again later on by Georgobiani et al. (2003) who suggested that the explanation resided in radiative transfer between the mode and the medium. Indeed, the observed radiation temperature corresponds to the gas temperature at local optical depth τ = 1. But optical depth depends on opacity, which non-linearly depends on temperature. Therefore, the temperature fluctuations due to the oscillating mode entails opacity fluctuations, which in turn impacts the “observed” radiation temperature. Given the non-linear nature of the κ − T relation, this modulation decreases the observed temperature fluctuations more significantly in the low-frequency wing of the mode than in its high-frequency wing. Since this radiative transfer does not impact the velocity measurements, this could explain the asymmetry reversal between velocity and intensity spectra. Using 3D simulations, Georgobiani et al. (2003) computed mode line profiles in both the velocity and the intensity power spectrum alternatively at mean unity optical depth and instantaneous unity optical depth. Their results indeed show that the modulation of the “observed” intensity fluctuations due to radiative transfer could be significant enough to reverse the sense of mode asymmetry. One of the hypothesis enjoying the most support for asymmetry reversal, however, is based on the effect of turbulent perturbations partially correlated with the mode, which thus impact its line profile (Nigam et al. 1998; Roxburgh & Vorontsov 1997; Rast & Bogdan 1998; Kumar & Basu 1999). Indeed, a part of these perturbations is coherent with the mode and, thus, leads to interference. This interference term may be constructive or destructive, depending on the phase difference between the mode and the coherent turbulent perturbations. For frequencies at which the interference is constructive, the power spectral density is slightly elevated, whereas it drops slightly for frequencies at which it is destructive. Typically, in the vicinity of a resonant mode, the dependence of the phase difference between mode and turbulent perturbation is such that the interference term is constructive for frequencies located in one wing of the mode and destructive in the other. Therefore, as a result of this interference behaviour, one of the wings falls off more slowly and the other more rapidly, leading to mode asymmetry. It has been suggested that the degree of correlation between the turbulent perturbations and the oscillation it excites is higher in intensity than in velocity, so that it changes the sign of mode asymmetry only in the intensity spectrum. While it is widely accepted that correlated turbulent perturbations must be taken into account to explain asymmetries in the intensity spectrum, the question of whether it has a significant impact on the velocity spectrum remains an open issue (see e.g. Jefferies et al. 2003).


The energy levels calculated by Fritzsche, Fischer & Fricke (1998) with grasp92 code are more closer to the NIST values as compared with other calculations within 3.6 per cent for the levels in the ground configurations. Our calculated MCDF energies agree well with NIST data within 6.8 per cent and the maximum error appears for ground state configuration (3s23p3) levels. The average percentage difference between our grasp1 energies and the measured values is 1.9 per cent. For the lowest 41 energy levels, we see that our calculated energies and previous fac energies (Landi & Bhatia 2010; Wang et al. 2012) belonging to the n = 3 complex in Ni xiv agree well with each other and both set of calculation are of the same accuracy. However, our calculated ground state configuration levels show better agreement with measured energies in comparison to those of fac calculations (7.2 per cent). When compared to MCDF calculations performed by Aggarrwal, Keenan & Msezane (2003) with grasp Dyall et al. (1989) code using a model of 14 configurations, our grasp1 levels in the excited configurations lie closer to the NIST ones. In the case of four energy levels (2D5/2,3/2,4P5/2,3/2), our calculated energy levels are more closer to NIST than those of Aggarrwal et al. (2003). The average percentage difference of these grasp energies with NIST values is 2.2 per cent, and the maximum error of 6.3 per cent appears for the first excited state (2D3/2) of ground configuration. For more accurate target states we adopt a model of 13 electronic configurations which yields target-states energies as closer to NIST values as possible. For instance, our calculated energy levels 2D3/2,5/2 associated with the configuration 3s3p4 lie more closer to the observed values as compared to existing calculations. The remaining set of energy levels are almost of the same accuracy as those of previous data when compared to experimental energies. From this comparison it is evident that present grasp1 calculated N-electron target wavefunctions demonstrate good agreement with experimental values, which is necessary for more accurate PI cross-sections of Ni xiii.


Gamma Doradus (γ Dor) stars, with 1.4 M⊙ ≲ M* ≲ 2.0 M⊙, and slowly-pulsating B-type (SPB) stars, with 2.5 M⊙ ≲ M* ≲ 8 M⊙, exhibit high-order gravity-mode (g-mode) pulsations, gravito-inertial pulsations (Van Reeth et al. 2016), and/or purely inertial pulsations, such as r-modes (Saio et al. 2018). The restoring forces for gravity-modes and purely inertial pulsation modes are buoyancy and the Coriolis force, respectively. In the case of gravito-inertial pulsation modes, both forces contribute. As predicted by asymptotic theory, the pulsation periods for γ Dor and SPB stars were observed to form period spacing patterns (e.g. Chapellier et al. 2012; Chapellier & Mathias 2013; Kurtz et al. 2014; Bedding et al. 2015; Saio et al. 2015; Van Reeth et al. 2015; Ouazzani et al. 2017). The pulsation periods are equidistant in the asymptotic regime (with radial order n ≫ spherical degree l) for a non-rotating chemically homogeneous star (Tassoul 1980). Chemical gradients in the deep stellar interior cause pulsation mode trapping, which introduces non-uniform variations in the spacings (Miglio et al. 2008). On the other hand, the stellar rotation leads to shifts in the observed pulsation mode frequencies (Bouabid et al. 2013; Salmon et al. 2014; Van Reeth et al. 2015; Moravveji et al. 2016). For slowly rotating stars, the observed pulsation modes are split into frequency multiplets that depend on the mode identification. For moderate to fast rotators, that is, with rotation in the order of or more than 20% of the critical rotation rate, the observed period spacing patterns have a clear slope (e.g. Van Reeth et al. 2016; Ouazzani et al. 2017). Prograde (azimuthal order m >  0) and zonal modes have a downward slope, that is, the spacing between consecutive pulsation periods decreases with increasing pulsation period, i.e. radial order n. The period spacing patterns of retrograde modes (with m   0) mostly have an upward slope. For stars with detected period spacing patterns, this has been exploited to derive the near-core stellar rotation (e.g. Kurtz et al. 2014; Saio et al. 2015, 2018; Triana et al. 2015; Murphy et al. 2016; Schmid & Aerts 2016; Van Reeth et al. 2016; Ouazzani et al. 2017).

Van Reeth et al. 2015
Van Reeth et al. 2015


With all this in mind, our last question is: What powers soft X-rays and [O III] in LINERs? This has no clear answer, but both are not tracing the same mechanism, since none of them match in morphologies. This is a clear difference between type-2 Seyferts and LINERs. In favour of the soft X-ray emission being originated by AGN photoionization, the RGS spectra studied by Gonzalez-Martin et al. (2010b) showed that in at least 30 per cent of their sample, a contribution of photoionization by the AGNs is required due to the presence of radiative recombination continua (RRC) from CV emission line. However, this does not guarantee a dominance of this emission mechanism. Moreover, cone-like morphologies at soft X-rays in some objects in this study point out again to the photoionization by the AGNs being responsible for the soft X-ray emission. Nevertheless, this assumes that we are seing LINERs with an LOS perpendicular to the accretion disc, which might not be the case. Indeed, the ultraviolet and X-ray variability detected for many of these LINERs (Maoz et al. 2005; Hernández-García et al. 2015) is in favour of a direct view of the AGNs (i.e. perpendicular to the disc under the UM). This is consistent with the fact that most of the [O III] morphologies found for LINERs are spheroids, if we assume that the [O III] traces the NLR. In addition, the fact that we detected a clear correspondence between soft X-ray and [O III] morphologies only in objects with log (LHX)>40, and also that all the objects where soft X-rays and [O III] match their morphologies seem to better follow the previously found relation between the size of the region and the hard X-ray luminosity (see Fig. 2 and Section 5.2), may argue in favour of the scenario in which the AGNs do not have enough thrust to ionize in the low-luminosity regime (Elitzur & Shlosman 2006; Elitzur & Ho 2009), ruling out photoionization by the AGNs at both soft X-ray and [O III] emissions. In this case, the most reasonable explanation for the [O III] is the host galaxy emission, which, anyhow, could also be on top of the AGNs, preventing its detection and erasing the connection (González-Martín et al. 2014). The host galaxy can contribute either as star formation or shocks to the total [O III] emission. Regarding the soft X-ray origin, Mingo et al. (2014) confirmed that jets are the main responsible for soft X-ray emission from their sources. In our sample, jets are identified in NGC 1052 (Kadler et al. 2004), where the jet position angle would be consistent with the extended soft X-ray emission shown here.


A huge amount of data at all wavelengths has been collected in the past 20 years on black hole X-ray binaries, hereafter XrBs (for a global review see Dunn et al. 2010). These objects spend most of their time in quiescence at very low accretion rates, but occasionally, they produce outbursts that last from a few months to a year. Their flux then rises by several orders of magnitude across the whole electromagnetic spectrum (see, e.g., Corbel et al. 2004, Fender et al. 2006; Remillard & McClintock 2006; Done et al. 2007, for recent reviews). During an outburst, XrBs show very different spectral and temporal states that can be easily distinguished in a hardness-intensity diagram (HID) where the X-ray luminosity is plotted versus the hardness ratio of the X-ray spectrum (see, e.g., Homan et al. 2001; Fender et al. 2004). The evolutionary track produces a typical q-shaped figure that reveals a hysteresis: outbursting XrBs have two distinct spectra with the same X-ray luminosity above 1–2% Eddington luminosity. At the beginning of the outburst, the system is in the so-called hard state: the spectrum has a hard power-law shape up to a few tens to hundreds of keV, requiring a very hot, optically thin plasma (referred to as the “corona”). Then, when the system reaches high luminosities (up to a few tens of the Eddington luminosity), it transits within a few days through a bright intermediate state into the so-called soft state (referred to as the “cold disk”). In this state, the spectrum is dominated by strong and soft X-ray emission, which is commonly interpreted as thermal emission from an optically thick geometrically thin accretion flow. In the latter state, the luminosity starts to decrease and the system returns to the hard state, transiting through a faint intermediate state. The luminosities at which a system transits from hard to soft states are several times higher than the luminosity of the reverse transition (see Appendix in Dunn et al. 2010).


EE Cet (ADS 2163 B) is the southern (slightly fainter) component of the visual binary WDS 02499+0856 (Mason et al. 2001). It was discovered by the HIPPARCOS mission (Perryman et al. 1997), by noticing the variability of the combined light of both visual components. Lampens et al. (2001) performed photometric measurements of the visual pair and gave (but only for one epoch) the following values V(A) = 9.47 mag and V(B) = 9.83 mag. Pribulla & Rucinski (2006) lists the orbital parameters (orientation and separation) of WDS 02499+0856 and gave θ = 194°, ρ = 5.66 arcsec and magnitude difference ΔV = 0.07 mag (the magnitude difference can be as large as ΔV = 0.36 mag, due to photometric variability of the eclipsing binary). WDS 02499+0856 turned out to be a quadruple system, when the northern component was found to be a double-lined (SB2) binary from the DDO spectroscopic observations (Pribulla & Rucinski 2006). D’Angelo et al. (2006) re-confirmed the multiplicity of the system, and listed it among the contact binaries with additional components. Radial velocity observations from Rucinski et al. (2002) resulted in a well-defined circular orbit of the contact binary, with K1 = 84.05 km s−1, K2 = 266.92 km s−1 (q = 0.315), and an F8V spectral type. Karami & Mohebi (2007) using their own velocity curve analysis method, arrived at almost identical results for the mass ratio. Djurašević et al. (2006) presented the first model, resulting in orbital inclination of i = 78.5° and a fill-out factor of f = 32.69 per cent, T2 = 6314 K, and T1 = 6095 K, when spots were added. Their no-spot model resulted in very close value for the fill-out factor but slightly different geometrical and orbital parameters. The physical parameters derived in this study were: M1 = 1.37 M⊙, M2 = 0.43 M⊙, and mean radii R1 = 1.35 R⊙, R2 = 0.82 R⊙. It is worth noting here that the light curves analysed by these authors included the visual component in the photometric aperture with a contamination of about 54 per cent.


SEP events with gigaelectronvolt particles are generally rare. Typically about a dozen events occur during each solar cycle, although only two GLEs were reported in cycle 24, probably due to the change in the state of the heliosphere (Gopalswamy et al. 2013a, 2014a; Thakur et al. 2014). It appears that the 2012 July 23 event would have been another GLE event if it had occurred on the front side of the Sun. The purpose of this paper is to examine the event from the perspectives of CME kinematics, SEP intensity and spectrum, and radio-burst association to see if the 2012 July 23 event can be considered as an extreme particle event. The reason for considering these properties is clear from the following facts. Particles up to gigaelectronvolt energies are accelerated by strong shocks driven by CMEs of very high speeds (∼2000 km s−1) and intense, soft X-ray flares (see Gopalswamy et al. 2010, 2012b). The high speed is typically attained very close to the Sun, so the density and magnetic field in the corona are high for efficient particle acceleration (e.g., Mewaldt et al. 2012; Gopalswamy et al. 2014a). The high CME speed implies that a fast-mode MHD shock forms close to the Sun, as indicated by the onset of metric type II radio bursts, typically at heights 1.5 solar radii (Rs). CMEs attaining high speeds near the Sun have to accelerate impulsively, so these events are characterized by high initial acceleration (∼2 km s−2, see Gopalswamy et al. 2012b). This is in contrast to slowly accelerating CMEs (from filament regions outside active regions) that form shocks at large distances from the Sun and do not accelerate particles to energies more than a few tens of megaelectronvolts (Gopalswamy et al. 2015a, 2015d). Accordingly, the SEP spectra of such events are very soft, as opposed to the hard spectra of GLE events. Whether an event has a soft or hard spectrum is important information because the hard-spectrum events have stronger space weather impacts (see, e.g., Reames 2013). SEP events with gigaelectronvolt components are accompanied by type II radio bursts from meter (m) wavelengths to kilometer (km) wavelengths (Gopalswamy et al. 2005b, 2010). Type II bursts occurring at such wide-ranging wavelengths imply strong shocks throughout the inner heliosphere (Gopalswamy et al. 2005a).


SEP events with gigaelectronvolt components are accompanied by type II radio bursts from meter (m) wavelengths to kilometer (km) wavelengths


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


Vortex formation in protoplanetary discs has been shown to proceed through various mechanisms. Klahr & Bodenheimer (2003) demonstrated that in discs with a radial entropy gradient, azimuthal perturbations are baroclinically unstable and can lead to the formation of vortices. The most commonly invoked mechanism to form a large-scale vortex in a protoplanetary disc is the Rossby wave instability (RWI). The RWI can be triggered at steep radial density gradients (Lovelace et al. 1999; Li et al. 2000, 2001); such a gradient may be generated at the viscosity transition between regions in which the magnetorotational instability can operate (e.g. Varnière & Tagger 2006; Lyra et al. 2009b; Lyra & Mac Low 2012; Regály et al. 2012). Steep radial density gradients are also found at the outer edge of a gap carved in the disc by a giant planet. Indeed, hydrodynamics simulations of protoplanetary discs containing a giant planet have successfully produced large-scale vortices (e.g. Li et al. 2005; Masset et al. 2006; de Val-Borro et al. 2007; Meheut et al. 2010; Lin & Papaloizou 2011; Lin 2012), and Regály, Juhász & Nehéz (2017) presented a comparison of vortices formed at a gap edge to those formed at a viscosity transition. However, Hammer, Kratter & Lin (2017) pointed out that the short growth time-scales of the giant planet prescribed in these simulations result in unphysically large perturbations that are capable of setting up the RWI-unstable density gradient at the gap’s outer edge. When the giant planet is grown over more realistic time-scales, vortex production is significantly suppressed because viscosity has time to smooth out any steep gradients and the planetary torque itself can reshape the gap edge. Under the most favourable conditions for vortex formation, vortex lifetimes were found to be limited. One may then argue that if these asymmetries are indeed vortices formed through the RWI triggered by giant planets, we must be seeing them just after the planet has formed. However, if a RWI-generated vortex typically survives for ∼103 orbits and discs are ∼105 orbits old, observing the vortex so soon after its formation is unlikely. It is therefore uncertain whether the non-axisymmetric substructures seen in observations can be explained by this mechanism.


Our initial sample comprised all 40 stars of the MMT-HVS survey that were revised by Kreuzer et al. (2020), together with 30 runaway stars from the collection of Silva & Napiwotzki (2011) for which we were able to obtain spectra. This covers the majority of objects with high ejection velocities in that compilation. This group was complemented by the prototype hyper-runaway star HD 271791 (Heber et al. 2008), the potential hyper-runaway stars SDSS J013655.91+242546.0 (J0136+2425 for short, Tillich et al. 2009) and HIP 60350 (Irrgang et al. 2010), the extreme disk-runaway star PG 1610+062 (Irrgang et al. 2019), the four candidate HVSs from the LAMOST survey (Zheng et al. 2014; Huang et al. 2017; Li et al. 2018), and the probable Hills star S5-HVS 1 (Koposov et al. 2020). Based on proper motions from Gaia EDR3, we then carried out spectroscopic and kinematic analyses (see Sects. 3 and 4 for details) of all members of this initial sample to filter out those with both a high ejection velocity and a relatively well-constrained origin within the Galactic disk. In order to account for the fact that massive stars are typically ejected at lower velocity, we chose a mass-dependent threshold for the deduced 1σ upper limit of the ejection velocity, that is, 400 km s−1 or 320 km s−1 for stars with masses below or above 5 M⊙, respectively. The first cut applies to almost all stars from the MMT-HVS survey, while most of the others fall into the second category. The chosen thresholds roughly represent the limits for the classical ejection scenarios (see, e.g., Tauris 2015; Irrgang et al. 2018a, and references therein). A disk origin was granted when the 1σ lower limit of the inferred galactocentric plane-crossing radius was below 25 kpc (motivated by Xu et al. 2015), while visual inspection was used to judge whether the origin was sufficiently well constrained. These criteria left us with 14 stars from the MMT-HVS survey, 7 stars from the Silva & Napiwotzki (2011) sample, all 4 stars from the LAMOST survey, and the 5 individual targets mentioned above, yielding a final sample of 30 program stars, the names of which are listed in Table 1.


The C/O ratio varies across exoplanets’ host star populations (Delgado Mena et al. 2010; Brewer & Fischer 2016; Brewer et al. 2017), and this variation is likely to be reflected in the composition of exoplanet atmospheres, assuming that they are formed with the same materials as their stars. Moreover, various processes in the protoplanetary disks and the planet formation process can affect the exoplanet compositions and have a significant impact on the final C/O ratio (Öberg et al. 2011; Mordasini et al. 2016; Espinoza et al. 2017; Madhusudhan et al. 2017). For these reasons, it is necessary to consider the effects of the C/O ratio on the atmospheric chemistry and the formation of aerosols. Numerous studies have been performed using chemical models (Madhusudhan 2012; Moses et al. 2013; Venot et al. 2015; Tsai et al. 2017; Heng & Lyons 2016; Goyal et al. 2018; Drummond et al. 2019), but corresponding laboratory experiments are still largely nonexistent. Laboratory investigations can provide essential insight into the effects of the C/O ratio on the atmospheric photochemistry and the formation of aerosols. In a previous work, we performed the first laboratory experiments dedicated to the study of the chemistry in hot Jupiter atmospheres (Fleury et al. 2019). This work focused on the chemistry in atmospheres with T > 1000 K and a C/O ratio of 1 (representing C enhancement compared to the solar value of 0.54), because chemical models predict that the abundances of hydrocarbon and nitrile species increase by several orders of magnitude in these atmospheres compared to atmospheres with a low C/O ratio (Venot et al. 2015). Therefore, they can be considered as better candidates for the formation of complex organic molecules with longer carbon chains. This first study revealed that photochemical aerosols could be produced at temperatures as high as 1500 K and that water could be efficiently formed through photochemical channels. In the present work, we performed new experiments to study the chemistry in hot Jupiter atmospheres at similar temperatures (1173–1473 K) but with lower C/O ratios. We used a gas mixture of H2, H2O, and CO that represents the simplest plausible atmosphere for a hot Jupiter with a C/O ratio  1. This new study, compared with our previous work, allows us to assess the evolution of the chemistry in hot Jupiter atmospheres as a function of the C/O ratio and atmospheric composition.


Finally, our observations are consistent with the bilobate shape of the nucleus of comet 8P/Tuttle. As noted in Sect. 1, this shape is likely common among comets because it was found for four out of the six comets for which we have spatially resolved images. This is also the case of the trans-Neptunian object 2014 MU69 (Ultima Thule) observed by the New Horizon spacecraft (Stern et al. 2019). This binary configuration has some implications for the formation and evolution of 8P/Tuttle. A contact binary could result from (i) the accretion at low velocity of two primordial objects (Massironi et al. 2015; Davidsson et al. 2016), (ii) the disruption of a monolithic object due to excessive spin-up resulting from non-gravitational forces or YORP5 effect followed by a reaccretion (Boehnhardt 2004; Ćuk 2007; Hirabayashi et al. 2016), or (iii) the catastrophic disruption of a monolithic object by a collision followed by a re-accretion (Jutzi & Benz 2017; Schwartz et al. 2018). On the one hand, with a low thermal inertia compared with NEAs, the YORP effect is low for comets, in particular for NIC, which have an elongated orbit and spend most of their time far from the Sun, and it may not be sufficient to increase the spin rate of the nucleus to the point where centrifugal exceed gravitational forces. On the other hand, comet 8P/Tuttle has been on a very stable orbit for centuries, and it is likely an evolved comet, as suggested by its low activity, so that it could have been much more active in the past. For cometary nuclei, the primary cause for spin-up is torques caused by outgassing, therefore it is possible that 8P/Tuttle formed as a monolithic body and became a contact binary after its injection into the inner Solar System as a result of excessive spin-up resulting from non-gravitational forces. This scenario has been proposed for comet 67P/Churyumov-Gerasimenko by Hirabayashi et al. (2016). Alternatively, if the binary nature of comet 8P/Tuttle is the result of a primordial accretion or a catastrophic collision in the early Solar Sytem, it could have persisted until now. Similar examples are offered by some binary asteroids that can be stable over the age of the Solar System (Chauvineau et al. 1991), or as proposed by Davidsson et al. (2016) for comet 67P/Churyumov-Gerasimenko. For comet 8P/Tuttle, it is however not possible to distinguish the solution of a binary nucleus that formed in the first billion years of our Solar System (e.g., Matonti et al. 2019) from a more recent origin following its injection into the inner Solar System (e.g., Hirabayashi et al. 2016).


Most of the clumps analyzed in this study lie in the optimal range of precise Tkin determination when using NH3 (1,1) and (2,2) lines (see Sects. 1 and 3.3). Figure 8 indicates that there is a large number of cold clumps with Tkin  20 K. The gas and dust are expected to be coupled at densities above about 104.5 or 105 cm−3 (Goldsmith 2001; Young et al. 2004). The temperatures derived from dust and gas are often in agreement in the active and dense clumps of Galactic disk clouds (Dunham et al. 2010; Giannetti et al. 2013; Battersby et al. 2014; Merello et al. 2019). This is also the case for Serpens South. Low gas temperatures are associated with Serpens South ranging from 8.9 to 16.8 K with an average of 12.3 ± 1.7 K, which is consistent with the mean value of 11 ± 1 K found by Friesen et al. (2016). The gas and dust temperatures (mean and standard deviations Tgas,avg ~ 12.3 ± 1.7 K versus Tdust,avg ~ 13.4 ± 0.9 K) scatter in Serpens South, but agree reasonably well as can be most directly seen in the right panel of Fig. 8 (blue points). However, in the HMSF region W 40, we find that the measured gas kinetic temperatures are higher than the dust temperatures (mean and standard deviations Tgas,avg ~ 25.1 ± 4.9 K versus Tdust,avg ~ 19.1 ± 2.2 K), which indicates that the gas and dust are not well-coupled in W 40 and that the dust can cool more efficiently than the gas. This is consistent with the relatively weak NH3 lines associated with the core region of W 40, indicating the presence of only small amounts of dense gas. This illustrates that the interplay between gas and dust cooling and heating is not uniform in the area covered by our observations. Such a difference between Tgas and Tdust is also seen in other regions and appears to be an often encountered property of massive-star formation regions. Battersby et al. (2014) and Koumpia et al. (2015) compare gas and dust temperatures in the massive-star-forming infrared dark cloud G32.02+0.05 and the high-mass-star-forming PDR S140, respectively, and find similar discrepancies between gas and dust temperatures. This likely indicates a lack of coupling between the gas and dust (Battersby et al. 2014) or could be due to the clouds beingclumpy (Koumpia et al. 2015). These may be potential mechanisms relevant to W 40, where the gas temperature is higher than the dust temperature.


Previous theorethical studies have outlined that the [C ii] emission originates from the cold (with temperatures of a few 100 K) neutral medium and from photo-dissociation regions (PDR, Vallini et al. 2013). This seems to suggest that its presence closely traces star formation sites, resulting in a linear relation, as found by De Looze et al. (2014) and Herrera-Camus et al. (2015). While at low-redshift and close to solar metallicity such a relation is well established, as shown by several observations (De Looze et al. 2014; Herrera-Camus et al. 2018) and also numerical simulations (see, e.g. Lupi & Bovino 2020), significant deviations can arise in different ISM conditions, like at lower metallicity or in presence of a strong ionizations field, that are more typically found in the high-redshift Universe. To address the impact of such conditions, several studies have analysed the [C ii] emission from typical high-redshift galaxies, by post-processing hydrodynamic zoom-in cosmological simulations with cloudy (Ferland et al. 2017; see, e.g. Olsen et al. 2017; Pallottini et al. 2017, 2019; Katz et al. 2019), or via ad-hoc methods, as in Arata et al. (2020), or also via on-the-fly non-equilibrium chemistry (Lupi et al. 2020). The main conclusion in all these studies is that a [C ii] deficit exists at high redshift, most likely due to the starbursting nature of these galaxies rather than their metallicity, since most of these systems are close to solar (see, e.g. Vallini et al. 2015; Lupi & Bovino 2020). Other studies have evidenced a weak dependence of [C ii] on metallicity. Harikane et al. (2020) showed that the L[C ii]/SFR ratio does not show a strong dependence on metallicity, which to first approximation was interpreted as the result of the proportionality between C abundance and metallicity Z and an inverse proportionality between PDR column density and Z in a dust-dominated shielding regime (Kaufman, Wolfir & Hollenbach 2006). In this framework, if PDR give a large conribution to the [C ii] emissivity, the [C ii] luminosity is not expected to strongly depend on Z (see also Ferrara et al. 2019; Pallottini et al. 2019).


Improvements in cosmological measurement in recent years have been said to hail an era of “precision cosmology,” with observations of the cosmic microwave background (CMB) temperature anisotropies (Hinshaw et al. 2013; Planck Collaboration et al. 2016a, 2016b), baryon acoustic oscillation (BAO) wiggles in the galaxy power spectrum (Beutler et al. 2011; Anderson et al. 2014; Ross et al. 2015), luminosity distance–redshift relation of Type Ia supernovae (SNIa; Riess et al. 2004, 2007; Kowalski et al. 2008; Betoule et al. 2014), local distance ladder (Riess et al. 2016), galaxy clustering and weak lensing (DES Collaboration et al. 2017), and direct detection of gravitational waves (Abbott et al. 2017), providing constraints on cosmological model parameters at percent, or subpercent, level precision. Since the discovery of the accelerated expansion of the universe, these observations have cemented the emergence of the flat ΛCDM model as the standard model of cosmology, in which global spatial curvature is zero, and the energy budget of the universe is dominated by “dark energy” in the form of a cosmological constant, Λ. However, beyond the ΛCDM paradigm, there is a large number of dark energy models aimed at explaining the accelerated expansion of the universe (see reviews by Li et al. 2011 and Joyce et al. 2015, and references therein), and so understanding the nature of dark energy remains one of the central pursuits in modern cosmology. To this end, it has become common observational practice to constrain the dark energy equation of state, w(z), and check for deviations from the ΛCDM value of w = const. = −1. While observational probes do not indicate any significant departure from ΛCDM (Huterer & Shafer 2017), there is still room to tighten constraints and thereby rule out competing alternatives for dark energy. In particular, by tuning the parameters of alternative theories of dark energy, one can recover the behavior of the ΛCDM model at both the background expansion and perturbation levels (Li et al. 2011; Joyce et al. 2015).


Recent detections of gravitational waves (GWs) have shown evidence for a high rate of black hole (BH)–BH and neutron star (NS)–NS mergers in the universe (Abbott et al. 2016a, 2016b, 2017a, 2017b, 2017c, 2019a; Zackay et al. 2019, 2020; Venumadhav et al. 2020). However, the proposed astrophysical pathways to mergers remain highly debated. Possible compact-object merger pathways include isolated binary evolution (Dominik et al. 2012; Kinugawa et al. 2014; Belczynski et al. 2016, 2017; Breivik et al. 2016; Giacobbo et al. 2018; Bavera et al. 2019; Spera et al. 2019) accompanied by mass transfer (Inayoshi et al. 2017a; Pavlovskii et al. 2017; van den Heuvel et al. 2017), common-envelope ejection (e.g., Paczynski 1976; Ivanova et al. 2013), envelope expansion (Tagawa et al. 2018), or chemically homogeneous evolution in a tidally distorted binary (de Mink & Mandel 2016; Mandel & de Mink 2016; Marchant et al. 2016), evolution of triple or quadruple systems (Antonini et al. 2017; Liu & Lai 2017, 2018, 2019; Silsbee & Tremaine 2017; Arca-Sedda et al. 2018; Hoang et al. 2018b; Randall & Xianyu 2018; Fragione & Kocsis 2019; Fragione et al. 2019; Michaely & Perets 2019), gravitational capture (O’Leary et al. 2009; Kocsis & Levin 2012; Gondán et al. 2018b; Rodriguez et al. 2018; Rasskazov & Kocsis 2019; Zevin et al. 2019; Samsing et al. 2020), dynamical evolution in open clusters (Banerjee 2017, 2018a, 2018b; Bouffanais et al. 2019; Kumamoto et al. 2019; Rastello et al. 2019) and dense star clusters (e.g., Portegies Zwart & McMillan 2000; O’Leary et al. 2006, 2016; Samsing et al. 2014; Ziosi et al. 2014; Mapelli 2016; Rodriguez et al. 2016a, 2016b; Askar et al. 2017; Fujii et al. 2017; di Carlo et al. 2019; Zevin et al. 2019; Zhang et al. 2019), and dynamical interaction in gas-rich nuclear regions (McKernan et al. 2012, 2014, 2018; Bellovary et al. 2016; Bartos et al. 2017; Stone et al. 2017; Leigh et al. 2018; Tagawa & Umemura 2018; Yi et al. 2018; Secunda et al. 2019; Yang et al. 2019a, 2019b; Gayathri et al. 2020; McKernan et al. 2020; Tagawa et al. 2020).


Another possibly important cooling delay may arise from the phase separation of 22Ne during crystallization (Isern et al. 1991; Althaus et al. 2010). Our current best understanding is that at the small 22Ne concentrations typical of C/O white dwarfs (∼1% by number), the presence of 22Ne should not affect the phase diagram, except near the azeotropic point of the C/O/Ne phase diagram. Thus, the crystallization of the C/O core initially proceeds as in the case without 22Ne with no redistribution of neon ions between the solid and liquid phases. After a significant fraction of the core has crystallized, the temperature approaches the azeotropic point and the existing calculations indicate that the liquid phase is enriched in 22Ne relative to the solid (Segretain 1996; García-Berro et al. 2008). The 22Ne-poor solid is lighter than the surrounding liquid and floats upward where it eventually melts. This gradually displaces the 22Ne-rich liquid downward toward the solid–liquid interface until the azeotropic composition is reached, thereby releasing a considerable amount of gravitational energy. Given our very limited knowledge of the ternary C/O/Ne phase diagram (Segretain 1996; Hughto et al. 2012), this effect cannot be quantitatively implemented in our evolution models. However, we note that our current understanding of 22Ne phase separation is remarkably consistent with the missing cooling delay. In Fig. 2 we show the luminosity function obtained by adding an artificial 0.6 Gyr delay when 60% of the core is crystallized. These parameters are entirely consistent with those found in preliminary studies (Segretain 1996; García-Berro et al. 2008) and yield an excellent fit to the crystallization pile-up3. Based on the current (albeit limited) knowledge of the C/O/Ne phase diagram, we propose that the phase separation of 22Ne in the advanced stage of crystallization significantly contributes to the pile-up in the luminosity function of 0.9−1.1 M⊙ white dwarfs (Fig. 2).


Independent of the traditional redshift surveys, in this work, we constrain the VDF of ETGs using the statistics of strong gravitational lensing systems (Turner et al. 1984; Biesiada 2006; Cao et al. 2012b,c). Assuming the concordance cosmological model (ΛCDM), several efforts have been made to include the distribution of lensed image separations in the study of the galaxy mass profiles and the evolution history of galaxies. Based on the CLASS and PANELS lens sample, the first attempt to constrain the redshift evolution of galaxies (since redshift z ∼ 1) was presented in Chae & Mao (2003). This study was then extended to the study of the shape of the VDF and the characteristic velocity dispersion (Chae 2005). However, the sample size of the data available at that time did not allowed for a firm determination of the galaxy VDF. Here, we present a new approach to derive the VDF based on the lens redshift distribution (Kochanek 1992) and to constrain its evolution out to z ∼ 1, given its strong dependency on the dynamical properties of galaxies (i.e. stellar velocity dispersion) and the number density of gravitational lenses (i.e. galaxy evolution). Compared with the previous works focusing on image separation distributions, constraining a VDF through lens redshift test is unique and promising, since it does not require the knowledge of the total lensing probability and the magnification bias in the sample (Ofek, Rix & Maoz 2003). The advantages of the lens redshift test have been extensively discussed in Matsumoto & Furamase (2008), Koopmans et al. (2009), Oguri et al. (2012), and Cao et al. (2012a). Therefore, it will be rewarding to investigate the VDF and evolution of the lensing galaxies by adopting the cosmological parameters determined by Planck and using a new lens sample better representing the distribution of the galaxy properties. In this work, we focus on a newly compiled sample of 157 galaxy-scale strong lensing systems, which are all early-type lenses (E or S0 morphologies) without significant substructures or close companion galaxies (Chen, Li & Shu 2019). Throughout the paper, we assume the concordance cosmology by adopting the cosmological parameters determined by the Planck 2016 data (Ade et al. 2016).


The remarkably bright nature of radio-jetted active galactic nuclei (AGNs) allows us to observe them at extreme redshifts and thus use their properties as an observational tracer of cosmological principles (Wang et al. 2021). Blazars, in particular, benefit from increased apparent luminosities due to relativistic boosting effects (Cohen et al. 2007b), and can thus be detected over a wide range of the electromagnetic spectrum, although at the cost of being observationally compact objects with small angles between their jets and the line of sight. Conversely, AGNs with radio jets that are at a larger angle to the line of sight are harder to detect with increasing distance. Because they can be observed over such a wide range of redshifts, they provide a unique insight into cosmology, galaxy evolution, and the evolution of AGNs (Dunlop & Peacock 1990; Georgakakis et al. 2017). In addition to probing the universe by observing targets at different redshifts, one should also account for differences in their evolutionary stage, the environment they are embedded in at that time, and their interactions with that environment. Many radio surveys have already been performed to investigate radio-loud AGN populations (e.g. Becker et al. 1995; Condon et al. 1998; Cohen et al. 2007a; Intema et al. 2017) and most find self-consistent relative number ratios of radio galaxies and blazars up to a redshift of ~3 (Volonteri et al. 2011). Beyond this redshift, matters are complicated by uncertainties about the density evolution and the build-up of high black hole masses in the early universe (Blundell et al. 1999; Shankar et al. 2008). However, there seems to be a consensus that there is a relative lack of higher redshift radio galaxies even when accounting for evolutionary effects and detection limits (e.g. Wu et al. 2017; Hodges-Kluck et al. 2021, and references therein). The reason for the deficit is still not fully understood. The currently favoured explanation was suggested by Ghisellini et al. (2015): interaction of the extended radio emission with the cosmic microwave background (CMB) could efficiently quench the brightness of the extended radio lobes. Morabito & Harwood (2018) find evidence to support this model based on a comparison of simulations and observational data. In this scenario the CMB energy density dominates over the magnetic energy density at very high redshifts, so that the jet electrons interact with the CMB photons by inverse Compton (IC) scattering to cool, while the synchrotron radiation is suppressed. Although quenched, the steep-spectrum isotropic radiation of the extended structures could nevertheless be detected by telescopes operating in the long wavelength radio regime, which can test and guide the theoretical models. Ghisellini et al. (2015) proposed a number of suitable blazars to spotlight this issue, and published expected radio fluxes for different model parameters. The International LOFAR Telescope (ILT) (van Haarlem et al. 2013) offers the resolution, sensitivity, and observing wavelengths necessary to detect the extended emission from these blazars and to address the questions associated with its possible suppression. For this study, we processed and analysed one ILT observation of GB 1508+5714 at z = 4.30 (Hook et al. 1995), which is one of the most distant quasars with a detected X-ray jet (Yuan et al. 2003; Siemiginowska et al. 2003). Throughout the paper we use the following cosmological parameters: H0 = 71 km s−1 Mpc−1, Ωm = 0.27, and ΩΛ = 0.73, hence a luminosity distance of 39.8 Gpc and a conversion scale where 1″ is about 6.9 kpc for the given source.


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


In Fig. 10, we plot the variation of the ratio of the outflow contribution to the FWHM and turbulent energy. The ratio of the outflow contribution  = 1 – ‘non-outflow contribution’/‘all contributions’. We observe that the outflow has a contribution in the FWHM: about 20 per cent in the local region at the H ii region (non-outflow contribution is about 81 per cent) and about 10 per cent even in the clumps. According to Eturb  = (3/16 ln 2)Mcloud × FWHM2, outflow has a contribution in the turbulent energy up to 35 per cent in the local region at the H ii region (1 − 0.812). It has a contribution of at least 15 per cent in the clump at early stages of massive star formation, which is lower than that reported in previous studies (e.g. Bally 2016; Drabek-Maunder et al. 2016). The outflow contribution decreases with time once the outflow action stops. This indicates that the outflows do not have a significant cumulative impact on the turbulent levels during the occurrence of several outflow actions. Thus, the outflow energy contribution to turbulent energy increases insignificantly with the evolutionary stages. Our results suggest that the outflow energy is large enough to maintain the turbulent energy in the clumps and that the outflow has some (not significant) effect on the turbulent energy. However, there is a better correlation between the outflow energy and turbulent energy (see Fig. 5). Therefore, we could not determine if the outflow significantly contributes to the turbulent energy in the clumps. This is consistent with the study conducted by Maud et al. (2015). They also reported that there is a better correlation between the outflow energy and turbulent energy, but the core turbulence is not driven by the local input from the outflows. However, Drabek-Maunder et al. (2016) and Yang et al. (2018) reported that there is no correlation between the turbulent and outflow energies. Urquhart et al. (2018) found that the clump mass and evolutionary stage are uncorrelated. For similar mass of massive star, it is likely that we can observe the obvious difference of turbulent energy between clump without and with outflow. However, for statistics, the mass parameter of turbulent energy is less constrained for each evolutionary stage. All these findings imply that the outflow action has some impact on the local environment and cloud itself, but the contribution from outflow does not mainly drive turbulence. This observation is consistent with several other studies that suggest that turbulence is mostly driven by large-scale mechanisms (Ossenkopf & Mac Low 2002; Brunt, Heyer & Mac Low 2009; Padoan et al. 2009; Arce et al. 2010; Mottram & Brunt 2012; Plunkett et al. 2015; Drabek-Maunder et al. 2016).


A natural help in observational studies of particularly faint objects is provided by strong gravitational lensing. In the last few years, much progress in this field has been driven by deep observations of massive galaxy clusters, carried out in the context of large Hubble Space Telescope programmes, in particular the Hubble Frontier Fields (HFF) survey (Lotz et al. 2017). Robust lens models of galaxy clusters are built thanks to the identification of large numbers of multiply lensed sources, which can span a large redshift range (Meneghetti et al. 2017; Bergamini et al. 2019). Thanks to strong-lensing effects produced by massive clusters of galaxies located along the line of sight, sources can be magnified by large factors (ranging from μ of the order of a few up to ∼100), allowing faint, compact objects to be studied with very high spatial resolution and signal-to-noise ratios (SNR) (and suprequent recurrencies) and in some cases, to probe their structural parameters down to scales of a few ∼10 pc. In this context, the determination of the redshift of the images is a key problem. In many cases, photometric redshift estimates are accessible, but a safe determination of the redshift generally has to rely upon a spectroscopic detection, achievable only with deep observations. In this regard, in recent times considerable, further progress was possible thanks to the significant use of powerful instruments such as the Multi Unit Spectroscopic Explorer (MUSE, Bacon et al. 2015) mounted on the VLT, which has enabled the spectroscopic confirmation of hundreds of multiple images at high redshift (z > 3, e.g. Caminha et al. 2017; Lagattuta et al. 2019). This has enhanced the production of highly accurate lens models, significantly mitigating systematic uncertainties in the computation of magnification maps in lensed fields. This recent progress has allowed one to determine absolute physical quantities such as luminosities, sizes, stellar mass values and SFRs of new objects, which before were impossible to study in non-lensed fields.


When in a rotation-powered state, many spiders exhibit a nonthermal (synchrotron radiation; SR) orbitally modulated emission component in the X-ray band, attributed to particle acceleration in an intrabinary pulsar wind termination shock (IBS) and Doppler boosting of a bulk flow along the shock tangent (e.g., Wadiasingh et al. 2015, 2017; Romani & Sanchez 2016). This type of geometry/radation picture was identified over two decades ago for the BW system involving the MSP B1957+20 (Arons & Tavani 1993) and later for the gamma-ray-emitting PSR B1259-63/Be star binary system (Tavani & Arons 1997). The existence of a shock is also indicated by orbital-phase- and frequency-dependent radio eclipses of the MSP (since plasma structures at the shock attenuates the radio), where in RBs the eclipse fraction can be >50% (e.g., Archibald et al. 2009, 2013; Broderick et al. 2016; Miraval Zanon et al. 2018) of the orbital phase (while the MSP remains largely uneclipsed at inferior conjunction of the pulsar). The hard power laws inferred in X-rays imply emission due to an energetic electron population. The X-ray spectra may furthermore extend to at least ≳50 keV with no suggestion of spectral cutoffs (e.g., Tendulkar et al. 2014; Kong et al. 2017b; Al Noori et al. 2018), constraining the shock magnetic field to Bsh ≳ 1 G (Wadiasingh et al. 2017). For a given pulsar spin-down power

 erg s−1, the magnetic field Bsh at the shock can be bounded using the Poynting flux

 for a magnetic field Bw ∝ R−1 in the striped wind outside the light cylinder. The flux can be integrated over a spherical surface of area

 at the shock radius Rsh to yield an isotropic electromagnetic luminosity

. One therefore arrives at the constraint

, which is detailed in Equation (1), being generally less than 100 G. This may be recast as a condition that the ratio of electromagnetic energy density to particle pressure, σ, is less than unity, i.e., that

 is dominated by the plasma wind contribution. As will be apparent in due course (see Section 3), if the particle acceleration is as fast and efficient (attaining the synchrotron burn-off limit) as in pulsar wind nebulae, MeV synchrotron components may be observable by future medium-energy, gamma-ray Compton/pair telescopes, such as e-ASTROGAM (De Angelis et al. 2017) and AMEGO.8

8
AMEGO: https://asd.gsfc.nasa.gov/amego/index.html (McEnery et al. 2019).


In order to study the behaviour of the soft residuals and attempt to distinguish between possible origins, we require a source that evolves across a dynamic range in spectral hardness; as can be seen from fig. 8 and tables 2 and 3 of M15, the ideal source for such a study is NGC 1313 X-1. However, both the inferred (deabsorbed) hardness ratio and our ability to reliably characterize the residuals is sensitive to the modelling of the continuum. M15 show, via use of covariance spectra (see Wilkinson & Uttley 2009; Uttley et al. 2014 for a review of the technique), that the ULX continuum emission originates from at least two components that cross at ∼1 keV. Mismodelling of the continuum will therefore have an adverse effect on detecting atomic features imprinted between 0.7 and 2 keV, whilst an inability to separate out the components in the time-averaged spectrum can lead to misleading hardness ratios. To better address this problem we model each of the observations (using both PN and MOS data) using the continuum described above (and including a normalization offset to account for differing responses, typically within ∼10 per cent of unity), finding that in five out of the available 11 observations we cannot distinguish between a solution where the soft component is intrinsically strong or weak. Middleton et al. (2015) show, through use of the covariance spectrum, that the variability is entirely contained within the hard component but that a soft excess must still be present (see also Middleton et al. 2011) whilst the highest S/N data clearly show that the soft component dominates over the hard component below ∼1 keV. Whilst we can force the spectra for the five observations into what we believe to be a more appropriate deconvolution (namely by fixing the normalization of the soft component – see M15), accurate modelling of the residuals requires the normalizations to be free to vary and so we exclude these observations from our subsequent analysis.


Solar energetic particle (SEP) events as can be observed in the Earth’s orbit are determined by a combination of the underlying acceleration, injection and transport conditions, and therefore carry fundamental information on these processes. In the classical picture introduced by Reames (1999), SEP events are separated into two groups according to their characteristics: impulsive and gradual. Impulsive events, which are electron and 3He-rich, are believed to be flare-associated and therefore show a narrow angular spread in interplanetary space. These events have an impulsive increase and a shorter decay. Gradual events, on the other hand, show much broader angular SEP spreads because of their association to extended shock fronts. The gradual increase is caused by the continuous acceleration by the coronal mass ejection (CME)-driven shock front. Gradual events are usually observed in protons and heavy ions, which can be efficiently accelerated by shocks. Recent observations during the STEREO era, however, question this simple picture, especially since the nature of events showing wide longitudinal SEP spreads appears to be more complicated. It was found that 3He-rich events extend over more than 130° in longitude (Wiedenbeck et al. 2013), and that near-relativistic electron events can spread up to almost all around the Sun. Dresing et al. (2012) suggested that a strong perpendicular transport may cause the wide SEP distribution. On the other hand, it is also possible that the injection of SEPs at the Sun can be much wider than expected from a flare-like point source. The driver of such extended injection regions may be of a different nature. Diverging magnetic field lines below the source surface (e.g., Klein et al. 2008) as well as the presence of a coronal shock may play a role. The importance of EIT-waves intersecting the magnetic footpoints of far separated spacecraft are also under discussion (Rouillard et al. 2012; Park et al. 2013; Lario et al. 2014). Statistical analyses of multi-spacecraft SEP events (e.g., Lario et al. 2013) show that event characteristics, such as peak intensities, onset delays, rise times, and anisotropies, show strongly varying longitudinal dependencies from event to event. The lack of a clear correlation to a single mechanism, such as the CME speed or width as a representative of the shock strength or extent (Richardson et al. 2014), as well as varying event characteristics suggests that there is not a single process providing these wide SEP distributions (Dresing et al. 2014). Therefore, when describing an SEP event, a possible mixture of different processes as well as a varying strength of these mechanisms must be taken into account.


At present, direct detection of the CGM in emission poses an observational challenge due to its diffuse nature (with hydrogen densities of the order of nH 0.1 cm−3). Cosmological hydrodynamical simulations concur that the emission signal is faint by current observational standards (Augustin et al. 2019; Péroux et al. 2019; Corlies et al. 2020; Wijers, Schaye & Oppenheimer 2020; Byrohl et al. 2021; Nelson et al. 2021; Wijers & Schaye 2021). For these reasons, detections in emission at high-redshifts are currently limited to deep fields (Wisotzki et al. 2016; Leclercq et al. 2017; Wisotzki et al. 2018; Leclercq et al. 2020, 2022) or regions around bright quasars (Cantalupo et al. 2005; Arrigoni Battaia et al. 2015; Farina et al. 2019; Lusso et al. 2019; Mackenzie et al. 2021) while detections at z1 are now becoming available (Epinat et al. 2018; Johnson et al. 2018; Chen et al. 2019; Rupke et al. 2019; Burchett et al. 2021; Helton et al. 2021; Zabl et al. 2021). Given this limitation, absorption lines detected against bright background quasars at UV and optical wavelengths provide the most compelling way to study the distribution, kinematics and chemical properties of CGM atomic gas to date. In these quasar absorbers, the minimum column density (which is tightly correlated to the volumic gas density, see Rahmati et al. 2013) that can be detected is set by the apparent brightness of the background sources and thus the detection efficiency is independent of the redshift of the foreground absorber host galaxy. In addition, absorption line-based metallicity measurements are independent of excitation conditions (Kewley, Nicholls & Sutherland 2019; Maiolino & Mannucci 2019). In fact, unlike emission lines metallicity estimates, they are largely insensitive to density or temperature and high column density systems tracing neutral gas require no assumption on a local source of excitation (Vladilo et al. 2001; Dessauges-Zavadsky et al. 2003). Importantly, multiple state-of-the-art cosmological hydrodynamical simulations and early observational results indicate that the chemical properties of the CGM gas probed in absorption show an inhomogeneous metal distribution around galaxies with indication of a trend with galaxy orientation (Péroux & Howk 2020; Wendt et al. 2021).


In order to understand the uniqueness of the recurrence of the 4U 1630–472 outbursts and to correlate this with the lack of high-energy emission, we investigated the ASM and BAT light curves of some of the brightest and active transient black hole X-ray binaries (BHXRBs) during the seven years (2005–2011) in which both instruments were operational. Many studies of the outburst evolution of these sources have been reported in the literature (e.g. Yu & Yan 2009; Capitanio et al. 2010; Dunn et al. 2010, and references therein); the various outbursts observed do not have any detectable recurrence period and, in addition, show a complex behaviour in both soft and hard energy ranges and very different luminosities. The only exception is H 1743–322; this BHC has shown only for some years outbursts equally spaced in time, as reported by Capitanio et al. (2010). In analogy with 4U 1630–472, the outburst of H 1743–322 that occurred in 2007 has a 2–12 keV behaviour mostly identical to some of the subsequent periodical outbursts but showing a fainter hard X-ray emission; the H 1743–322 ASM 2007 peak flux (1–12 keV) is ∼250 mCrab and the BAT 2007 peak flux (15–50 keV) is ∼60 mCrab. The subsequent H 1743–322 outburst (2008–2010) presents a similar 1–12 keV flux but with a 15–50 keV flux of ∼200 mCrab. As Fig. 10 shows, the difference in the ratio between the BAT HS–HSS transition luminosity and the ASM peak flux of H 1743–322 is not enough to bring the outburst totally out of the correlation reported by Yu & Yan (2009) as in the case of the 2006 and 2008 outbursts of 4U 1630–472. However, as reported by Corbel & Tzioumis (2008), the HS–HSS transition occurred before the peak of the hard X-ray emission and thus it is only an upper limit. For the 2007 and 2008–2010 outbursts of H 1743–322, the relation between the hard X-ray luminosity peak and the outburst waiting time is also not respected. In contrast, during the subsequent outbursts, a similar waiting time corresponds to a similar peak luminosity in the 15–50 keV energy range.


One major difficulty afflicts the study of SNRs to learn about their supernovae: separating ejected material from swept-up surrounding unmodified interstellar medium (ISM) or modified CSM. Abundance clues are powerful but have limitations. Ideally, one would observe the youngest possible remnant that is large enough for adequate spatial resolution. That remnant appears to be the youngest Galactic SNR, G1.9+0.3 (Reynolds et al. 2008; see Figure 1). This object is about

100′′

 in diameter, the smallest angular size of any confirmed Galactic SNR. Unfortunately, it is very highly absorbed, with an X-ray column density of about 5 × 1022 cm−2 (Reynolds et al. 2009), implying A

V
 ∼ 23
m
, so radio and X-rays are the only useful observational channels. The angular expansion rate of 0.64 arcsec yr−1 obtained from comparing X-ray images from 2007 and 2009 (Carlton et al. 2011) gives an upper limit for the age of about 160 yr, less if (as is almost certainly the case) deceleration has occurred; spatial variations in expansion rate (Borkowski et al. 2014) are consistent with an age of about 100 yr, or a date of around 1900. The high extinction would have rendered it unobservable in optical telescopes of that era. Furthermore, its X-ray spectrum is almost entirely synchrotron emission, making it a member of the small class of X-ray synchrotron–dominated SNRs. However, long observations with Chandra have allowed the detection of thermal emission from small regions (Borkowski et al. 2011, 2013b), with spectroscopic widths of ∼14,000 km s−1 confirming the large expansion proper motion, refined with a second Chandra observation (Carlton et al. 2011). The distance is still uncertain; the high column—higher than the entire Galactic column along nearby sight lines—suggests an association with the Galactic center, and a provisional distance of order 8.5 kpc has been assumed. Nearer would be very unlikely in view of the high absorption, but too much farther would make the expansion proper motion unreasonably large. An H i observation with the Giant Metrewave Radio Telescope (Roy & Pal 2014) has been used to set a lower limit of 10 kpc, certainly consistent with the known properties of G1.9+0.3.