The theoretical models mentioned above have made assumptions. The validity of these assumptions needs to be examined. Besides, all these models involve parameters to be determined. These problems could be better understood through numerical simulations. Hurlburt et al. (1994) performed a two-dimensional numerical simulation of compressible flow on downward overshooting. They investigated the dependence of subadiabatic extent δ on stability parameter S. They revealed a scaling law of δ ∝ S−1 in the penetrative layer and δ ∝ S−1/4 in the overshooting layer, respectively. This result is in good agreement with Zahn’s analytic model (Zahn 1991). Freytag et al. (1996) performed two-dimensional numerical simulations with a realistic description of radiation and ionization on A-type stars and DA white dwarf stars. They described the overshooting as a diffusive process, and derived an exponential decay parameter for the diffusion. Early attempts of low-resolution three-dimensional numerical simulations on overshooting were made by Singh et al. (1994; upward overshooting), Singh et al. (1995, 1998), and Saikia et al. (2000) (downward overshooting). The scaling laws derived from the numerical simulations of downward overshooting (Singh et al. 1995, 1998; Saikia et al. 2000) agree well with Zahn’s analytical model. Only a qualitative result was given in the numerical simulations of upward overshooting (Singh et al. 1994). High-resolution numerical simulations of downward overshooting across a wide range of parameters were presented by Brummell et al. (2002). They confirmed the −1/4 scaling law of the thermal adjustment overshooting layer, while the −1 scaling law of the nearly adiabatic penetrative layer was absent in the simulations. Based on a semianalytic model, Rempel (2004) argued that the absence of the nearly adiabatic penetrative layer is caused by the large energy flux specified in the numerical simulations. Numerical experiments on Boussinesq flow were performed by Korre et al. (2019). They reported steeper scaling laws of δ ∝ S−1/3 or δ ∝ S−1/2, depending on the steepness of the background radiative temperature gradient. Simulations with realistic physical variables on stellar core convection were performed by Browning et al. (2004) and Brun et al. (2005). The effects of rotation and magnetic field are considered. They found that the penetrative convection yields a prolate shape of a nearly adiabatic region. Kitiashvili et al. (2016) performed 3D radiative hydrodynamic simulations of the outer layer of a moderate-mass star (1.47 solar mass). Their result discovered a nearly adiabatic layer and a deeper subadiabatic layer. The recent work of Brun et al. (2017) simulated the differential rotation and overshooting in solar-like stars. Their result indicated that slow rotators favor a wider overshooting region near the poles and fast rotators at mid-to-low latitude. Hotta (2017) performed numerical simulations on the solar overshooting with very low energy fluxes F. He found that the overshooting distance obeys a scaling law of δ ∝ F0.31. Käpylä (2019) conducted numerical experiments on downward overshooting by considering the effect of the smoothness of the heat conduction profiles. He discovered that the power-law index of the overshooting distance on the energy flux is smaller in the smooth heat conduction profile than in the step profile. Efforts on prediction of 321D turbulent theory were made by Arnett et al. (2015) and Arnett & Moravveji (2017). They separated the overshooting region into three layers: a fully mixed layer, a partially mixed wave layer, and an extra diffusive mixing layer. With the scale analysis of turbulent plumes and eddies, Viallet et al. (2015) discussed the three possible regimes of turbulent overshooting: a diffusion-dominated regime (only mix composition), a penetrative regime (transition within the boundary layer), and an entrainment regime (mix both entropy and composition). The selection criterion of different regimes during a stellar evolution calculation is not well defined yet.


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.


We have tested the pixel-ICA algorithm, i.e., a non-parametric method proposed by Morello et al. (2014, 2015) to detrend Spitzer/IRAC primary transit observations, on simulated data sets. Systematics similar to the ones present in Spitzer/IRAC data sets are obtained by combining instrumental jitter with inter- or intra-pixel sensitivity variations. A variety of jitter timeseries is used to test the pixel-ICA method with:

1.
periodic signals with different frequencies, phasing, and shape;

2.
non-stationary signals with varying amplitudes or frequencies;

3.
sudden change.

The detrending performances of pixel-ICA method have been compared with division by a polynomial function of the centroid, in this paper PCD method, and PLD method (Deming et al. 2015). Here we summarize the main results found:

1.
Pixel-ICA algorithm can detrend non-stationary signals and sudden changes, as well as periodic signals with different frequencies and phasing, relative to the transit.

2.
Inter-pixel effects are well-detrended with pixel-ICA method.

3.
Even if the instrument PSF is not entirely within the array of pixels, pixel-ICA leads to results which are consistent at ∼1σ with the input parameters.

4.
In most cases, pixel-ICA outperforms PCD method, especially if the instrument PSF is narrow, or it is not entirely within the photometric aperture.

5.
Intra-pixel effects are only detectable if the PSF is relatively small.

6.
Intra-pixel effects cannot be totally detrended by any of the three methods, but pixel-ICA, in most cases, outperforms PCD method, which is largely case-dependent. Also, pixel-ICA method provides consistent results within the error bars.

7.
It is possible to fit the astrophysical signal after detrending or together with the other components. The only differences are registered if at least one of the non-transit components has a similar shape at the time of transit, in which case the first approach is preferable, but the two results were consistent within 1σ.

8.
The PLD method, updated to include cross-term between pixel fluctuations and the astrophysical signals, lead to very similar results than pixel-ICA, particularly if the astrophysical signal is fitted together with the other components.

In conclusion, we have found in a variety of simulated cases that pixel-ICA performs as well or better than other methods used in the literature, in particular polynomial centroid corrections and PLD (Deming et al. 2015). The main advantage of pixel-ICA over other methods relies on its purely statistical foundation without the need of imposing prior knowledge on the instrument systematics, therefore avoiding a potential source of error. The results of this paper, together with previous analyses of real Spitzer/IRAC data sets (Morello et al. 2014, 2015), suggest that photometric precision and repeatability at the level of one part in 104 can be achieved with current infrared space instruments.


Given the number densities within the mass-dissociation index plane of Fig. 8, we now ask ourselves whether known dissociated clusters, such as the Bullet cluster, are expected in L210N1024NR? The Bullet Cluster has a mass of $\sim 1.5 \times 10^{15} \, {\rm M}_{\odot }$ (e.g. Clowe et al. 2004; Bradač et al. 2006; Clowe et al. 2006) and we estimated a dissociation index of SBullet ∼ 0.335 ± 0.06. As seen in Fig. 8 there are no Bullet cluster analogues (structures of approximate mass and dissociation) in L210N1024NR, this is unsurprising as a simulation requires a significantly larger volume than that of L210N1024NR ((210cMpc h−1)3) to expect such an object (e.g. Lee & Komatsu 2010; Thompson & Nagamine 2012; Bouillot et al. 2015; Kraljic & Sarkar 2015; Thompson et al. 2015). From the distribution presented in Fig. 8, it is trivial to estimate the required cosmological volume (the effective volume, Veff) to expect structures of a given mass and dissociation index. By separating the 2D distribution on the mass-dissociation index planes into the component 1D distributions of mass and dissociation the effective volume is computed as
(12)$$\begin{eqnarray}
V_\text{eff}~^{-1} &=&\int \int \,{\rm{ d}} S \, {\rm{ d}} M \phi (S, M) \\
&=& \int _{S_\text{a}}^{S_\text{b}} \, {\rm{ d}} S \phi _S(S) \int _{M_\text{a}}^{M_\text{b}} \, {\rm{ d}} M \phi _M(M)~,
\end{eqnarray}$$where ϕS(S) is the number density function associated with S and $\phi _\mathit {M}(\mathit {M})$ is the mass function presented in Fig. 7. Assuming a probable range of S = 0.335 ± 0.06 and $1 \lt M \lt 2 \times 10^{15} \, {\rm M}_{\odot }$ we estimate a number density ∼4.92 × 10−10 Mpc−3 or that an effective volume of ∼2.03 Gpc3 would be required to observe a single Bullet-like cluster. This result is inline with the number density estimate of the order of ∼10−10 Mpc−3 by Thompson et al. (2015), which improves on previous estimates (e.g. Lee & Komatsu 2010; Thompson & Nagamine 2012; Bouillot et al. 2015) due to more sophisticated halo finding methods (e.g. Behroozi, Wechsler & Wu 2013). Conversely, it was estimated by Kraljic & Sarkar (2015) (utilizing the same halo finder as Thompson et al. 2015) that given an effective volume of ∼14.6 Gpc3, no Bullet cluster analogues are expected, however as indicated by a pairwise velocity distribution it would be expected that present binary halo–halo orbits have the potential to form a Bullet-like object.


All responses calculated in this paper only account for the direct response to a perturbing potential. In general, though, the response also has an indirect component that arises from the fact that neighboring regions in the disk interact with each other gravitationally. This self-gravity of the response, which we have ignored, triggers long-lived normal-mode oscillations of the slab that are not accounted for in our treatment. Several simulation-based studies have argued that including self-gravity is important for a realistic treatment of phase spirals (e.g., Darling & Widrow 2019a; Bennett & Bovy 2021). Using the Kalnajs matrix method (Kalnajs 1977; Binney & Tremaine 2008), we have made some initial attempts to include the self-gravity of the response in our perturbative analysis, along the lines of Weinberg (1991). Our preliminary analysis shows that the self-gravitating response is a linear superposition of two terms: (i) a continuum of modes given in Equation (12), dressed by self-gravity, that undergo phase mixing and give rise to the phase spiral; and (ii) a discrete set of modes called point modes or normal modes (see Mathur 1990; Weinberg 1991) that follow a dispersion relation. The continuum response can be amplified by self-gravity when the continuum frequencies, nΩ
z
 + kv

x
, are close to the point-mode frequencies, ν. Depending on the value of k, the normal modes can be either stable or unstable. Araki (1985) finds that in an isothermal slab the bending normal mode undergoes fire hose instability below a certain critical wavelength if σ

z
/σ ≲ 0.3, while the breathing normal mode becomes unstable above the Jeans scale. In the regime of stability, the normal modes are undamped oscillation modes in absence of lateral streaming (Mathur 1990) but are Landau damped otherwise (Weinberg 1991). For an isothermal slab with typical MW-like parameter values, the point modes are strongly damped since their damping timescale (inverse of the imaginary part of ν) is of order their oscillation period (inverse of the real part of ν), which turns out to be of order the vertical dynamical time, h

z
/σ

z
. Moreover, the normal-mode oscillations are coherent oscillations of the entire system, independent of the vertical actions of the stars, and are decoupled from the phase spiral in linear theory since the full response is a linear superposition of the two. Based on the above arguments, we conclude that self-gravity has little impact on the evolution of phase spirals in the isothermal slab, at least in the linear regime. We emphasize that Darling & Widrow (2019a), who found their phase spirals to be significantly affected by the inclusion of self-gravity, assumed a perturber-induced velocity impulse with magnitude comparable to the local velocity dispersion in the solar neighborhood; hence, their results are likely to have been impacted by nonlinear effects. Moreover, the self-gravitating response of an inhomogeneous disk embedded in a DM halo, as in the simulations of Darling & Widrow (2019a), can be substantially different from that of the isothermal slab. We intend to include a formal treatment of self-gravity along the lines of Weinberg (1991) in future work.


Methyl formate is the species for which the largest number of transitions were identified. In total 24 transitions from both A and E species were observed (18 unblended), with energy levels between 100 and 500 K, allowing to constrain the properties of the emitting region from the LTE model. We ran a set of models using one source component of 0.6″ in size (the angularresolution of the ALMA band 6 observations), and we modified the temperature and column density to fit the observed spectra. However, it was difficult to fit all the lines with only one component. The problem became more evident when using the deuterated substitutions, CH3OCOD and CH2DOCOH, and the vibrationally excited states νt = 1 and νt = 2. We have detected 12 transitions from CH3OCOD and four transitions from CH2DOCOH (three and two, respectively, are blended with other species), with upper energy levels between 90 and 170 K. In both cases the model gave better results when decreasing the temperature with respect to the best CH3OCOH model. On the other hand, the vibrationally excited lines (13 unblended transitions from νt = 1, and one transition from νt = 2), supported the high temperature model. Therefore, we built a model of the source with two components. One warm and compact component at 200 K and a size of 0.35″ (that of the continuum compact emission obtained by ALMA Band 7 observations, Gerin et al. 2017), and another larger (0.6″, approximately the angular resolution of the Band 6 observations) and colder component at 60 K. Figure B.4 shows two examples of the best one component models obtained using the main CH3OCOH (200 K), and the deuterated methyl formate lines (60 K), together with the final two component model. While some species give reasonable agreement with observations using either model (mostly those which observed transitions have similar energy levels), there are others (besides the ones discussed above) that fail in one of the models (e.g. HNCO and t-CH3CH2OCOH). We have checked that using other temperatures (between 50 and 250 K) in the one component models does not reproduce satisfactorily the observations. For the vibrationally excited states, we only used the compact component at 200 K, since the low temperature one does not contribute much to the line intensities. Indeed, energy levels of the observed transitions range between 300 and 500 K, supporting this scenario. We have also observed five transitions of 13CH3OCOH, with energies ≤200 K and intensities of the order of 500 mK or below. Since the lines are weak, any of the models give reasonable agreement with the observations. Acetaldehyde is the other species for which many lines are observed. We have detected 15 transitions (10 unblended) from the main species, with energies between 100 and 300 K. We have also detected one transition arising from the deuterated substitution CH3CDO, and four transitions (two of them blended) from the vibrational state νt = 1, with energy levels of ~300–400 K. We used the same model as methyl formate, except for CH3CHO νt = 1, for which only the compact and hot component was considered. The model allows to reproduce all transitions reasonably well, except for a few lines that are overestimated: two CH3OCOH transitions (Fig. B.1, second panel), three CH3OCOH νt = 1 lines (top panel in Fig. B.1, and second panel in Fig. B.3), and two lines from CH3CHO (see Fig. B.3, second and third panels). These are transitions with the lowest energies (~100 K) and the highest line strengths and Einstein coefficients, and may consequently have high opacities. We estimate the error in the fit to be ~50%.


The direct detection of the first gravitational waves from the merger of two heavy black holes (BHs) in GW 150914 confirmed one of the toughest predictions of Einstein’s theory of general relativity. But while satisfying the world of physics in general, for astrophysics this was only the beginning: many were surprised by the large BH masses of, respectively, 36 and 29  M⊙ (Abbott et al. 2016), showcasing how the new field of multimessenger astrophysics had just re-opened the field of stellar evolution in a spectacular fashion. Stellar mass BHs had previously been revealed by their interaction in binary systems (Orosz et al. 2011), but the maximum stellar BH mass in our Milky Way is not higher than roughly 15–20  M⊙ (Belczynski et al. 2010). While we know that very massive stars (VMS) above 100  M⊙ exist (Crowther et al. 2010; Vink et al. 2015), this mass is significantly diminished via stellar winds already during core hydrogen (H) burning (Vink & Gräfener 2012). The heavy nature of the BH, as measured by LIGO/VIRGO therefore supported the assumption that the gravitational wave event occurred in a part of the Universe still pristine in its enrichment with heavy elements (‘metallicity (Z)’), lowering stellar wind mass-loss (Vink, de Koter & Lamers 2001; Vink & de Koter 2005). A low-Z solution was widely accepted until the announcement of a 70  M⊙ BH in LB-1 (Liu et al. 2019), spurring stellar evolution theorists to avoid heavy mass-loss in the Milky Way (Belczynski et al. 2020; Groh et al. 2020), either by arbitrarily lowering the mass-loss rates of VMS – seemingly contradicting VMS mass-loss calibrations (Vink & Gräfener 2012) – or by invoking the presence of a strong dipolar surface magnetic field that could quench the wind (Petit et al. 2017). While such magnetic fields in some 5–10 per cent of massive OB stars do indeed exist, no B-fields have yet been detected in VMS (Bagnulo et al. 2020). The problem of the formation of a $70\, \mathrm{ M}_\odot$ BH in a solar metallicity environment apparently resolved itself when the spectral signatures of LB-1 were re-interpreted (Abdul-Masih et al. 2020; El-Badry & Quataert 2020).


To obtain a more complete picture of the physical processes that shape star formation in the early Universe, very deep radio surveys overwide areas of sky are required to complement deep submillimetre surveys. Previous work has used high-resolution radio observations, typically at 1.4 GHz, as a method of pinpointing the position of submillimetre sources detected in single-dish surveys (Ivison et al. 2002; Chapman et al. 2005); however, such work has been limited by the depth of available radio sky surveys,with dedicated deep surveys over only small regions of sky, resulting in a view biased towards the brighter radio sources. Studies have largely included limited radio spectral coverage of SMGs, focusing on the nature of the FIRC and its relation to properties such as stellar mass and redshift (e.g. Yun et al. 2001; Ivison et al. 2010; Smith et al. 2014). The Low Frequency Array (LOFAR; van Haarlem et al. 2013) has opened up new ways of studying galaxies in the radio, and a number of studies have used LOFAR’s capabilities to investigate this relationship between star formation and radio luminosity in the low-frequency regime – for example Gürkan et al. (2018), Read et al. (2018), Smith et al. (2021), and Wang et al. (2019a). However, these studies generally investigate the statistical properties of large samples of galaxies, in optically selected samples at low redshift (z ≲2), rather than probing the shapes of individual radio spectra. Thomson et al. (2019) conducted an in-depth study of high-frequency (>610 GHz) spectral curvature in SMGs, finding evidence of curved spectra that they attributed to spectral ageing of the synchrotron emission from star formation; their results implied estimated starburst ages consistent with expected SMG lifetimes. Studies at low frequencies, where we may be able to observe absorption processes affecting the shape of the spectrum, have been hampered by a lack of sufficiently deep, wide-area data. More comprehensive observations of the shape of the radio spectrum, extending to lower frequencies, can provide a probe of the physical conditions that give rise to extreme star formation in SMGs. Calistro Rivera et al. (2017) exploit LOFAR’s frequency range to investigate the spectral shapes of star-forming galaxies and AGN, finding evidence of low-frequency spectral flattening in the star-forming sample. This sample is also constrained in redshift, focusing on local galaxies rather than the peak of star formation at z > 2, and so does not probe the bulk of the highly star-forming SMG population. Chyży et al. (2018) also find weak spectral flattening in local star-forming galaxies with LOFAR but largely attribute this slight effect to synchrotron losses, predicting stronger low-frequency spectral flattening due to free–free absorption at high redshift, where galaxies with high SFRs are more common.


It is now clear that binary stars hold the key to understanding the formation of many planetary nebulae (PNe; Jones & Boffin 2017a). However, with much of the recent focus being placed on common envelope evolution (Boffin & Jones 2019), the role of wider binaries remains almost completely unconstrained (Tyndall et al. 2013). To date, only three wide binary central stars of PNe have confirmed periods (Jones et al. 2017) with other systems either being so wide that they are resolved (Ciardullo et al. 1999) or displaying composite spectra with giant companions (Tyndall et al. 2013). Four central star systems are known to be barium stars (Bond, Pollacco & Webbink 2003; Miszalski et al. 2012, 2013; Löbling, Boffin & Jones 2019) with only one having a known orbital period (LoTr 5; Jones et al. 2017; Aller et al. 2018). Barium stars are mostly – but not only: see e.g. Escorza et al. (2019) – giant stars of spectral type G-K that display enhanced abundances of carbon and s-process elements such as barium and strontium, and are now known to all be long-period binaries (100 d ≲ Porb ≲ 104 d; McClure, Fletcher & Nemec 1980; Jorissen et al. 2019). The chemical contamination of barium stars is believed to be due to accretion of chemically enriched material from an evolved binary companion, likely through wind (Boffin & Jorissen 1988) or wind Roche lobe overflow (WRLOF; Theuns & Jorissen 1993; Nagae et al. 2004). WRLOF will occur when the acceleration radius of the asymptotic giant branch (now a white dwarf in these barium star systems) star’s stellar wind is comparable to or greater than its Roche lobe radius (Mohamed & Podsiadlowski 2012), meaning that the wind itself is strongly influenced by the binary potential and can be accreted on to the companion via the first Lagrangian point. This accreted material chemically contaminates the surface of the companion as well as increases its spin rate due to the conservation of angular momentum (Theuns, Boffin & Jorissen 1996). Intriguingly, the amount of material required to account for the observed contamination is often in excess of that which would be expected to result in critical rotation rates in the companion, providing an indication that significant (and as yet not understood) angular momentum losses must be experienced in these systems (Matrozis, Abate & Stancliffe 2017). PNe with barium central stars offer an important window into this process as the presence of the short-lived nebula (τ ≤ 30 000 yr; Jacob, Schönberner & Steffen 2013) means that the mass transfer has occurred too recently for significant changes in the companion’s spin rate, and moreover the nebula itself traces the mass-loss history of the system as it is formed from the material that has escaped the binary potential (Jones 2018).


Since their initial discovery with AIA on board the Solar Dynamics Observatory (SDO), HCs have been generally regarded as proxies for magnetic flux ropes (MFRs; volumetric plasma structures with magnetic field lines that wrap around a central axis). This is supported by the following observational studies: (1) Cheng et al. (2014a) observed an HC that showed helical threads winding around an axis. Simultaneously, cool filamentary materials descended spirally down to the chromosphere, providing direct observational evidence of an intrinsic helical structure for the HC. (2) Cheng et al. (2011) reported that an HC can grow during an eruption, similar to the MFR growth process according to the classic magnetic reconnection scenario in eruptive flares. Song et al. (2014a) presented the formation process of an HC during a coronal mass ejection (CME) and found that the HC was formed from coronal arcades through magnetic reconnection. These works further support the idea that an HC is an MFR structure based on the relation between the HC and magnetic reconnection. (3) Cheng et al. (2014b) found that an HC was initially cospatial with a prominence. Then a separation of the HC top from that of the prominence was observed during the eruption initiated by the ideal kink instability (Török et al. 2004). It is widely accepted that a prominence/filament can exist at the dip of a flux rope (Rust & Kumar 1994). Therefore, this observation offered further important support for the idea that an HC is an MFR; beside an HC, several lines of observations in the lower corona have also been proposed as MFRs, including sigmoid structures in an active region (Titov & Démoulin 1999; McKenzie & Canfield 2008) and coronal cavities in quiescent regions (Wang & Stenborg 2010). A sigmoid has either a forward or reverse S-shape with enhanced X-ray emissions (implying an entity of high temperature) with its center straddling along the polarity inversion line of the hosting active region. Zhang et al. (2012) showed that the HC initially appeared as a sigmoidal structure and then changed to a semi-circular shape. Therefore, a sigmoid and an HC might represent the same structure, and their different shapes are likely from different perspectives and evolution phases. Both structures feature a high temperature, a possible result of flare magnetic reconnection (e.g., Song et al. 2014a, 2014b). A coronal cavity, on the other hand, which is observed as a dark circular or oval structure above the solar limb in coronal images with temperatures close to the background corona (Fuller et al. 2008; Gibson et al. 2010; Kucera et al. 2012), is also interpreted as an MFR. As mentioned, the long-studied feature of solar filaments/prominences shown best in Hα images has been interpreted as being situated along the dip in the MFR. Therefore, a prominence lying in the dip of a coronal cavity is not rare. The eruption of a coronal cavity (or filament) from a quiescent region does not show a high-temperature signature like an HC, which might be attributed to a lack of obvious heating acquired from the weak magnetic reconnection (e.g., Song et al. 2013).


Among the existing IACT systems, HESS has the largest FoV and hence provides the highest sensitivity for the diffuse γ-ray flux. Its electron spectrum analysis technique could be directly used to obtain a measurement of the diffuse Galactic γ-ray flux above energies of several TeV in the Galactic Ridge (|l|  30°, |b|  2°) region; see Figs. 3 and 4. A multi-year exposure of HESS could be sufficient for detection of the diffuse emission even from regions of higher Galactic latitude. This is illustrated in Fig. 5, where thick blue and red data points show mild high-energy excesses of the electron spectra derived by Kraus (2018), Kerszberg et al. (2017), Kerszberg (2017) over broken power-law models derived from the fits to lower energy data. Comparing these excesses with the level of the IceCube astrophysical neutrino flux and with the Fermi/LAT diffuse sky flux from the region |b| > 7° (corresponding to the data selection criterium of HESS analysis Kerszberg et al. 2017; Kerszberg 2017) we find that the overall excess flux levels are comparable to expected diffuse γ-ray flux from the sky region covered by the HESS analysis (the quoted systematic error on the electron flux is Δlog(EFE) ≃ 0.4). The overall excesses within 805 and 1186 h of HESS exposures (Kraus 2018; Kerszberg 2017) are at the levels of >4σ for the analysis of Kraus (2018) and 1.7σ for the analysis of Kerszberg (2017). A factor-of-ten longer exposure (which is potentially already available with HESS) could reveal a higher significance excess at the level of up to 5σ. Such an excess is predicted in a range of theoretical models including interactions of cosmic rays injected by a nearby source (Andersen et al. 2018; Neronov et al. 2018; Bouyahiaoui et al. 2019) or decays of dark matter particles (Berezinsky et al. 1997; Feldstein et al. 2013; Esmaili & Serpico 2013; Neronov et al. 2018) or a large-scale cosmic ray halo around the Galaxy (Taylor et al. 2014; Blasi & Amato 2019).


Sagittarius A* (Sgr A*) is a supermassive black hole system that allows one to observationally test the aforementioned GRMHD models of accretion flows (Goddi et al. 2017). Millimeter-Very Long Baseline Interferometry (mm-VLBI) is capable of resolving the shadow of the event horizon (Falcke et al. 2000), making this an ideal laboratory not only to tests Einstein’s General Theory of Relativity (GR) but also to investigate electron acceleration in the vicinity of a black hole. Most of the radiative models for Sgr A*, which are based on post-processing GRMHD simulations, assume that electrons have a thermal, relativistic (Maxwell–Jüttner) distribution function, and that the proton-to-electron temperature ratio is constant across the simulation domain (Goldston et al. 2005; Noble et al. 2007; Mościbrodzka et al. 2009; Dexter et al. 2010, 2012a; Shcherbakov et al. 2012). When the proton-to-electron temperature is constant, the disk dominates the images and spectra since most of the matter resides there. We have recently extended these radiative models by making the temperature ratios a function of the plasma β parameter, where

$\beta = \frac{P_{\textrm{gas}}}{P_{\textrm{B}}}$

β=

P

gas

P
B

 is the ratio of gas to magnetic pressures. In these extended models, the electrons are hotter in the more magnetized plasma, which is usually outflowing from the system. The reason for this is that the previously mentioned models do not recover the flat radio spectra. The β parameterization enforces that the disk emission is suppressed by significantly decreasing the temperature of the electrons in those regions. As a consequence of this, the jet will be the dominant source of emission. These modifications to the electron temperature model allowed us to recover some basic observational characteristics of Sgr A* (a roughly flat radio spectral slope and a size vs. wavelength relationship that is in agreement with observations) (Mościbrodzka & Falcke 2013; Mościbrodzka et al. 2014; Chan et al. 2015b,a; Gold et al. 2017). Our model for the electron temperatures as a function of the β plasma parameter is now roughly confirmed with extended-GRMHD simulations that self-consistently take into account the evolution of the electron temperatures (Ressler et al. 2015, 2017). Moreover, GRMHD simulations with the new electron temperatures can naturally explain the symbiosis of disks and jets observed in many accreting black hole systems (Falcke & Biermann 1995; Mościbrodzka et al. 2016a).


The ice layer covering refractory grains in dense MCs consists mainly of amorphous water ice (Tielens & Allamandola 1987). A key property of the icy mantle is its porosity, which determines its ability to adsorb, desorb, and trap atoms and molecules. The actual degree of porosity of interstellar ices is still debated. There are indeed indications that the buildup of the ice in cold environments results in the formation of pores as shown by laboratory measurements (e.g., Dohnálek et al. 2003; Bossa et al. 2014) and simulations (Cuppen & Herbst 2007; Clements et al. 2018). These two studies, based on Monte Carlo simulations, suggest a significant level of porosity at the surface/subsurface, in particular in cold and dense environments. On the other hand, UV photons, exothermic reactions, and energetic ions tend to compact astrophysical ices. Estimates of the timescale for mantle compaction calculated from experiments range from a few up to 50 Myr (Raut et al. 2008; Palumbo et al. 2010; Accolla et al. 2011). It has also been suggested that the compaction of icy mantles may not be completed within the typical lifetime of MCs if they consist of ice mixtures, since compaction is slower for mixtures than for pure ices (Palumbo 2006). Transient events like the impact of energetic ions can also generate cavities in the ice surface and/or subsurface. Such energetic events induce a strong local increase of the ice temperature, produce fragments, and are associated with sputtering and evaporation along the ion track. Such cavities are short-lived since the heated ice rearranges while relaxing (Mainitz et al. 2016). The missing O–H dangling features near 3700 cm−1 in astronomical spectra have been taken as an indication of a low level of porosity of interstellar ices. However, laboratory data and simulations indicate that the absence of the O–H dangling modes does not necessarily imply the complete absence of porosity (Raut et al. 2007; Isokoski et al. 2014).


SHT has some inherent geometrical advantages, especially for large-angle and deep surveys. A significant advantage is that the spherical coordinates apply to wide-angle surveys like BOSS without any flat-sky approximation. A traditional P(k) analysis relies on the flat-sky approximation to distinguish between transverse and line-of-sight modes, which is critical for accurately representing RSDs and distinguishing continuum foregrounds from line signal. By contrast, in the SHT formalism, both foregrounds and linear RSDs take exact, simple forms. This geometric advantage is shared with the related analysis technique of spherical Fourier-Bessel (SFB) decomposition (Fisher et al. 1995; Heavens & Taylor 1995; Leistedt et al. 2012; Rassat & Refregier 2012; Yoo & Desjacques 2013; Lanusse et al. 2015; Liu, Zhang & Parsons 2016; Grasshorn Gebhardt & Doré 2021), which, in addtion to spherical harmonic decomposition, involves a further Fourier-Bessel transform and data-compression along the line-of-sight. However, SFB does not share another important feature of SHT, which is its ability to capture redshift-dependent change over cosmological time in deep surveys. For deep surveys, structure growth and changes in star formation rate break the assumption of translational invariance in the line-of-sight direction, rendering the P(k) or SFB statistic insufficient. However, since Cℓ(z, z′) does not compress data along the line-of-sight direction, it describes redshift evolution. A study (Mondal et al. 2022) of simulated 21-cm data from the EoR found that an implementation of the SHT technique, MAPS (Mondal, Bharadwaj & Datta 2018; Mondal et al. 2019, 2020), obtains ∼2 times more stringent error bars on model parameters than techniques that fail to capture redshift evolution due to data compression along the line-of-sight, such as P(k) or SFB. A final geometric advantage is that Cℓ(z, z′) describes the data in observing coordinates of angle and frequency (or, equivalently, redshift) rather than re-gridding the data on to cosmological distances in an assumed cosmological model. An MCMC likelihood analysis that constrains cosmological parameters would therefore not need to recompute the data statistic at each step, which in principle would be needed for a P(k) or SFB analysis.


Sudden outbursts of NH3 simultaneously with H2S detected with the ROSINA-DFMS instrument on the Rosetta S/C point to the presence of abundant ammonium hydrosulphide in or on carbonaceous grains from comet 67P/Churyumov-Gerasimenko. There seems to be a clear distinction between the nucleus ice, where H2S and NH3 exist independently and grains, where they desorb together. S2 is much more abundant on grains compared to water than in the ice of the comet, while S3 is found only in grain impacts. This higher abundance points to radiolysis in these grains, which means they must have been exposed to energetic particles over an extended time. While for operational reasons, S4 could not be measured close to the dust impacts, S4 was clearly identified in periods where the coma was very dusty (Calmonte et al. 2016). Longer sulphur chains very likely are refractory, not sublimating at temperatures reached in the instrument or on grains in the coma. While Sn can also be formed from pure H2S ice by photo processing (Cazaux et al. 2022), the fact that S3 is clearly related to dust and is not found in the normal nucleus ice, where H2S is quite abundant, indicates that S3 is a product of radiolysis of the ammonium salt. In addition, photo processing of H2S results not only in Sn, but also in H2S2 (Cazaux et al. 2022), a species not detected in the DFMS m/z 66 and m/z 65 (HS2) spectra. This exposure rules out a contemporary formation of the salt on the surface or in the interior of the comet or a formation of the salt in the mid-plane of the protoplanetary disc, while the comet accreted. A pre-stellar formation is therefore likely. The salt is semivolatile, less volatile than water and could probably have survived quite high temperatures. It seems that on these grains, acids and ammonia are all locked in salts, be it sulphur, halogens, or carbon bearing acids like HOCN. If indeed, a relatively large part of sulphur and nitrogen is therefore in a semivolatile state in these grains, then the depletion of nitrogen in comets and of sulphur in star-forming regions could probably be explained, primarily because salts escape detection unless they experience temperatures above water sublimation. With the JWST S/C in orbit, there is hopefully the possibility to detect salts, or at least several of the acids in ices, which are supposed to be part of ammonium salt, like HOCN, H2CO, and formamide while looking for ammonium salts in star-forming regions and possibly comets.


Any massive stellar source from ~8 M⊙ can burn hot enough to completely ionise the surrounding molecular material to form an H II region (Wood & Churchwell 1989; Churchwell 1990; Kurtz 2005) and destroy any complex chemical tracers that are traditionally used to understand the kinematics of their natal environments and their accretion discs. Initial arguments by Walmsley (1995) argued that high accretion rates will cause a very dense H II region that is optically thick to radio emission and thus the H II would not be seen. However, for heavily accreting massive YSOs the onset of the H II region could be delayed via stellar bloating (Palla & Stahler 1992; Hosokawa & Omukai 2009; Hosokawa et al. 2010; Kuiper & Yorke 2013) where the effective temperature of the star is much cooler than it would be considering a main sequence star of the same luminosity. In these models, a halt or considerable reduction in accretion (≪10−3 M⊙ yr−1), or growth beyond ~30−40 M⊙, will result in the YSO contracting to a “main-sequence” configuration, heating significantly, and being able to create an H II region. The fine details of this transition are still somewhat unclear since they depend on the assumed accretion law and the initial conditions chosen for the stellar evolution calculations (Haemmerlé & Peters 2016). Observations in the infra-red (IR) have been made in search of cool stellar atmospheres that point to bloated stars, however these studies remain inconclusive (Linz et al. 2009; Testi et al. 2010). Alternative scenarios are that H II regions can be gravitationally trapped at very early ionisation stages (see Keto 2003, 2007), or flicker due to chaotic shielding of the ionising radiation by an accretion flow, leading to a non-monotonous expansion (Peters et al. 2010b). Hyper Compact (HC) H II regions (0.03 pc) are thought to be the earliest ionisation stage and therefore could relate to the halt of accretion, be a marker of a transition phase.


The final location of close-in giant planets in our models reflects the strength of the tides that we include in our modeling, which play a very important role in the decay of planetary orbits. These are dynamical tides (e.g., Lai 1997; Ivanov & Papaloizou 2004, 2007, 2011) and in our simulations we used a formulation given by Ivanov & Papaloizou (2007) as described inSect. 2. However, the impulse approximation used in the evaluation of dynamical tides becomes a poor approximation when the circularization proceeds (e.g., Mardling 1995a,b) and the eccentricity becomes low. Equilibrium tides become then effective (e.g., Beaugé & Nesvorný 2012 and references therein) and the tidal evolution may occur on a longer timescale. In short, at the beginning of the orbital evolution that leads to the formation of hot/warm Jupiters, dynamical tides are important in forcing the decay of the orbit. In the last part of the dynamical evolution when the eccentricity has become low, equilibrium tides are more important in determining the location where the planet stops. Unfortunately, at present it is not known when and how the two tides switch. When we change the magnitude of two tides, the final location of the planets can be adjusted (Beaugé & Nesvorný 2012). However, rather than introducing artificial effects, we continue to use dynamical tides in our simulations even for low eccentricities but we stop our simulations when the energy, decreasing from the tide at the pericenter, overcomes the orbital energy leading to a clustering of tidally circularized planets around 0.02 au. However, the final distribution of the inclination of the planets does not depend on this choice and highly misaligned planets would be produced anyway. Since the tidal evolution of planets with arbitrary inclinations is still not well known, we assume that planetary inclination is not significantly changed during tidal evolution (Barker & Ogilvie 2009). Thus, the planets maintain the inclination they have when the circularization begins.


The catalogue used in this work is based on a far-IR sample selected in the ∼2 deg2-wide COSMOS field and obtained within the Herschel-PEP survey (Lutz et al. 2011). We consider the latest released blind catalogue selected at 160-μm (DR1, 7047 sources) with >3σ flux density, corresponding to a flux limit of ∼9.8 mJy. The choice of considering as parent sample a far-IR catalogue is guided by the necessity of having several detections at different wavelengths for each system to constrain the dust masses, and yet with a very simple selection function (see Section 3.1). From the original 160-μm selection, we built a multiband catalogue taking advantage of the extensive multiwavelength coverage in the COSMOS field. Concerning the other far-IR PACS band (100 μm) and the mid-IR 24-μm band, we use the association available in the DR1 release and based on the maximum likelihood technique (Sutherland & Saunders 1992; Ciliegi et al. 2001). For the cross-match with the SPIRE far-IR bands (250, 350, and 500 μm), we used the same catalogue considered in previous PACS-based works (i.e. Gruppioni et al. 2013; Delvecchio et al. 2015), the ones provided by the HerMES collaboration (Roseboom et al. 2010) using the Spitzer-MIPS 24-μm positions as priors to extract the SPIRE fluxes. Finally, the IRAC/optical/UV fluxes taken from the COSMOS2015 catalogue (Laigle et al. 2016) were merged to the PACS-160-μm sample by matching the 24-μm counterparts listed in both. The COSMOS2015 is NIR selected, where objects have been detected from the sum of the UltraVISTA-DR2 YJHK and z++ images. By construction, in comparison to the previous i-selected catalogue, this catalogue is missing a fraction of blue, faint, star-forming galaxies (Laigle et al. 2016). For this reason, we decided to cross-match the far-IR sources with no counterparts in the COSMOS2015 catalogue with the Ilbert et al. (2009) i-selected catalogue. Totally, among the 160-μm selected sources (7047), 6002 are with 24-μm counterparts (${\sim }86{{\ \rm per\ cent}}$), of which 5993 with available NIR or optical counterparts (${\sim }99.9{{\ \rm per\ cent}}$, 5783 in the COSMOS2015 and 210 in the Ilbert et al. 2009 catalogue). While the cross-matching with the optical/NIR bands does not involve almost any source loss, a moderate (14${{\ \rm per\ cent}}$) but not negligible fraction of the far-IR sources does not have 24-μm counterparts. A fraction of these sources are likely spurious sources, as shown by the simulations done for the DR1 release PEP catalogue (∼5 per cent at the 3σ flux level). In Section 3.1, we will describe our method to correct for incompleteness and for the presence of spurious systems.


Figure 12 shows the results of our tidal evolution calculations. The left panel of Fig. 12 shows the planetary rotational evolution of GJ 1148 b due to star–planet tides. After ~850 Myr, GJ 1148 b reaches a rotation period that is 2∕3 of the orbital period, and remains there with Prot = 27.5 d. During the integration the planetary semi-major axis and eccentricity are mostly unaffected. An asymptotic rotation period that is shorter than synchronous and 2/3 of the orbital period is expected for eb ≳0.24 in the constant Q tidal model (Goldreich & Peale 1966; Cheng et al. 2014). The time for GJ 1148 b to reach asymptotic rotation is inversely proportional to the initial Prot, as long as the initial Prot is much less than 27.5 d, and it depends on the other parameters of GJ 1148 b according to Eq. (3) of Barnes (2017) and Eq. (15) of Cheng et al. (2014). The rotational period of GJ 1148 b is thus very likely much longer than the orbital periods of the hypothetical exomoons, which could be dynamically stable only with orbital periods between 0.7 and 2 d. The right panel of Fig. 12 shows that the longer rotational period of GJ 1148 b (Prot = 27.5 d) leadsto strong orbital decay of the stable exomoon orbits due to tidal interactions with the planet. An exomoon eventually reaches the Roche limit where it is tidally disrupted by the gas giant. Not even one hypothetical “stable” exomoon in the context of Sect. 5.3.1 had survived this test. The maximum time a Mars-like exomoon could survive is ~55 M yr, while for Titan-like moons the maximum survival time is longer, ~255 M yr. The latter is longer by roughly the mass ratio of Mars to Titan, which can be understood from Eq. (2) of Barnes (2017) and Eq. (16) of Cheng et al. (2014). These timescales are optimistic since the orbital decay would start before the planet reaches the asymptotic spin state. In both cases the survival times are much shorter than the age of the system. Therefore, given the relatively fast orbital decay in the small stable region around the planet, we conclude that exomoons around GJ 1148 b are unlikely to exist.


Previous observations of AGN that investigate correlations between αOX and Eddington ratio have revealed some similarities with X-ray binary outbursts at high Lbol/LEdd, but these comparisons have not been possible below the critical Lbol/LEdd ≲ 10−2, where an inversion in this correlation is predicted to occur. At higher Eddington ratios of Lbol/LEdd ≳ 10−2, single-epoch X-ray and UV observations of large samples of AGN have previously revealed a hardening of αOX as Lbol/LEdd drops from ∼1 to ∼10−2 (e.g., Vignali et al. 2003; Strateva et al. 2005; Steffen et al. 2006; Just et al. 2007; Grupe et al. 2010; Jin et al. 2012; Wu et al. 2012; Trichas et al. 2013; Vagnetti et al. 2013). This correlation was also observed in multi-epoch UV/X-ray observations of the fading of Mrk 1018 (Noda & Done 2018), which confirms this behavior in an individual AGN. However, the predicted softening of αOX below Lbol/LEdd ≲ 10−2 (thus causing an inversion in the correlation between αOX and Lbol/LEdd) has not been previously observed. This is primarily due to the difficulty of robustly measuring both αOX and Lbol/LEdd for AGN below Lbol/LEdd ≲ 10−2, for three main reasons. First, at low Eddington ratios, AGN are often dust-obscured (Fabian et al. 2008), and thus measuring their intrinsic UV luminosities (and αOX) is difficult. Second, broad emission lines often disappear in low-luminosity AGN below Lbol/LEdd ≲ 10−2, making it difficult to measure MBH (and LEdd). Third, using a sample of AGN with a wide range of Eddington ratios to trace how αOX changes as a function of Lbol/LEdd can be hampered by the

 scaling of the thin disk temperature with MBH at a fixed Eddington ratio. If the AGN sample has a large range in MBH, this can cause an additional scatter in αOX. Thus, we would ideally use a sample of AGN with a narrow range in MBH, but the difficulty of measuring MBH at Lbol/LEdd ≲ 10−2 also hampers the construction of such a sample. In this paper, we will use a new method to bypass all of these issues, with the goal of extending this spectral comparison between X-ray binaries and AGN to Lbol/LEdd ≲ 10−2.


We assume the time-scales we observe here are generated in the corona itself (and note that longer time-scale changes will be driven by the disc outside of the corona) and are made visible by a changing electron temperature and density as a result of local turbulence and coupling to mass accretion rate propagations through the flow from rout to rin. We note that we can discount variations in the seed photon population as the driver for changes in the power spectrum, as the UV emission from the disc is established to be considerably less variable than the corona in NLS1s (Leighly 1999; Smith & Vaughan 2007; Ai et al. 2013; Alston, Vaughan & Uttley 2013; Done & Jin 2016). We assume that the variability generated locally at each radius (rν) is at the viscous frequency (see Churazov et al. 2001) such that
(9)$$\begin{eqnarray}
r_{\nu } = \left[ \frac{2\pi \nu }{\alpha }\left(\frac{H}{R}\right)^{-2}\right]^{-2/3} ,
\end{eqnarray}$$where the frequency is in units of c/Rg (see e.g. Kato, Fukue & Mineshige 1998; Arévalo & Uttley 2006). In the above, α and $\frac{H}{R}$ are the dimensionless viscosity parameter of Shakura & Sunyaev (1973) and scale height of the accretion disc, respectively. We assume that our frequency range of interest, 0.01−1 mHz (i.e. the range over which we can practically fit to the data) corresponds to radii between the ISCO (rin) and some radius within the true outer edge of the corona (i.e. rout ≤ rcorona). The actual frequencies generated in our model therefore depend on the SMBH spin and the combination $\left(\frac{H}{R}\right)^2 \alpha$ (and somewhat on the SMBH mass – although here the range is small). Given the reported high spin values for these bright AGNs (Ogle et al. 2004; Fabian et al. 2013; Done & Jin 2016; Kara et al. 2017; Buisson et al. 2018b), we expect the ISCO to sit at ∼1.25Rg. For the corona at the ISCO to produce variability above our upper frequency limit of 1 mHz requires $\left(\frac{H}{R}\right)^2 \alpha \gtrsim 0.01$. We note that for the mass range subtended by our AGN sample (from 106.00 to 106.63 M⊙, see Table 2), should we instead assume zero spin (rin = 6Rg), the viscous frequency at rin is lower and we have strong curvature in our observed bandpass.


We subsequently considered the time evolution of a number of selected cores (based on the requirement that we have sufficient data to follow at least 200 kyr of evolution), finding a remarkably similar chemical evolution in all cores, including one that is strongly stabilized by turbulence and magnetic field and therefore not going through gravitational collapse. Assuming a more or less chemically homogeneous initial condition, the chemical evolution of the cores, particularly regarding deuteration effects, is thus very similar. Of course, environmental effects such as the local cosmic ray ionization rate could induce potential differences, by changing the ionization degree. Similarly, metallicity effects at lower densities may depend on the local conditions. At least within one filament, it is however plausible that the deuteration fraction is indeed indicative of chemical age. We find here that about two free-fall times (as defined for cylindrical systems, see Toalá et al. 2012) are sufficient to reach core deuteration fractions of ≳0.1. We finally investigated also the radial structure of the core, finding overall similar properties as in the isolated collapsing cores studied by Körtgen et al. (2017). The H2 ortho-to-para ratio appears to be approximately flat and only weakly dependent on radius. Both the deuteration fraction and the gas surface density show a peak on scales of about 1000–2000 au, which is particularly pronounced in the case of parallel magnetic fields. As found previously, this peak moves outward with increasing turbulent Mach number, indicating the amount of support against gravity. The difference in the visibility of the peak may result from the difference in the fragmentation mode in both cases, as previously described by Seifried & Walch (2015), thus potentially affecting the structure of the resulting cores. Overall, our results have shown that the observed high deuteration fraction in prestellar cores can be readily reproduced in simulations of turbulent magnetized filaments. We further found that deuteration fractions of order 0.1 can be produced independent of the specific history of the cores, both for high and low virial parameters. The latter suggests that deuteration is potentially very efficient.


The broad-band spectral energy distribution (SED) of blazars is characterized by two broad humps, one at optical/UV/X-ray bands and the other in the HE γ-ray band (see Padovani et al. 2017 for a recent review). It is believed that the first peak (low-energy component) is mostly due to synchrotron emission from relativistic electrons, whereas the origin of the second component is highly debatable. Within conventional leptonic scenarios, this component is produced when the synchrotron-emitting electrons inverse Compton up scatter the photons of internal (synchrotron self-Compton, SSC; Ghisellini, Maraschi & Treves 1985; Maraschi, Ghisellini & Celotti 1992; Bloom & Marscher 1996) or external (external inverse Compton, EIC; Sikora, Begelman & Rees 1994; Błażejowski et al. 2000; Ghisellini & Tavecchio 2009) origin. The nature of the external photon fields depends on the distance of the emitting region from the central black hole (Sikora et al. 2009) and can be dominated either by the photons directly emitted from the accretion disc (Dermer, Schlickeiser & Mastichiadis 1992; Dermer & Schlickeiser 1993) or disc photons reflected from the broad-line region (BLR; Sikora et al. 1994) or IR photons emitted from the dusty torus (Błażejowski et al. 2000). Recently, after associating TXS 0506+056 with the IceCube-170922A neutrino event (IceCube Collaboration et al. 2018a,b; Padovani et al. 2018), it is more evident that the HE component could be initiated by the interaction of energetic protons when they are effectively accelerated in the blazar jets. The HE component can be either from proton synchrotron emission (Mücke & Protheroe 2001) or from secondary particles from pion decay (Mannheim & Biermann 1989; Mannheim 1993; Mücke & Protheroe 2001; Mücke et al. 2003; Böttcher et al. 2013). In the latter case, blazars are also sources of very high energy neutrinos (Ansoldi et al. 2018; Keivani et al. 2018; Murase, Oikonomou & Petropoulou 2018; Padovani et al. 2018; Sahakyan 2018; Cerruti et al. 2019; Gao et al. 2019; Righi, Tavecchio & Pacciani 2019; Sahakyan 2019).


In the following, all measurements and maps derived from snapshots prior to t = 800 Myr are therefore using the original simulation (R+13), with the others extracted from the simulation at 1 pc resolution (for the gaseous component). Note that star formation was turned on at t ∼ 745 Myr in the simulation as to avoid gas being prematurely consumed. Details on the implemented recipes for star formation, stellar feedback (photoionization, radiative pressure, supernova explosions) are described in R+13. Adding on AGN feedback would significantly impact on the distribution, kinematics and physical status of the gas, specifically for the close environment of the black hole (Ciotti & Ostriker 1997; Haehnelt, Natarajan & Rees 1998; Silk & Rees 1998; Kauffmann & Haehnelt 2000). For the present simulations, however, we do not include the potential feedback from an AGN, thus focusing on a time window (t ∼ 750–830 Myr) when we consider that the AGN itself is quiet (or in an ‘off-state’). This is partly justified by the assumption that AGN have low duty cycle at low redshift and for black holes of a few 106 M⊙ (Haehnelt & Rees 1993; Wang et al. 2009; Shankar et al. 2010; Shankar, Weinberg & Miralda-Escudé 2013) and by the short time range we are considering. More importantly, it allows us to narrow down our study to probe the interplay between the dynamical evolution and the effect of star formation (similarly to e.g. Levine et al. 2008; Hopkins & Quataert 2010a). Turning on the AGN in such a simulation would be paramount to understand any potential fuelling cycle starting from the large-scale down to the vicinity of the black hole, and such an implementation has already been included in ramses by a direct calculation of the Bondi accretion rate (see Teyssier et al. 2011; Gabor & Bournaud 2014, and references therein). It would nevertheless require to probe various feedback schemes, and triggering mechanisms, which is beyond the scope of the present paper.


The coronal mass ejections (CMEs) are frequent discharge of huge energy and massive magnetized plasma from the solar corona into the heliosphere. They are of paramount importance in space physics for their key role in extreme space weather and geo-effectiveness, e.g. (Gosling 1993; Low 2001; Schrijver & Siscoe 2010; Cannon et al. 2013). In last few decades, the understanding of CMEs improved significantly because of space and ground-based observational data with the help of various modelling efforts. The studies are focused on the morphological and kinematic evolution of CMEs in the heliosphere, e.g. (Lindsay et al. 1999; St Cyr et al. 2000; Zurbuchen & Richardson 2006; Chen 2011; Webb & Howard 2012; Wang et al. 2016; Lugaz et al. 2017). By considering the number of CMEs emitted from the Sun during solar maximum and variations in their respective speeds, the interaction between multiple CMEs in the heliosphere is expected to be more frequent. The collision of multiple CMEs highly affect their dynamic evolution properties and contribute to enhanced geo-effectiveness, e.g. (Wang, Wang & Ye 2002; Farrugia & Berdichevsky 2004; Lugaz, Manchester IV & Gombosi 2005; Wang et al. 2005; Xiong et al. 2007; Shen et al. 2011, 2012; Lugaz et al. 2012; Temmer et al. 2012). To predict space weather effects near the Earth, an accurate estimation of arrival time of CMEs at the Earth is crucial (Mishra & Srivastava 2014). Besides this, the study of CME–CME and CME–solar wind interactions provide unique observational evidences to understand energy dissipation of large-scale magnetic clouds in interstellar medium and authenticate the physical processes predicted theoretically. Therefore, interaction of multiple CMEs needs to be examined in detail. The various results obtained from studies have justified CME–CME collision as an inelastic/elastic collision or superelastic collision, e.g. (Lugaz et al. 2012; Shen et al. 2012, 2016; Lugaz et al. 2017; Mishra et al. 2017). The magnetohydrodynamics (MHD) numerical simulations have striven to understand the physical mechanism involved in CME–CME interaction, CME–CME driven shock interactions and their consequences, e.g. (Niembro et al. 2015; Jin et al. 2016; Shen et al. 2016; Wu et al. 2016).


An example of these implications is the so-called ‘dust budget crisis’ introduced in Section 4.4: the dust masses currently estimated at z > 5 are not compatible with standard dust production channels and require an overhaul in our models of the initial mass function for star formation, of supernova production rates, or of dust growth in the ISM. Overall, the dust production rate would need to increase by one to two orders of magnitudes, as shown by Rowlands et al. (2014). The growth of dust grains through accretion in the ISM has been proposed as a solution (e.g. Mancini et al. 2015; Michałowski 2015; Popping et al. 2017), but there are doubts on the efficiency of accretion at high z, where high dust temperatures due to the CMB (see Section 3.3) keep the desorption time-scale for accreted materials short (Ferrara et al. 2016). The dust budget crisis is not only a problem at high redshift; it is observed, e.g. in the Magellanic Clouds (SMC, LMC). As explained in Srinivasan et al. (2016) using the dust mass fits by Gordon et al. (2014), the dust replenishment time-scale in the SMC from stellar sources alone is expected to be larger than the dust destruction time-scale and, in the worst-case scenario, longer than the lifetime of the Universe. Similarly, the ratio between the best LMC dust mass estimate by Gordon et al. (2014) and the dust injection estimates by Riebel et al. (2012) results in an LMC replenishment time-scale of 34 ± 8 Gyr, exceeding the age of the Universe. Both the high redshift and the local Universe, therefore, show a dust budget crisis that could be alleviated – and, in the best case scenario, fully resolved – if the actual dust masses turned out to be lower than currently estimated, as our results suggest. More specifically, Rowlands et al. (2014) mention that dust opacity needs to be increased by just a factor of 7 to solve the high-redshift crisis (provided dust destruction by SNe is not efficient); in the LMC, the aforementioned replenishment time-scale would decrease to less than 2 Gyr if the dust mass were decreased by a factor of 20.


Compared to various studies based on in situ measurements of MFR structures after eruption, the origination of CME-MFRs before and during eruptions remains elusive due to the complex environment in the solar source region and limited observations. At the present time, there are certain hypotheses on the formation process of MFRs. Some studies indicate that MFRs could exist prior to the eruption. For example, both Fan (2001) and Magara (2004) reported findings from magnetohydrodynamic (MHD) simulation that a twisted MFR initially formed below the photosphere can partially emerge into the low corona by magnetic buoyancy. Other studies suggest that the presence of preeruptive MFRs is not necessary and MFRs could be built up in the corona via magnetic reconnection processes associated with flares (Amari et al. 2003; Moore et al. 2001; Antiochos et al.1999; Jiang et al. 2021a, 2021b). To understand the physical processes more precisely for flare–CME events, extensions of the standard 2D flare model have been proposed to account for much broader ranges of quantitative measurements with three-dimensional (3D) features intrinsic to realistic solar eruptions (Longcope et al. 2007; Aulanier et al. 2012; Priest & Longcope 2017; Aulanier & Dudík 2019). For example, quasi-3D models have been developed with a nonvanishing magnetic field component along the axis of the MFR and to illustrate the scenario that sequential reconnection along the magnetic polarity inversion line (PIL) forms the MFR in the first place (van Ballegooijen & Martens 1989; Longcope et al. 2007; Schmieder et al. 2015). This scenario has been widely applied to infer and interpret magnetic reconnection properties based on the observed flare ribbon morphology (Qiu et al. 2002, 2004, 2010; Hu et al. 2014; Kazachenko et al. 2017; Zhu et al. 2020). From such analyses, Qiu et al. (2004) illustrated that there is a temporal correlation between the magnetic reconnection rate and the acceleration of the CME (considered as the eruptive MFR) in the low corona. Such a correlation has been further established by Zhu et al. (2020) based on a statistical study of ∼60 events. In addition, Qiu et al. (2007) and Hu et al. (2014) showed a correlation between the magnetic reconnection flux and the flux contents of the corresponding ICME/MC flux ropes based on modeling results employing in situ spacecraft measurements. These results support the hypothesis that CME-MFRs can be formed by magnetic reconnection during the corresponding flare process. Recent simulation results also indicate clearly that the reconnection flux contributes to the axial (toroidal) flux of the CME-MFR in the early stage (Jiang et al. 2021a; Inoue et al. 2018).


Although it is still unknown why the disc fragmentation for the primordial cases is well described by the simple relation such as equation (1), an important fact is that a barotropic EOS with γeff ≃ 1.1 approximately represents the gas thermal evolution during the cloud collapse for $n \lesssim 10^{19}\, \mathrm{cm}^{-3}$ (Omukai & Nishi 1998). In fact, several simulations study the disc fragmentation assuming the same barotropic EOS with γeff = 1.1 for n ≤ nth, resulting in the evolution described by equation (1) (Susa 2019). Since nth is only the characteristic quantity for this case, the simple scaling of equation (1) may be convincing. This suggests that the disc fragmentation with a different EOS should provide different evolution of Nc,b. For instance, it is well known that adding a tiny amount of heavy elements and dust grains alters the EOS of a collapsing cloud (e.g. Omukai 2000; Bromm et al. 2001; Omukai et al. 2005; Schneider et al. 2006, 2012a; Smith, Sigurdsson & Abel 2008; Jappsen et al. 2009; Safranek-Shrader, Milosavljević & Bromm 2014; Chiaki et al. 2015; Chiaki, Yoshida & Hirano 2016). While previous studies demonstrate that the dust cooling enhances the fragmentation during the cloud collapse (e.g. Meece, Smith & O’Shea 2014; Smith et al. 2015; Chiaki & Wise 2019), its effect on the disc fragmentation remains to be further explored. Tanaka & Omukai (2014) investigate the evolution of the circumstellar disc in metal-poor environments developing 1D semi-analytical models. They predict that the discs with $Z \sim 10^{-5}\!-\! 10^{-3}\, \mathrm{Z}_{\odot }$ are subject to the efficient dust cooling and are more unstable than those for the primordial cases. Machida & Nakamura (2015) consider the disc fragmentation with various metallicities $0 \le Z \le 1\, \mathrm{Z}_{\odot }$, performing a suite of 3D numerical simulations. They find qualitative differences between the cases with $Z \lesssim 10^{-4}\, \mathrm{Z}_{\odot }$ and $Z \gtrsim 10^{-4}\, \mathrm{Z}_{\odot }$; the vigorous disc fragmentation only occurs for the former metal-poor cases. Whereas Machida & Nakamura (2015) use the metallicity-dependent barotropic EOS, Chiaki & Yoshida (2020) recently report 3D simulations of the disc fragmentation solving the energy equation with relevant thermal processes coupled with a non-equilibrium chemical network. They find that for the metal-poor cases with $Z \le 10^{-3}\, \mathrm{Z}_{\odot }$, the disc fragmentation does not necessarily prevent the mass growth of the most massive protostar as many clumps are short-lived owing to the frequent merger or tidal disruption events. Although the above studies suggest the metallicity-dependence of the disc fragmentation, they both only follow the short-term evolution for $\sim 100\, \mathrm{yr}$ since the first emergence of a protostar.


Comparison with z ≈ 2−4galaxies. High-ionization UV lines have been detected in the spectra of z ≳ 2 galaxies through gravitational lensing (e.g., Stark et al. 2014; Patrício et al. 2016; Vanzella et al. 2016, 2017; Berg et al. 2018), spectral stacking (e.g., Nakajima et al. 2018b; Rigby et al. 2018; Saxena et al. 2020), and deep spectroscopic observations (e.g., Erb et al. 2010; Maseda et al. 2017; Amorín et al. 2017; Nanayakkara et al. 2019). The EWs of He II, O III]λ1666, and C III] from these works are larger than those measured in the average spectra of our LAEs, with the exception of some of the MUSE sources at z ≳ 3 studied by Patrício et al. (2016) and Nanayakkara et al. (2019), some of the stacks from Nakajima et al. (2018b), and some of the VANDELS He II emitters from Saxena et al. (2020). The EWs from Nakajima et al. (2018b) are computed from average spectra of a z ≈ 3 LAE population whose median UV luminosity is about two orders of magnitude brighter than ours. Most of the 2.4   z   3.5 UV-selected, low-luminosity galaxies from Amorín et al. (2017) have higher He II and C III] EWs, most likely because of their higher SFR (see Fig. 2). The line measurements from Saxena et al. (2020) are performed on the stacked spectra of UV continuum, bright He II emitters (−19   MUV   −22). The strong line emitters from Erb et al. (2010) and Berg et al. (2018) are brighter and more massive than the median value of our LAEs. The lensed galaxies from Vanzella et al. (2016, 2017) are among the least massive, most metal-poor, young, and faintest systems observed at z ∼ 3. With MUV >  −16, the source ID14 from Vanzella et al. (2017) is roughly one order of magnitude fainter that the faintest LAE in our sample, while the source ID11 from Vanzella et al. (2016) has an remarkable blue UV slope (β = −2.95). Recently, Du et al. (2020) measured C III] EWs in z ∼ 2 analogs of galaxies in the reionization era, obtaining values from 13.2 Å down to 1 Å, reaching values as low as those of our LAEs. The authors also found differences in the C III] EW depending on the selection criteria, with higher values of C III] EW for emission lines rather than for continuum-selected galaxies. Mainali et al. (2020) detected two targets with C III] emission reaching EW ≈ 17 − 21 Å in the spectra of z ∼ 2 galaxies selected for their strong rest-optical line ([O III]λ5007+Hβ) EWs. These values are above the ones of our LAEs and are similar to those observed at z >  6 (e.g., Stark et al. 2015b, 2017; Hutchison et al. 2019).

Nakajima et al. 2018b
Nakajima et al. (2018b)
Nakajima et al. (2018b)

Background Background Similarities Similarities Differences Differences


Here we shall set the potential

 and make the change of variable

; hence, the vortical parts of the footpoint equations of motion are cast into a Hamiltonian form. The Hamiltonian describing the dynamics of magnetic footpoints driven by the vortical component of the turbulence on the photosphere is
50

The footpoint Hamiltonian

 has the physical dimension of a frequency (s−1). From Figure 2 in Rincon et al. (2017), we further notice that the vortical component of the photospheric surface velocity field has a structure reminiscent of 2D Euler turbulence, which admits a vortex point representation (Eyink & Sreenivasan 2006) also on the sphere (Pavlov et al. 2001). There are three important parameters that can be extracted from the vortical component of photospheric turbulence. These parameters are the typical amplitude of the velocity fluctuations

, the correlation length

, and the correlation time

 of the turbulence, where

 is the rms amplitude of the fluctuating stream function Φ and

 is the angular size of the turbulent eddies on the source surface. These three independent parameters

,

, and

 can all be derived from a more fundamental quantity, which is the covariance function

, i.e., the autocorrelation function of the turbulent stream function (Creasey & Lang 2018). The covariance function is sufficient to characterize the vortical component of the surface flows provided that the stream function Φ does not significantly deviate from a stationary isotropic Gaussian random field on the sphere. Hamilton equations with the Hamiltonian (50) determine a genuine problem of chaotic mixing (Ott 1993; Morrison 1998) on the sphere. We emphasize that mixing of footpoints on the photosphere relies on the time dependence of the Hamiltonian. In fact, the footpoint dynamics is regular (quasi-periodic) when the Hamiltonian is a constant of time, independently of the number of modes involved in its decomposition. The reason is that the dynamics generated by 1 degree of freedom Hamiltonians, here for the pair of canonically conjugate variables μ and ϕ, is regular. A simple mathematical proof of this statement is given by Morrison (1998). In one version of the protocol used by Giacalone & Jokipii (2004) to model the magnetic footpoint dynamics, the time dependence of the flow results from the (random) phase of the (complex) toroidal coefficients being renewed at random times, following the work of Simon et al. (1995).


Methanol is believed to be formed on dust grains (Watanabe & Kouchi 2002) by subsequent hydrogenation of carbon monoxide, and its detection towards prestellar cores is already a challenge for current models given the absence of efficient desorption processes in these sources. Thermal desorption is out of question because of the low dust temperature. Recent laboratory studies showed that the photo-desorption of methanol from ices is likewise negligible (Bertin et al. 2016; Cruz-Diaz et al. 2016). The main desorption products when irradiating pure and mixed methanol ices are photo-fragments of methanol. An alternative route to explain the presence of methanol in the gas phase is the reactive/chemical desorption that has been theoretically proposed by Garrod et al. (2007) and Vasyunin & Herbst (2013) and experimentally studied by Dulieu et al. (2013) and Minissale et al. (2016). On the other hand, c-C3H2 is mainly formed in the gas phase (e.g. Spezzano et al. 2013) and is expected to preferentially trace dense and chemically young gas, that is, gas where C atoms have not yet been mainly locked into CO. This gas rich in C atoms is expected in the outer envelope of an externally illuminated dense core (e.g. Aikawa et al. 2001). However, towards L1544, c-C3H2 only appears to trace one side of the core, the one closer to the sharp N(H2) edge and away from the CH3OH peak. This indicates that photo-chemistry is not uniformly active around L1544, most likely because the distribution of the envelope material (belonging to the filament within which L1544 is embedded) is not uniform, as is clearly shown by the Herschel map in Fig. 1. This figure shows that methanol traces a region farther away from the southern sharp edge of the N(H2) map, which is possibly more shielded from the ISRF and where most of the carbon is locked in CO. CH3OH is preferentially found at the northern edge of L1544 because here photochemistry does not play a major role (so C is locked in CO) and the density is low enough to maintain a higher fraction of CH3OH in the gas phase, but above the threshold value for CO freeze-out, a few ×104 cm-3 (Caselli et al. 1999). Based on the Keto & Caselli (2010) model (that was updated by Keto et al. 2014), the volume density at the distance of the methanol peak is predicted to be 8 × 104 cm-3, which is just above the threshold value. In contrast, cyclopropenylidene has the most prominent peak towards the southern sharp edge of the H2 column density and extends along the semi-major axis of the core, almost parallel to the south-west edge of the N(H2) map. This behaviour is also clearly shown in Fig. 2, where the integrated intensities of both methanol and cyclopropenylidene are plotted against N(H2). c-C3H2 is also present at values of N(H2) that are lower than those of methanol, and it maintains a flat intensity profile, suggestive of a layer-like structure, with no significant increase towards the core centre. The CH3OH intensity instead shows a sharp rise up to column densities of about 1.6 × 1022 cm-2, and it declines at higher values.

Background Background Background Background Background Differences


Extended radio emission in galaxies is associated with both radio jets and lobes and with outflows, seen often as aligned radio sources in the opposite directions with respect to the central compact radio core. Giant radio galaxies (GRG) are extreme cases of this phenomenology with jets and lobes extending on ∼ Mpc scales suggesting that they are either very powerful or very old site for electron acceleration. In this respect, GRGs have a crucial role in the acceleration of cosmic rays over large cosmic scales (e.g. Kronberg et al. 2004), in the feedback mechanism of AGNs into the intergalactic and intracluster medium (e.g. Subrahmanyan et al. 2008) and in the seeding of large-scale magnetic fields in the universe (e.g. Kronberg et al. 2004) and they are excellent sites to determine the total jet/lobe energetics in AGN-dominated structures (see e.g. Colafrancesco 2008, Colafrancesco & Marchegiani 2011). To date our knowledge of GRGs (see e.g. Ishwara-Chandra & Saikia 1999, 2002; Lara et al. 2001; Machalski, Jamrozy & Zola 2001; Schoenmakers et al. 2001; Kronberg et al. 2004; Saripalli et al. 2005; Malarecki et al. 2013; Butenko et al. 2014) is limited by their sparse numbers and by the difficulty of detecting them over large areas of the sky. Low-frequency radio observations have an enhanced capacity to detect the extended old electron population in these objects (see e.g. the recent Low Frequency Array – LOFAR – observation of the GRG UGC095551), but high-frequency radio observations are less efficient in this task due to the steep-spectra of giant radio lobes. In this context these sources will be ideal targets for the next coming deep, wide-field surveys like, e.g. the ATLAS survey of the Australia Telescope Network Facility (ATNF; see Norris et al. 2009) or the Square Kilometre Array (SKA) deep surveys that will have the potential to study their population evolution up to high redshifts and thus clarifying their role on the feedback for the evolution of non-thermal processes in large-scale structures.

Background
Background
Future Work
Future Work


We assume that gas and dust are well mixed along each line of sight in which case the gas surface density (Σgas) is proportional to the dust surface density (Σdust) and the proportionality factor is the gas-to-dust mass ratio (rgd). The dust masses derived by SED fitting methods vary significantly and systematically (e.g. Galliano et al. 2011; Gordon et al. 2014) depending on the applied method and assumed dust optical properties. It is therefore important to use a value of rgd consistent with the used SED fitting methodology, i.e. the value of rgd that gives the correct gas mass given the derived dust mass. We have calibrated the rgd using the available gas tracers on a large scale. Within a 500 arcsec radius centred on NGC 346, we find an atomic gas mass of 2.7×106 M⊙ using the Parkes+ATCA H i map (Kim et al. 2003) and a spin temperature of 60 K (Bernard et al. 2008). The molecular gas mass determined from CO(J = 1–0) within the same aperture is 7.4×104 M⊙ when using a CO-to-H2 column density conversion factor (XCO) of 1021 [cm−2 (K km s−1)−1] (Bolatto, Wolfire & Leroy 2013). If we use an XCO of 1022 [cm−2 (K km s−1)−1], we find a molecular gas mass of 7.5×105 M⊙. Such an elevated XCO may be more appropriate given the harsh radiation field that is prevalent in the region, which may induce enhanced photodissociation of the CO molecules. Thus, we derive a total gas mass in the range of 2.7×106–3.4×106 M⊙. The dust mass derived using the dust continuum photometry in this aperture and applying the same SED fitting routine we use for the pixel-by-pixel analysis yields 2.7×103 M⊙. The derived rgd ranges from ∼1000 to ∼1250. In the following, we use a fiducial value for rgd of 1250, which is much higher than the Galactic value (100; Draine & Li 2007) due to the lower metallicity of the SMC. Our value for rgd of 1250 is lower than the total SMC integrated value of 1740 from Gordon et al. (2014). The global value includes a significant amount of atomic gas at low column density in the outskirts of the SMC which is not detected in dust emission. This drives up the global rgd.


Here, we report on molecular gas observations of NGC 0708, the BCG in the low-mass galaxy cluster Abell 262, itself part of the Perseus–Pisces galaxy supercluster. NGC 0708 lies 58.3 ± 5.4 Mpc away (estimated using infrared surface brightness fluctuations; Jensen et al. 2003). It is a giant elliptical galaxy with a weak dust lane (Ebneter & Balick 1985; Wegner et al. 1996) and an effective radius of 33 arcsec ($\approx \, 9.3$ kpc; Wegner et al. 2012). See Fig. 1 for an HST image of NGC 0708. Abell 262 was identified as having an X-ray emitting ICM by Jones & Forman (1984), and Stewart et al. (1984) measured the cooling time to be 1.3 × 109 yr, smaller than the age of the Universe so that the cluster is expected to form a cooling flow. The 20-cm observations of Parma et al. (1986) revealed a double-lobed, ‘S’-shaped jet and led to the classification of NGC 0708 as a weak Fanaroff–Riley Class I radio source (Blanton et al. 2004). The top panel of Fig. 1 also has 330 MHz continuum observations from Clarke et al. (2009) overlaid (blue contours) to show the shape and orientation of the large-scale jet. Analysis of Chandra observations revealed a hole or bubble within the ICM, cospatial with the eastern lobe of the jet (Blanton et al. 2004). Clarke et al. (2009) found additional 3–6 kpc radius cavities at differing position angles within the X-ray gas, and at a range of radial distances from the BCG (8–29 kpc), indicating multiple episodes of AGN activity from a precessing SMBH jet. They concluded that the total AGN emission should be capable of counteracting the cooling flow over several outbursts. Using their multifrequency observations of NGC 0708, Clarke et al. (2009) also calculated the radio spectral index (α) from 235 to 610 MHz, finding the spectrum to be flat in the core (α = −0.5), typical of new particles in a jet. They also estimated a lower limit on average outburst repetition time-scales in Abell 262 to be τrep ≥ 28 Myr.


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.


Critical luminosity (Lcrit) is the luminosity above which a state transition from subcritical to supercritical takes place. The subcritical state (LX Lcrit) is known to be the low luminosity state whereas the supercritical state is high luminosity state (LX > Lcrit) (Becker et al. 2012). The critical luminosity is crucial to determine whether the radiation pressure of the emitting plasma is capable of decelerating the accretion flow (Basko & Sunyaev 1976; Becker et al. 2012). The luminosity during the 2020 giant outburst reached a record high, which was significantly higher than the critical luminosity (Reig & Nespoli 2013). The source entered a supercritical regime from a subcritical regime during the outburst. In the supercritical regime, radiation pressure is high enough to stop the accreting matter at a distance above the neutron star, forming a radiation-dominated shock (Basko & Sunyaev 1976; Becker et al. 2012). For the subcritical regime, accreted material reaches the neutron star surface through nuclear collisions with atmospheric protons or through Coulomb collision with thermal electrons (Harding 1994). These accretion regimes can also be probed by noting changes in the cyclotron line energies, pulse profiles, and changes in the spectral shape (Parmar, White, & Stella 1989; Reig & Nespoli 2013). During the transition from the subcritical to the supercritical regime, sources show two different branches in their hardness–intensity diagram (HID) which are known as horizontal branch (HB) and diagonal branch (DB) (Reig & Nespoli 2013). The HB implies the low-luminosity state of the source, which is represented by spectral changes and high X-ray variability. The DB corresponds to the high-luminosity state that appears when the X-ray luminosity is above the critical limit. The classification HB and DB depends on HID patterns that the source follows. The HB pattern is generally observed in the subcritical regime and the DB pattern is observed in the supercritical regime (Reig & Nespoli 2013).


C18O (J = 2–1) observations revealed a rotational structure in the north–south direction at the center of IRAS 4C, but whether the rotation is Keplerian is not known due to the low signal-to-noise ratio (S/N) (Tobin et al. 2015). Spitzer IRAC observations show an outflow cavity structure highlighted by scattered light and shocked emission to the east side of the central source, with the west side being much fainter (Figure 19 of Tobin et al. 2015). The east side is therefore inferred to be the blueshifted side, because the blueshifted outflow cavity tends to be brighter than the redshifted cavity in NIR and MIR as it is less extincted. Despite the outflow cavity structure seen in infrared, there was no clear evidence of a molecular outflow from mm or submm observations. Previous 12CO observations either reported no detection of outflow emission toward this source (Plunkett et al. 2013; Tobin et al. 2015) or only weak compact blueshifted emission towards east of the continuum source (Stephens et al. 2018). One possible explanation for the weak 12CO outflow emission is that the outflow lies close to the plane of sky, so that the low-velocity outflow emission is easily mixed with the emission of the ambient gas, especially for abundant species like 12CO. Indeed, the inclination of the source is estimated to be nearly edge-on (Tobin et al. 2015) to about 25° between the disk plane and the line of sight (Segura-Cox et al. 2016). On the other hand, the 13CO (J = 2–1) emission reveal a compact (≲2″) structure with the blueshifted emission slightly offset to the east of the redshifted emission, which was explained as a slow outflow (Koumpia et al. 2016). Here, we report that the outflow cavity structure is clearly detected in the CCH and CS emissions, with kinematics consistent with rotation with respect to the outflow axis. This allows us to measure the angular momentum distribution in the outflow, and further constrain its launching radii and launching mechanism.


Recent studies have used the spectral indices [OII], Hδ, and Dn4000 to probe the stellar population of galaxies at intermediate redshifts (0.5 ≲ z ≲ 1.2) because they are available in the observed optical frame. All these indicators, when combined, can be used to distinguish actively star-forming, (post-) starburst, and old or passive galaxies because they are expected to occupy different regions of the possible parameter space (e.g. Couch & Sharples 1987; Balogh et al. 1999; Poggianti et al. 1999, 2009; Fritz et al. 2014). The [OII]λ3737 emission traces on-going star formation (timescales of ∼10 Myr, e.g. Couch & Sharples 1987; Poggianti et al. 1999, 2006; Kennicutt 1998; Kewley et al. 2004), but it also depends on the metallicity and can be a poor tracer for dusty galaxies (e.g. Kewley et al. 2004; Yan et al. 2006; Kocevski et al. 2011). By measuring the [OII] equivalent width (EW), we can also crudely trace the specific SFR (sSFR), which is found to be anti-correlated with stellar mass (e.g. Bridge et al. 2015; Cava et al. 2015; Darvish et al. 2015a), with more massive star-forming galaxies having lower [OII] EWs. Additionally, higher density environments are found to depress [OII] emission (e.g. Balogh et al. 1999; Darvish et al. 2015a). The Hδ line (and other strong Balmer absorption lines) can be indicative of a post-starburst phase (≈100 − 1000 Myr after the burst, e.g. Couch & Sharples 1987; Balogh et al. 1999; Poggianti et al. 1999, 2009; Dressler et al. 2004; Vergani et al. 2010; Mansheim et al. 2017a) if a strong absorption (typical of A stars, where hydrogen absorption is strongest) is observed and no tracers of on-going star formation are found (Couch & Sharples 1987). Recently, Wu et al. (2018) found that the Hδ EW correlates with stellar mass, with more massive galaxies having weaker Hδ absorption lines, but they did not study the effect of the environment (see also e.g. Siudek et al. 2017, for a similar result on passive galaxies). Finally, a measure of the flux break at 4000 Å (D4000 and Dn4000, as defined by Bruzual 1983; Balogh et al. 1999, respectively) traces the age of the galaxy and also the stellar metallicity (especially for older systems) to a lesser degree. This break is produced by a combination of metal absorption on the atmosphere of old and cool stars and the lack of flux from young and hot OB stars (e.g. Poggianti & Barbaro 1997; Kauffmann et al. 2003), and so it is sensitive to the average age of the stellar population. The 4000 Å break is also found to be stronger for galaxies with higher stellar mass (e.g. Muzzin et al. 2012; Vergani et al. 2008; Hernán-Caballero et al. 2013; Siudek et al. 2017; Wu et al. 2018), which indicates that their stellar populations might be older, in an average sense. In terms of local density, Muzzin et al. (2012) found that galaxies in cluster environments have stronger breaks on average than their field counterparts at similar stellar masses, which the authors argued can be explained by the different fractions of star-forming and quiescent galaxies in different environments.


To date, large surveys focused on detecting AGN systems have been conducted at a range of different wavelengths and, in particular, for the IR and X-ray domains (Alexander et al. 2005, 2008; Ivison et al. 2004; Lutz et al. 2005; Menéndez-Delmestre et al. 2007, 2009; Valiante et al. 2007; Pope et al. 2008; Bonzini et al. 2013; Smolčić et al. 2017; Wang et al. 2013; Stach et al. 2019). Due to the dust extinction in the near-IR, optical, and UV, as well as gas absorption in X-ray bands, these surveys are often incomplete. In the mid- and far-IR, incompleteness of AGN surveys may arise from the fact that not all AGN have significant IR emission from a dusty torus and therefore may not be detected. It is postulated that up to a third of AGN are undetected in these surveys (Mateos et al. 2017). Moreover, other studies have compared AGN selected from various wavebands and find that their host galaxies tend to have different properties in terms of colour (Hickox et al. 2009) and star-formation rates (SFR; Juneau et al. 2013; Ellison et al. 2016). In particular, Hickox et al. (2009) illustrated that there is only very little overlap between their 122 radio-selected AGN and those selected by X-ray or IR. Therefore, dust-free radio surveys are needed to provided a more complete census of the AGN population. Traditional radio surveys are only sensitive to radio-loud (RL) AGN, which only represent a tiny fraction (10 ∼ 20%) of the whole AGN population; however, modern radio surveys can achieve a flux depth where radio-quiet AGN can be detected (see Prandoni et al. 2018 for a review). Recent work has focused on the radio as it is sensitive to AGN and star formation concordantly, thus providing a method of surveying AGN and star-formation activity across cosmic time (e.g. Smolčić et al. 2017; Padovani et al. 2015). A lot of work has also been done to look for AGN-driven radio emission, which has been identified by an excess of radio emission compared to what is expected based on the radio-FIR correlation, holding for star-forming galaxies (e.g. Ivison et al. 2010; Condon et al. 2002; Thomson et al. 2014; Magnelli et al. 2015).