The reasons for studying the dynamic properties of small-scale magnetic fields in the quiet photosphere are manifold. Firstly, magnetic fields provide an opportunity to probe some aspects inherent to turbulent convection (see, e.g. Abramenko et al. 2011; Lepreti et al. 2012; Giannattasio et al. 2013, 2014a,b; Giannattasio et al. 2019; Abramenko 2014, 2017; Del Moro et al. 2015; Caroli et al. 2015; Chian et al. 2019; Giannattasio & Consolini 2021) and energy propagation to the upper atmospheric layers (see, e.g. Viticchié et al. 2006; Jefferies et al. 2006; Tomczyk et al. 2007; De Pontieu et al. 2007; Chae & Sakurai 2008; Stangalini et al. 2014, 2015, 2017; Stangalini 2014; Rouppe van der Voort et al. 2016; Gošić et al. 2018; Bellot Rubio & Orozco Suárez 2019; Rajaguru et al. 2019; Keys et al. 2019, 2020; Guevara Gómez et al. 2021; Jess et al. 2021) that cannot be addressed otherwise from an observational point of view. Secondly, they allow us to constrain the available energy in the quiet Sun and infer some details of the processes that amplify and organise them from subgranular to supergranular scales (see, e.g. November 1980; Roudier et al. 1998; Berrilli et al. 1999, 2002, 2004; Berrilli et al. 2005, 2013, 2014; Consolini et al. 1999; Getling & Brandt 2002; Rast 2002; Del Moro 2004; Del Moro et al. 2004; Getling 2006; Nesis et al. 2006; Centeno et al. 2007; Brandt & Getling 2008; de Wijn et al. 2008; Yelles Chaouche et al. 2011; Orozco Suárez et al. 2012; Giannattasio et al. 2018, 2020; Requerey et al. 2018). Thirdly, their study provides important constraints for theoretical models and/or models implemented in simulations of the photospheric layer (see, e.g. Stein & Nordlund 1998, 2001; Cattaneo et al. 2003; Vögler et al. 2005; Rempel et al. 2009; Shelyag et al. 2011; Beeck et al. 2012; Rempel 2014; Danilovic et al. 2015; Khomenko et al. 2017). All these aspects coalesce, advancing our knowledge of the processes capable of accumulating, transporting, and eventually dissipating the enormous amount of energy available in the photosphere of the quiet Sun.


The standard cosmological model stands on the shoulders of a fundamental assumption: that the universe is statistically homogeneous and isotropic on the largest scales. This assumption has been thoroughly tested over the last years both with cosmic microwave background (CMB) and Large-scale structure data. In particular, the analysis of CMB data, most notably from the Wilkinson Microwave Anisotropy Probe (WMAP; Bennett et al. 2013) and Planck (Planck Collaboration I 2020) experiments, has not yet provided conclusive evidence for the hypothesis of Cosmological Isotropy (Eriksen et al. 2004, 2007; Hajian, Souradeep & Cornish 2005; Land & Magueijo 2007; Hansen et al. 2009; Samal et al. 2009; see also Planck Collaboration VII 2020 and references therein). Moreover, Galactic foreground contamination or known systematic effects in the data alone can not explain the observed CMB ‘anomalies’, i.e. large-scale deviations from the concordance Lambda cold dark matter (ΛCDM) model (see e.g. Rassat et al. 2014; see Planck Collaboration VII 2020 for a recent overview). Power asymmetry from CMB data has also been a matter of intense debate and scrutiny (Gaztañaga, Fosalba & Elizalde 1998; Eriksen et al. 2007; Lew 2008; Hoftuft et al. 2009; Paci et al. 2010; Axelsson et al. 2013; Shaikh et al. 2019, see also Dai et al. 2013 for a comprehensive discussion and references therein), and evidence has been reported that this could source deviations from isotropy on cosmological scales (Hansen et al. 2009). However, a more recent analysis based on Planck data finds no evidence for such power asymmetry when all scales are taken into account (Quartin & Notari 2015). This is in qualitative agreement with the latest results from the Planck Collaboration analysis (Planck Collaboration VII 2020) where they conclude that the observed power asymmetry is not robust to foreground contamination or systematic residuals. It is important to note that previous analysis have concentrated on quantifying potential deviations from statistical isotropy using a statistical prior. First analyses using WMAPdata looked for the direction of maximal asymmetry in the sky, thus quantifying anisotropy for a given preferred direction (Hansen et al. 2009). In turn, this led to proposing a particular angular distribution of power in the sky to simply capture the observed anisotropy, such as the so-called ‘dipole anisotropy’ modulation (Prunet et al. 2005; Gordon 2007). This same model has been further constrained with Planck data (Planck Collaboration XXIII 2014; Planck Collaboration XVI 2016; Planck Collaboration VII 2020; Aiola et al. 2015; Mukherjee et al. 2016). Alternatively, a recent analysis (Ho & Chiang 2018) focuses on quantifying possible CMB peak shifts across the sky, finding significant variations, but they attribute this behaviour to possible systematic effects or the solar dipole. Complementary evidence for cosmological anisotropy has been investigated using probes of the low-redshift universe (see Colin et al. 2011; Secrest et al. 2021 and references therein).


Rather than AGN feedback, it is possible that the effects we are seeing are from a different process coeval or prior to the onset of AGN accretion. Several works have pointed out that AGN activity coincides with a recent starburst, with the AGN having significant accretion events at least ∼200 Myr after the starburst has occurred (Davies et al. 2007; Wild et al. 2007; Wild, Heckman & Charlot 2010; Yesuf et al. 2014) giving the neutral material time to propagate out to the impact parameters probed by COS-AGN (Heckman et al. 2017). With a sample of QSO sightlines probing the CGM around 17 low-redshift starburst and post-starburst galaxies, Heckman et al. (2017) have observed a similar signature of enhanced EWs of Ly α, Si iii, and C iv (the latter of which is not measured in our control sample) relative to a control-matched sample (matched in stellar mass and impact parameter). In the range of impact parameters and stellar masses probed by COS-AGN, the strength of our enhanced EW signature is consistent with the values probed by Heckman et al. (2017). However, the results of Heckman et al. (2017) show strong offsets in the kinematics of the gas from the host galaxy (≈100 km s−1; see fig. 5 from Heckman et al. 2017), whereas the COS-AGN sightlines do not (bottom panel of Fig. 6). Assuming that the AGN activity was triggered by the starburst, a minimum delay time of 200 Myr could allow for any starburst-driven winds to dissipate and kinematic offsets to no longer be present at the impact parameters of the COS-AGN sample. Although this starburst picture provides a possible explanation of our observations, we caution that starbursts are not the only astrophysical event linked to AGN accretion activity. For example, mergers that trigger the AGN (Ellison et al. 2011, 2013; Satyapal et al. 2014; Silverman et al. 2014; Goulding et al. 2018) could potentially affect the surrounding CGM gas. Past and future work focusing on the CGM of galaxy mergers can further test this result (Johnson et al. 2014; Hani et al. 2017; Bordoloi et al. in preparation).


We derived stellar parameters, [C/M], and [N/M] using SLAM. To avoid bad fits at the edges of the parameter space, we exclude stars with spectral S/N in the g band less than 50, and metallicity less than −1.4. The derived C and N abundances are shown in Figure 8. Clearly, in the top panel, the CH-strong, CH-normal, and metal-poor field stars are separated, and their relative distribution in the N–C parameter space is similar to the case of APOGEE abundances (left panel of Figure 7): (1) metal-poor field stars form a sequence in the lower left of the top panel. As evolved stars ascend the RGB, C and N abundances may be changed by first dredge-up (Iben 1964, 1967) and extra mixing (Gratton et al. 2000; Charbonnel & Lagarde 2010). Given that for a typical halo/thick-disk star of 1 M⊙, the first dredge-up occurs around Teff = 5200 K (Boothroyd & Sackmann 1999), and most of our sample stars have

 K and log g  2.5, we infer that most stars have already undergone first dredge-up. On the other hand, the C and N abundances of these stars could be altered by extra mixing. Stars with brighter K-band absolute magnitudes tend to have higher [N/Fe] and lower [C/Fe] (middle and bottom panels of Figure 8), which is consistent with extra-mixing theory and observation (Gratton et al. 2000; Charbonnel & Lagarde 2010); (2) CH-normal stars show an enhanced median N abundance and slightly depleted median C abundance. Clearly, the median N abundance of CH-normal stars is enhanced compared to that of normal metal-poor field stars with similar C abundances. In other words, the enhanced N abundances in CH-normal stars cannot be explained by the extra-mixing effect alone. We notice that a few CH-normal stars may have low N abundances, probably due to large uncertainties when spectra of a particular type are scarce in the training set, i.e., high-N metal-poor stars. The statistical similarity between APOGEE C and N abundances and LAMOST-derived C and N abundances further strengthens our statement above.


W51e2 is the strongest and best-studied HC HII region in the W51 Main cluster, and it is believed to be powered by an O8-type young star (e.g., Shi et al. 2010a). A number of interferometric studies conducted with varying angular resolutions, at centimetre (cm) and (sub)millimetre (mm) bands, identified molecular and ionized gas undergoing infall and rotation toward W51e2. VLA observations of the NH3 inversion lines (1, 1) and (2, 2) seen in absorption (1\hbox{$\farcs$}.̋1 beamsize) revealed radial infall on scales larger than 5000 AU toward the W51e2 core (Zhang & Ho 1997). Higher angular resolution observations of the (3, 3) NH3 absorption line (0\hbox{$\farcs$}.̋3 beamsize) showed signatures of rotation within 2000 AU based on a position-velocity (pv) diagram (Zhang & Ho 1997). Zhang et al. (1998) identified a velocity gradient in a CH3CN transition at 2 mm, deriving a position angle (PA) of 20 ± 20°. Keto & Klaassen (2008) imaged the H53α radio recombination line (RL) with the VLA (0\hbox{$\farcs$}.̋45 beamsize) and they claimed rotation in the ionized gas along the axis of a molecular bipolar outflow (oriented NW-SE) imaged with the SMA in the CO (2−1) line (1′′ beamsize), suggesting a simple inflow/outflow picture in a single high-mass young stellar object (YSO). However, higher resolution observations, using the SMA at the wavelengths of 0.85 mm (0\hbox{$\farcs$}.̋3 beamsize) and 1.3 mm (0\hbox{$\farcs$}.̋7 beamsize), revealed a more complex picture, by resolving W51e2 into three subcores (Shi et al. 2010a): W51e2-W, corresponding to the HC HII region, W51e2-E, located about 1′′ east of the HC HII region and corresponding to the brightest dust continuum source, and W51e2-NW, the weakest continuum component, located about 1′′  NW of the HC HII region. Shi et al. (2010b) imaged the CO (3−2) line (with a 0\hbox{$\farcs$}.̋7 beamsize) and established that the driving source of the powerful molecular outflow in this region is the protostellar core W51e2-E, and not the HC HII region W51e2-W, challenging the scenario proposed by Keto & Klaassen (2008). Etoka et al. (2012) used MERLIN to image the Class II 6.7 GHz CH3OH masers (typical signpost of HMSF), and found that the bulk of maser emission is indeed concentrated toward W51e2-E, and not the HC HII region W51e2-W. This further supports the scenario proposed by Shi et al. (2010a), where the ongoing star formation activity in the region is not concentrated on the HC HII region but toward its companion 1′′ to the east.


Molecular outflows are a common and essential component in the formation process of low- and high-mass stars. In the past 40 yr, astronomers have mapped outflows in the whole mass range of young stellar objects (YSOs; e.g., Frank et al. 2014; Bally 2016; Anglada et al. 2018; Ray & Ferreira 2021). Magnetohydrodynamical (MHD) simulations have shown that the magnetic field plays a crucial role in the launching of molecular outflows (e.g., Pudritz & Ray 2019), more significantly so in the case of massive YSOs (e.g., Matsushita et al. 2018). Here, for instance, the presence of a magnetic field leads to the formation of early outflows. These reduce the radiation pressure, which allows the protostar mass to grow further (Banerjee & Pudritz 2007; Rosen & Krumholz 2020). In addition, the intensity of the magnetic field may influence the collimation of the outflows in massive YSOs. The outflows are well collimated for weak fields and poorly collimated for strong fields (Hennebelle et al. 2011; Seifried et al. 2012). In case of strong magnetic fields, the structure of the outflows is determined by the large-scale geometry of the magnetic field lines (Matsushita et al. 2017). Recently, Machida & Hosokawa (2020) have found a strong dependence of the evolution of outflows in massive YSOs on the initial magnetic field strength of the prestellar cloud for different accretion rates. In their 3D MHD simulations, they grouped the results into three categories: successful outflows, failed outflows, and delayed outflows. In the successful outflows, the outflows appear only when the prestellar cloud is strongly magnetized (μ1 = 2,3), and after an evolution time of ~104 yr, they reach a distance from the central protostar of about 104 au. When the magnetic field is weak (μ ≥ 5), we have failed and delayed outflows; even though small outflows of about 100–1000 au are observed in both cases, only in delayed outflows they can overcome the ram pressure and can ultimately grow. In a massive YSO, a large molecular outflow is therefore formed only if the initial magnetic field strength is B0 ≳B0,cr = 10−4(Mcl∕100M⊙) G, where Mcl is the cloud mass (Machida & Hosokawa 2020).


As in G18, we compiled existing constraints on the molecular gas fraction fgas of quiescent and pSB galaxies from recent literature, namely: local QGs consisting of the ATLAS3D (Young et al. 2011; Cappellari et al. 2013; Davis et al. 2014) and HRS (Boselli et al. 2014; Lianou et al. 2016) ETG samples as well as the samples of pSB galaxies (hereafter, the “low-z pSB” sample) of French et al. (2015) and Alatalo et al. (2016); at low and intermediate redshift, the ETG sample of Spilker et al. (2018) and the pSB sample of Suess et al. (2017); at intermediate and high redshift, constraints from Hayashi et al. (2018) on gas in z ∼ 1.46 cluster ETGs, as well as on individual galaxies from Sargent et al. (2015), Bezanson et al. (2019), and Rudnick et al. (2017). Given its size, we divided the ATLAS3D sample into high- and low-mass subsamples, choosing 5 × 1010 M⊙ as the cut-off mass. In addition, we also included fgas estimates derived from the (median) stacked FIR spectral energy distributions of ETGs at z ∼ 1.8 (G18; 977 galaxies), z ∼ 1.2, z ∼ 0.8, and z ∼ 0.5 (1394, 1536, and 563 galaxies, respectively; Magdis et al. 2020, hereafter M20). Finally, at higher redshift (z ∼ 3), we converted star formation rates (SFR) estimated from spectroscopy (Schreiber et al. 2018a; D’Eugenio et al. 2020) into gas masses assuming the star formation efficiency found by G18. As a consequence of our zmax = 3.5, we did not include higher-redshift quiescent galaxies (Glazebrook et al. 2017; Schreiber et al. 2018b; Tanaka et al. 2019; Valentino et al. 2020) in the analysis and considered z ∼ 3 galaxies as pSB. The dust-based estimates of G18 and M20 (and, by extension, the z ∼ 3 semi-constraints) assume a gas-to-dust ratio (G/D). It is dependent on metallicity, which is presumed to be solar or higher owing to both the relatively high gas-phase metallicity of MS galaxies at z ≲ 1 (e.g., Mannucci et al. 2010) and the already high stellar metallicities of QGs at z >  1 (Onodera et al. 2015; Estrada-Carpenter et al. 2019). Here we adopted an intermediate value between the solar and supersolar G/Ds used in M20, and we increased the error bars of these points to include both the solar and supersolar confidence estimates. These various samples, which are summarized with their selection criteria in Table B.1, combine into a nonhomogeneous dataset: some were specifically selected as ETGs, and others were based on varying degrees of quiescence. In particular, pSB galaxies are not necessarily truly quiescent and could, in principle, resume normal star formation. However, as a possible precursor of QGs, they provide useful, though not constraining (see Sect. 4), comparison samples for the model. Here we refer to all equally as either QGs or pSB galaxies, and we make the assumption that, on average, these different samples are not otherwise significantly biased with regard to their gas content compared to the full population, given each mass limit and type.


With the identification of the ∼6.6 day stellar rotation period, the question remains, what is origin of the ∼9.0 day signal in the periodogram? Because of K2’s large pixel size, we considered the possibility of contamination from additional sources in the field and found that images from DSS, Galex, 2MASS, WISE, and PanSTARRS show that there are no objects of comparable brightness within 1′ of CI Tau. We also examined the potential for multiplicity in the system. High-resolution observations reaching 5σ contrast at 025 separation (Uyama et al. 2017) provide no evidence for a companion down to ΔH = 6.8 that could contribute to the photometric signal. However, there is evidence in support of a substellar body. Johns-Krull et al. (2016) reported the detection of a planet orbiting CI Tau using data from an extensive optical and infrared RV survey. The planet mass they derived is Mp = 11.29 ± 2.16 MJup and the orbital period is Porb = 8.9891 ± 0.0202 days, consistent with the ∼9.0 day period shown in both of the Lomb–Scargle periodograms in Figure 1. Our current understanding of the CI Tau system is that the planet does not transit. This is supported by evidence that the disk is inclined i ∼ 45° (Guilloteau et al. 2014), though it is possible that a planet could be in an orbit misaligned with disk mid-plane (e.g., Kepler-63; Sanchis-Ojeda et al. 2013). However, the ∼9.0 day periodic signal may be the result of a planet–disk interaction because the presence of a massive planet in an actively accreting disk should show both spectroscopic and photometric variability. Indeed, Johns-Krull et al. (2016) find evidence in the Hα profile variations of CI Tau that the planet may be modulating the accretion of disk material onto the star. Although hotspots located at the foot of accretion streams can affect RV measurements mimicking the signal of an orbiting body (Kóspál et al. 2014; Sicilia-Aguilar et al. 2015), Johns-Krull et al. (2016) specifically looked for these signals and found no evidence that hotspots produced the RV signals seen in photospheric absorption lines. Given the stellar mass of 0.80 M⊙ (Guilloteau et al. 2014), Johns-Krull et al. (2016) determined a semimajor axis of 0.079 au for the planetary orbit. This would place the planet inside the inner edge of the disk at 0.12 au (McClure et al. 2013). It is probable that an 11.3 MJup planet so close to the inner edge of the disk would stimulate the accretion of material and possibly modify accretion onto the star, creating non-axisymmetric accretion flows (Tofflemire et al. 2017a, 2017b). As the planet orbits the star, this interaction could produce a periodic variation in the Hα emission, a tracer of accretion. The impact on stellar accretion could produce photometric variability on the ∼9.0 day period of the planet’s orbit, which K2 data show as a periodic component in the system brightness. Additionally, the strength of this periodic component can be expected to fluctuate because of the sporadic nature of accretion on short timescales (Herbst et al. 2007). This is observed in the analysis of the first and second halves of the data and is in contrast to the relatively consistent signal strength of the ∼6.6 day periodic component in brightness, which is caused by cold starspots that are long-lived in young stars (e.g., Stelzer et al. 2003) and produce relatively consistent fluctuations in brightness as the star rotates (Herbst et al. 2007; Bradshaw & Hartigan 2014). If the 9.0 day periodic signal is the result of stellar rotation, it would call into question the legitimacy of the planet. On the other hand, the similar RV amplitudes seen in the optical and the IR and the null results on tests for RV variations produced by an accretion hotspot (Johns-Krull et al. 2016) attest to the significance of planet’s detection. In addition, we would then need to explain the source of the 6.6 day signal, which is the most persistent signal observed in Figures 1 and 2.


For these four remaining FHSC candidates (L1451-mm, MC35-mm, SM1N, and Oph A-N6) that have been observed at intermediate scales (few 100 au to few 1000 au) a final confirmation of their true evolutionary state requires higher resolution observations. For L1451-mm, the compact outflow needs to be resolved to investigate its morphology and kinematics, as a higher velocity component (an indication of protostellar nature) could be revealed by observations with a beam smaller than 100 au, similar to the case of B1b-N (Hirano 2019). An additional goal of high-resolution observations for L1451-mm and the remaining youngest candidates should be to investigate the temperature and density profiles of the envelope at scales from few au to 100 au. This is because simulations show that the temperature remains lower than ∼30 K even at several tens of au up to 100 au from the centre (Bate et al. 2014; Tomida et al. 2015; Hincelin et al. 2016; Young et al. 2019) during the FHSC stage. On the other hand, Class 0 sources show temperatures of 20–30 K or higher at scales of several 100 au (sufficient for thermal evaporation of CO) that results in the inner envelope and disc being easily detected using C18O observations (Yen et al. 2015, 2017; Stephens et al. 2018). This holds even in very low luminosity objects, for which the unexpected large extent of C18O is interpreted as evidence of a previous burst of accretion (Frimann et al. 2017; Hsieh et al. 2018). As for the density profile, simulations of the FHSC stage show a flat inner region, corresponding to the FHSC structure and extending up to ∼10 au (Tomida et al. 2013; Bate et al. 2014). For a protostar, on the other hand, the density profile should increase towards the central ∼1 au region (Young et al. 2019). Observations of the continuum emission with a resolution better than a few tens of au are likely required to model the emission and provide a density and temperature profile that can probe the relevant scales. Additional line observations with a similar resolution can also help to further distinguish between the different models. We note that, as pointed out in Young et al. (2019), distinguishing a dense core with only an FHSC and one that has recently formed a protostar but in which the FHSC structure is still present is likely not possible, even with high-resolution observations. Given the optically thick nature of the FHSC core, it is difficult to probe the physical properties within the FHSC structure. Despite this, finding a source with density and temperature profiles as well as with outflow properties consistent with the theoretical predictions will provide convincing evidence in support of a bona fide FHSC.


Other important components of the X-ray sky are X-ray binaries, the hot gas present in our own Galaxy and the extragalactic hot gas. Amongst these X-ray sources, the large hot gas reservoir (Tvir ∼ 107 K) filling the space between the galaxies in the clusters, known as the ICM, has been observed in its X-ray emission for a long time (Reichert et al. 1981; Jones & Forman 1984; Branduardi-Raymont et al. 1985; Oukbir, Bartlett & Blanchard 1997; Diego et al. 2003a; Diego, Silk & Sliwa 2003b; Cavagnolo et al. 2009; Hurier et al. 2015). However, the hot gas (Tvir > 106 K) present in the form of circumgalactic medium (CGM) in massive galaxies (Mh ∼ 1012–1013 h−1 M⊙; Birnboim & Dekel 2003; Kereš et al. 2005; Singh et al. 2015) is less explored in X-rays due to its fainter X-ray emission. Some of the recent observations and studies (Grcevich & Putman 2009; Anderson & Bregman 2011; Dai et al. 2012; Putman, Peek & Joung 2012; Anderson, Bregman & Dai 2013; Bogdán et al. 2013a,b; Gatto et al. 2013) indicate that the CGM can account for a good fraction of the baryons in these galaxies. The X-ray emission from the CGM, therefore, is a promising tool to put strong constraints on the distribution and energetics of the gas (Singh et al. 2016) with eROSITA. At energies above 2 keV, the extragalactic point sources like AGN completely dominate the X-ray sky (Lehmann et al. 2001; Kim et al. 2007). Even below 2 keV, where the X-ray emission from the hot gas in the ICM and CGM is significant, the major contribution to the observed X-ray sky comes from AGNs (Sołtan 2007). Therefore, studying the X-ray emission from the AGN is crucial to understand the origin and evolution of the AGN as well as to extract the X-ray signal from the subdominant components. We thus also compute the angular power spectrum of the unresolved AGNs that are expected to contribute to the diffuse X-ray background of eROSITA and contaminate the angular power spectrum due the ICM/CGM in the 0.5–2 keV X-ray band.


We explore another mechanism that can possibly result in torque reversals in the neutron star on long time-scales. It has been known for a long time that radio pulsars (which are usually isolated systems) show unexplained stochastic deviations in their spin-down behaviour (known as ‘timing noise’) on varied time-scales of a few hundred days to a few tens of years. This manifestation is akin to the random-walk behaviour in spin frequency observed in wind-fed accretion powered pulsars like Vela X-1. In an interesting study of timing irregularities of a sample of 366 pulsars, Hobbs, Lyne & Kramer (2010) found some radio pulsars showing quasiperiodic structures in their long-term timing residuals. From power spectrum analysis, significant periodicities ranging from about 1.4 to 10 yr were found in PSR B1540−06, PSR B1642−03, PSR B1818−04, PSR B1826−17, PSR B1828−11, and PSR B2148+63 (Hobbs et al. 2010). Interestingly, we also find quasiperiodic variations in the long-term spin evolution of Vela X-1 on time-scales of about 5.9 yr that is comparable to those inferred for radio pulsars showing quasiperiodic changes in their timing residuals. The underlying phenomena causing quasiperiodic structures in timing noise of radio pulsars is elusive. However, it has been suggested that these changes are driven by changes in the magnetosphere of the neutron star (Lyne et al. 2010). In this ‘state-switching model’, the magnetosphere of the neutron star is suggested to harbour two or more magnetospheric states which can be stable on time-scales of years but the pulsar can switch abruptly between these states driven by changes in the parameters regulating the spin-down (Lyne et al. 2010). This can possibly happen in Vela X-1 where the coupling between the dynamic magnetosphere and the neutron star can change in a quasiperiodic fashion. Interestingly, the disc-fed pulsar LMC X-4 has been found showing a near cyclic spin period evolution on time-scales of about 6.8 yr (Molkov et al. 2016) which is within a factor of 1.2 of the inferred time-scale in wind-fed pulsar Vela X-1. Recent observations of transient pulsar V0332+53 suggests switching of coupling between the accretion disc and the neutron star magnetosphere in a disc-fed pulsar (Doroshenko et al. 2017).


Since the star-formation histories of galaxies (ETGs included, e.g. De Lucia et al. 2006; Maraston et al. 2009) can be stochastic and include multiple bursts, we also verify the full-spectrum fitting capabilities to retrieve more complex SFHs. In particular, we take an 11 Gyr old composite stellar population with an exponentially delayed SF (τ = 0.3 Gyr) as the main SF episode (this age is compatible with the age of the Universe at z ~ 0.15, which is the median redshift of our sample, see Sect. 3). We then define more complex SFHs by combining this single CSP with a burst of SF at different ages (5, 6, 7 Gyr) and with different mass contributions (3, 5, 10 %). In all cases, we consider a solar metallicity for the main SF episode and, according to the results of Maraston et al. (2009), a subsolar metallicity (Z = 0.004) for the later one. We do not mask any spectral feature of the input spectra, we assume AV  =  0.1 mag for the two components and apply a velocity dispersion of 200 km s-1. We show the results for a S/N of 80, which matches the typical S/N of the SDSS median stacked spectra analyzed in the following (see Sect. 3). Useful information can be derived from the comparison between the output SFH obtained from these input simulated spectra and the one provided when the single CSP alone is taken as input SFH. Fig. 5 shows that the single CSP alone is well recovered by the full spectrum fitting. In particular, ~80% of the stellar mass is retrieved within ~1 Gyr from the SFH peak. When a burst is added to this major episode of SF, the full-spectrum fitting is able to recognize the presence of a more complex SFH, as indicated by the tail appearing at smaller ages, and the total mass percentage of the later burst is retrieved within 1 Gyr from the expected age. However, we note that the main episode of SF is spread on a time interval longer than expected, and 50% of the stellar mass is retrieved around ~1 Gyr from the SFR peak. We also find that, in this case, the mean properties of the global stellar population are well retrieved, with a percentage accuracy larger than 10% starting from S/N ~ 15 for age, ~7 for metallicity, ~20 for AV, ~8 for σ and that the metallicities of the two SF episodes are separately recovered. These S/Ns are well below those typical of the stacked spectra analyzed in the following sections.


The ReTOF results from irradiated phosphine and deuterated methane ice provide crucial information regarding the mechanism of formation for methylphosphanes by analyzing the intensities of various isotopologues. Figure 8 shows the possible formation routes that would lead to each of the three observed isotopologues of methylphosphine (CH3PH2). To obtain m/z = 50 (CHD2PH2), CD4 has to decompose via the loss of molecular hydrogen or two deuterium atoms to form carbene (CD2), which has been observed in previous irradiated ice studies (Holtom et al. 2005; Bennett & Kaiser 2007), and then insert into a phosphorus–hydrogen bond of phosphine (reaction (5)). If the carbene is formed in its first excited singlet state (a1A1), the insertion is barrierless (Gordon et al. 1987). For m/z = 51 (CD3PH2), methane and phosphine each lost a hydrogen or deuterium atom, and the resulting methyl (CD3) (Kaiser et al. 1997) and phosphino (PH2) radicals recombined barrierlessly (reaction (6)). Finally, the formation of m/z = 52 (CD3PHD) mirrors that for CHD2PH2 but in this case phosphine lost two hydrogen atoms or molecular hydrogen to create the phosphinidene (PH) radical and then inserted into a carbon–deuterium bond of methane (reaction (7)). Phosphinidene, like imidogen (NH) (Fueno et al. 1983), is expected to insert barrierlessly in its first excited singlet state (a1Δ):
5a

5b

6a

6b

6c

7a

7b

Therefore, our results provide compelling evidence that methane decomposes not only to the methyl radical, but also to carbene. Likewise, phosphine was found to fragment to the phosphino radical and also to phosphinidene. The ratio of ion intensities for m/z = 50:51:52 is 2:10:1, indicating that radical recombination was the preferred formation pathway with CD3PH2 as the most abundant isotopologue. This could either be a result of the methyl and phosphino radicals reacting quickly or that more of these radicals were produced than carbene and phosphinidene.


In addition to the galaxy colors (e.g., Baldry et al. 2004; Bell et al. 2004; Borch et al. 2006; Xue et al. 2010; Salim 2014; Lee et al. 2015; Wang et al. 2017), there are other indicators characterizing the star formation nature of galaxies, e.g., the morphology (Strateva et al. 2001; Barro et al. 2013, 2014; Pan et al. 2013) and some spectral features such as the Balmer absorption line (e.g., Kuntschner et al. 2002; Kim et al. 2013; Kim & Yoon 2017) and the 4000 Å break (e.g., Kauffmann et al. 2003; Lambas et al. 2012; Rowlands et al. 2018; Angthopo et al. 2019). Using these indicators, a number of studies have found that the color or SFR transition of galaxies is associated with the consumption of their gas content (e.g., Kereš et al. 2005; Dekel & Birnboim 2006; Kruijssen 2015; Nelson et al. 2018). If this “quenching” scenario is correct, the timescales of the galaxy color/SFR transition and their gas depletion must be consistent. Some authors have studied galaxy quenching by quantifying the evolution of SMFs (or luminosity functions) of SFGs and QGs at high redshifts (e.g., Fritz et al. 2014; Rowlands et al. 2018). The others, with the help of some infrared or submillimeter surveys (e.g., Hershel and ALMA), have managed to study the cosmic evolution of the gas content as well as the gas-depletion rate of galaxies with different SFRs (e.g., Geach et al. 2011; Lagos et al. 2011; Tacconi et al. 2018; Liu et al. 2019; Castignani et al. 2020; Magnelli et al. 2020). These studies have revealed that both the galaxy quenching and gas-depletion timescales increase with decreasing redshifts. The typical quenching timescale of GV galaxies can be as long as several billion years in the local universe (Rowlands et al. 2018; Correa et al. 2019; Phillipps et al. 2019). Methods such as fitting the spectral energy distributions (SEDs) of galaxies (e.g., Belfiore et al. 2018; Phillipps et al. 2019; Zick et al. 2018) and using cosmological simulations (e.g., Feldmann et al. 2017; Nelson et al. 2018; Correa et al. 2019; Donnari et al. 2019) have been widely used to derive the star formation histories of galaxies and their lifetimes.


For the spectral fitting, the astrophysical background components are determined from a simultaneous fit to data from the RASS4 (Snowden etal. 1997). The extraction region for the RASS data is an annulus from 0.7 to 1 around the cluster centre (for NGC4636, NGC1399 and A3526 r500 is larger than 0.7, so the RASS data were extracted from 1.5 to 2). The particle background was directly subtracted from the Chandra spectra using the stow events files from an epoch close to the observation date. The stow events files are created when the ACIS detector is in a position where it is not exposed to the sky and the HRC-I camera is in the field of view. This configuration is also called event histogram mode. As shown by comparisons to dark moon observations only particle events are recorded in the stow position (Markevitch etal. 2003; Wargelin etal. 2004). For each annulus, the same detector region was used to extract the particle background spectra. These background spectra are normalized by the ratio of the (9.512)keV band count rate of the observation and the stow events file to account for variations of the quiescent particle background component. The cluster emission is modelled by an absorbed thermal model (phabs*apec), where all parameters apart from the redshift and the NH are left free to vary. Following Willingale etal. (2013), the hydrogen columns density used as a tracer for the X-ray absorption,

(16)

\begin{eqnarray}
N_\mathrm{H\, tot} = N_\mathrm{H\,\small {I}} + 2\cdot N_{\mathrm{H}_2\mathrm{m}} \cdot \left[ 1-\exp \left(-N_\mathrm{{\rm H\,\small {I}}}\cdot \frac{ E\left(B-V\right) }{ N_\mathrm{c}} \right) \right]^\alpha , \nonumber\\
\end{eqnarray}

where the parameters NH2m  7.2  0.3  1020cm 2, Nc3.0  0.31020cm2 and 1.1  0.1 were calibrated using X-ray afterglows of Gamma-ray bursts in the aforementioned reference. Both, the absorption E(BV) from the IRAS and COBE/DIRBE infrared dust maps (Schlegel, Finkbeiner  Davis 1998) and the $N_\mathrm{H\,\small {I}}$ from Kalberla etal. (2005) are computed at each cluster position. The combined effect of the uncertainties of these parameters, the scatter of this scaling relation (0.087) plus accounting for a 10percent uncertainty on $N_\mathrm{H\,\small {I}}$ and E(BV) has only an 11percent effect on NHtot, which typically affects best-fitting temperatures by 1percent. Since this is much smaller than the typical statistical uncertainties, any statistical uncertainty of NHtot is neglected. For the relative abundance of heavy elements the Asplund etal. (2009) abundance table was used. For each observation, all spectra from the different regions and chips5 are fit simultaneously. The temperature and metallicity of spectra from the same region but different chips are linked together, while the normalizations are not because of spatial variations of the density distribution. For all observations, the steppar command was run on the temperatures. This task calculates the 2 for the parameter within a given range of values in order not to get best-fitting parameters of a local minimum of the likelihood distribution. The reduced 2 of all spectral fits was on average 1.03, while in 95percent of the cases it was below 1.17. This gives a hint that the spectral modelling is appropriate.


AFGL 2136 IRS 1 (also referred to as CRL 2136, G17.64+0.16, and IRAS 18196−1331) is a luminous (1.0 × 105 L; Lumsden et al. 2013), high-mass (45 ± 10 M; Maud et al. 2019) protostar that is believed to be in the latter stages of its evolution due to a variety of observed characteristics (Boonman & van Dishoeck 2003; Maud et al. 2018 and references therein). It is located at a distance of 2.2 kpc away from the Sun (Urquhart et al. 2014), and has been extensively observed from centimeter to micron wavelengths, at low and high angular resolution, and low and high spectral resolution. The myriad observations paint a picture where a single, isolated massive protostar is driving a wide-angle bipolar outflow through its natal cloud. The large scale outflow is observed in CO emission at millimeter wavelengths, with both the red and blue lobes being about 100″ in extent (Kastner et al. 1994; Maud et al. 2018). Closer to the central source (2″–10″), the outflow cavity walls are seen in scattered light at near-infrared wavelengths (Kastner et al. 1992; Murakawa et al. 2008; Maud et al. 2018). The cool molecular envelope exhibits ice and dust absorption bands (Willner et al. 1982; Keane et al. 2001b; Dartois et al. 2002; Gibb et al. 2004), as well as molecular emission at millimeter wavelengths (van der Tak et al. 2000a, 2000b), but a much warmer component is also inferred from several different molecules seen in absorption in the near- to mid-infrared (Mitchell et al. 1990; Lahuis & van Dishoeck 2000; Keane et al. 2001a; Boonman et al. 2003; Boonman & van Dishoeck 2003; Goto et al. 2013, 2019; Indriolo et al. 2013a). The presence of a dust disk on small spatial scales was suggested by near-infrared polarization imaging (Minchin et al. 1991; Murakawa et al. 2008) and by mid-infrared interferometric observations (de Wit et al. 2011; Boley et al. 2013). A compact source was marginally resolved at centimeter wavelengths, along with a cluster of nearby 22 GHz H2O masers (Menten & van der Tak 2004), but only with the recent ALMA 1.3 mm continuum observations has the 93 × 71 mas dust disk been fully resolved (Maud et al. 2019). Thermal line emission at 232.687 GHz from the H2O ν2 = 1–1, 55,0–64,3 transition has the same spatial extent as the dust emission, and the H2O gas velocities indicate Keplerian rotation within the disk (Maud et al. 2019). It is ideal that the reader has a clear picture of the AFGL 2136 region in mind to best understand the discussion throughout this paper. In particular, Figure 10 of Maud et al. (2018) provides an up-to-date schematic diagram of the AFGL 2136 region, and Figures 1 and 2 of Maud et al. (2019) present the compact disk observed in dust and gas emission, respectively.


There have been a number of analytical solutions and numerical studies for rotating flows with viscous angular momentum transport (e.g. Shakura & Sunyaev 1973; see reviews by Pringle 1981; Kato, Fukue & Mineshige 2008, references therein). Among those, we here focus on accretion flows which cannot lose internal energy via radiative cooling because of very low gas density. Such radiatively inefficient accretion flows are quite interesting since many observed BHs accrete at rates of only a small fraction of the Bondi accretion rate and their radiation luminosity is as low as ∼10−1 to 10−9 LEdd (Ho 2008, 2009). Sagittarius A* (Sgr A*) is inferred to be accreting at a rate of 10−3 to $10^{-2}\ \dot{M}_{\rm B}$ (e.g. Yuan, Quataert & Narayan 2003; Quataert 2004), where $\dot{M}_{\rm B}\simeq 10^{-5}\ {\rm M}_{\odot }\, {\rm yr}^{-1}$ is measured from the temperature and density near the Bondi radius with X-ray observations (Baganoff et al. 2003). Because of such a low accretion rate, the bolometric luminosity of Sgr A* (M• ≃ 4 × 106 M⊙; Ghez et al. 2003) is as small as Lbol ∼ 1036 erg s−1 ∼ 2 × 10−9 LEdd. The second example is a BH at the centre of the giant elliptical galaxy M87. The gas accretion rate at the vicinity of the BH is estimated as ≲ 9.2 × 10− 4 M⊙ yr− 1 (Kuo et al. 2014), which is lower than ${\sim } 10^{-2}\ \dot{M}_{\rm B}$ (Russell et al. 2015). Since the BH mass is estimated as $M_\bullet = 6.6^{+0.4}_{-0.4}\times 10^9\ {\rm M}_{\odot }$ (Gebhardt et al. 2011) and $M_\bullet = 3.5^{0.9}_{-0.7}\times 10^9\ {\rm M}_{\odot }$ (Walsh et al. 2013), the bolometric luminosity of Lbol ∼ 2 × 1041 erg s−1 is ∼3 × 10−7 LEdd. The third example is a BH at the centre of the Andromeda Galaxy (M31). The estimated BH mass is $M_\bullet \simeq 1.4^{+0.7}_{-0.3}\times 10^8\ {\rm M}_{\odot }$ (Bender et al. 2005). The Bondi accretion rate and the X-ray luminosity are estimated as $\dot{M}_{\rm B}\simeq 7\times 10^{-5}\ {\rm M}_{\odot }\, {\rm yr}^{-1}$ and LX ≃ 2 × 1036 erg s−1 ≃ 10−10 LEdd, respectively (Garcia et al. 2010). The corresponding bolometric luminosity is inferred as ≃10−9 LEdd by assuming the bolometric correction factor to be ≃10 (Hopkins, Richards & Hernquist 2007).


The first multi-messenger GW event was discovered on 17 August, 2017. About 1.7 s after the GW170817 signal detected by LIGO and Virgo (Abbott et al. 2017a), the Fermi Gamma-ray Burst Monitor was successfully triggered by GRB 170817A (Abbott et al. 2017b; Goldstein et al. 2017; Zhang et al. 2018) and subsequently a large number of follow-up observations monitored the afterglow emission in different electromagnetic bands from the radio to X-rays (Alexander et al. 2017; Hallinan et al. 2017; Margutti et al. 2017; Troja et al. 2017; D’Avanzo et al. 2018; Ghirlanda et al. 2019; Lazzati et al. 2018; Lyman et al. 2018) and the kilonova AT 2017gfo in the ultraviolet–optical–infrared band (Abbott et al. 2017c; Andreoni et al. 2017; Arcavi et al. 2017; Chornock et al. 2017; Coulter et al. 2017; Covino et al. 2017; Cowperthwaite et al. 2017; Evans et al. 2017; Hu et al. 2017; Kilpatrick et al. 2017; Lipunov et al. 2017; Nicholl et al. 2017; Smartt et al. 2017; Soares-Santos et al. 2017; Tanvir et al. 2017). The observations of GRB 170817A and its afterglows robustly confirmed the long-standing hypothesis that SGRBs can originate from compact binary mergers. Moreover, it became possible to explore the angular structure of the SGRB jet from an off-axis view (Lamb & Kobayashi 2017; Granot et al. 2018; Lazzati et al. 2018; Mooley et al. 2018a,b; Li et al. 2019). Meanwhile, the observations of AT 2017gfo indicated the existence of the merger ejecta, which suggests that the progenitor binary should at least contain one NS. In more detail, the existence of a “blue” and possibly also a “purple” component in the AT 2017gfo emission further indicated that the merger product of the GW170817 event is very likely to be a hypermassive NS, which lasted for at least a few hundred milliseconds, as an immediately formed black hole can only be associated with a “red” kilonova1 (Cowperthwaite et al. 2017; Perego et al. 2017; Tanaka et al. 2017; Tanvir et al. 2017; Villar et al. 2017; Kawaguchi et al. 2018). Therefore, in summary, the progenitor of the GW170817 event can be identified as a DNS system, which is consistent with the result of the GW analysis.


Recent work by Longmore, Chevance & Kruijssen (2021) has revealed an intriguing correlation between stellar phase-space density and the architecture of planetary systems, in particular the multiplicity. This work followed a similar analysis by Winter et al. (2020), which uncovered a correlation between stellar phase-space density and the occurrence of hot Jupiters. Using Gaia DR2 data (Gaia Collaboration et al. 2018), Longmore et al. (2021) computed the local stellar phase-space density of planet-hosting stars and their neighbours (within 40 pc) to determine whether the exoplanet host was in a relatively low or high phase-space density zone compared to its neighbours. They hypothesized that stars in current stellar overdensities were previously part of dense stellar clusters, from which only local residual overdensities remain. They showed that Kepler systems in local stellar phase-space overdensities have a significantly larger single-to-multiple ratio compared to those in the low phase-space density environment. The origin of this correlation is puzzling, as stellar clustering is expected to affect mostly the outer part of planetary systems in very dense environments (Laughlin & Adams 1998; Malmberg, Davies & Heggie 2011; Parker & Quanz 2012; Cai et al. 2017; Li, Mustill & Davies 2020a). Recent works have also suggested that the correlation is weaker when using a smaller unbiased stellar sample (Adibekyan et al. 2021), and that the current stellar overdensities could be associated with stellar age or to galactic-scale ripples as opposed to dense birth clusters (Mustill, Lambrechts & Davies 2021; Kruijssen et al. 2021). Alternatively, new studies have suggested that stellar flybys can excite the eccentricities and inclinations of outer planets/companions, which then trigger the formation of hot Jupiters from cold Jupiters via high-eccentricity migration (Wang et al. 2020; Rodet, Su & Lai 2021). For this flyby scenario to be effective, certain requirements (derived analytically in Rodet et al. 2021) on the companion property (mass and semimajor axis) and the cluster property (such as stellar density and age) must be satisfied. In this paper, we will examine a similar ‘outside–in’ effect of stellar flybys on the SE systems. Earlier, Zakamska & Tremaine (2004) examined the excitation and inward propagation of eccentricity disturbances in planetary systems. Our work focuses on inclination disturbances, as they are most relevant in determining the co-transit geometry of multiplanet systems.


Despite a number of attempts of employing aspherical models for the matter distribution in the analysis of X-ray and lensing observations of galaxy clusters (see e.g. Corless, King & Clowe 2009; Samsing, Skielboe & Hansen 2012; Sereno et al. 2013), all dynamical methods are based on spherical symmetry. As the first step in addressing the problem of asphericity in mass measurements based on kinematics of galaxies in clusters, we study how dynamical mass estimators assuming spherical symmetry depend on the orientation of galaxy clusters with respect to the line of sight. We assess this effect by studying dynamical masses inferred from mock kinematic data of galaxy clusters generated from cosmological simulations. We restrict our analysis to dynamical masses measured with the so-called caustic technique (Diaferio 1999), which is one of the commonly used methods of mass determination in galaxy clusters (see e.g. Biviano & Girardi 2003; Rines & Diaferio 2006; Lemze et al. 2009; Geller et al. 2013; Rines et al. 2013). The caustic technique does not explicitly assume dynamical equilibrium beyond the virial radius, therefore it can be used to measure masses of galaxy clusters at distances larger than their virial radius and allows us to study the mass bias in a wide range of radii. As all dynamical methods currently applied to cluster data, it assumes spherical symmetry and testing this assumption is an objective of this work. Dependence of the mass measurement on the orientation of galaxy clusters with respect to the sight line is expected not only due to clusters’ intrinsic phase-space shapes, but also due to co-alignment of the surrounding large-scale structures. The latter effect has been clearly shown both in cosmological simulations (Libeskind et al. 2013) and observations (Paz et al. 2011), and it is expected to modulate the contribution of background galaxies in kinematic samples and thus to affect the final estimate of dynamical mass.


The relative abundances of the three species are derived from the column densities in Table 2 and are compared with other star-forming regions and comets in Table 3. The (CH2OH)2/CH2OHCHO abundance ratio of ~0.3–0.5 previously derived in IRAS 16293 by Jørgensen et al. (2012) was revised. Indeed, the assignment in Jørgensen et al. (2012) was based on only one line of the gGg′ conformer of ethylene glycol about 200 cm-1 (~290 K, Müller & Christen 2004) above the lowest-energy aGg′ conformer – and thus tentative. An analysis from observations of six transitions of the lower energy conformer from ALMA Cycle 1 observations at 3 mm (four spectral windows at 89.48–89.73, 92.77–93.03, 102.48–102.73, and 103.18–103.42 GHz; Jørgensen et al., in prep.) results in a higher ethylene glycol-to-glycolaldehyde abundance ratio of 1.0 ± 0.3. This new estimate is consistent with the ratio expected between the aGg′ and gGg′ conformers under thermal equilibrium conditions at 300 K, the excitation temperature of glycolaldehyde derived in IRAS 16293 (Jørgensen et al. 2012). The (CH2OH)2/CH2OHCHO abundance ratio in IRAS2A is estimated at 5.5 ± 1.0 if we consider the column densities derived from the rotational diagrams. It is slightly lower (4.6), however, if we use the column density of ethylene glycol of 1.1 × 1016 cm-2 that does not overproduce the peak intensities of a few lines (see Fig. 3). The (CH2OH)2/CH2OHCHO abundance ratio consequently is a factor ~5 higher than in the Class 0 protostar IRAS 16293. It is also higher than in the other star-forming regions (see Table 3), but similar to the lower limits derived in comets (≳3–6). This indicates that the glycolaldehyde chemistry may in general vary among hot corinos. It is possible that like IRAS2A, other very young low-mass protostars show high (CH2OH)2/CH2OHCHO abundance ratios, in agreement with the cometary values. The CH3OCHO/CH2OHCHO column density ratio found in IRAS2A (~20) ranges between the values derived in the molecular clouds from the Galactic center (~3.3–5.2) and the high-mass star-forming regions (~40–52). A lower limit of 2 was derived for comet Hale-Bopp.


In principle, Fig. 5, central panel G, shows that (469219) 2016 HO3 may have been locked in a Kozai–Lidov resonance with ω librating about 270° for nearly 100 kyr and probably more. Because of the Kozai–Lidov resonance, both e (central panel E) and i (central panel F) oscillate with the same frequency but out of phase (for a more detailed view, see Fig. 4, panels E and F); when the value of e reaches its maximum the value of i is the lowest and vice versa ($\sqrt{1 - e^2} \cos i \sim$ constant, see Fig. 4, panel B). During the simulated time and for the nominal orbit, 469219 reaches perihelion and aphelion the farthest possible from the ecliptic. Fig. 5, G-panels, show that for other incarnations of the orbit of 469219, different from the nominal one, ω may librate about 90° as well during the simulated time interval. However, is this a true Kozai–Lidov resonance? Namouni (1999) has shown that the secular evolution of co-orbital objects is viewed more naturally in the erωr-plane, where er and ωr are the relative eccentricity and argument of perihelion computed as defined in Namouni's work (see equations 3 in Namouni 1999); these are based on the vector eccentricity and the vector inclination. Fig. 6 shows the multi-planet erωr-portrait for the nominal orbit of this object. It clearly resembles figs 13 and 19 in Namouni (1999). Asteroid 469219 librates around $\omega _{\rm r}=-90{^\circ }$ for Venus, the Earth, and Jupiter. This behaviour corresponds to domain III in Namouni (1999), horseshoe-retrograde satellite orbit transitions and librations (around $\omega _{\rm r}=-90{^\circ }$ or 90°). For a given cycle, the lower part corresponds to the horseshoe phase and the upper part to the quasi-satellite or retrograde satellite phase. This is not the Kozai–Lidov resonance; in this case, the Kozai–Lidov domain (domain II in Namouni 1999) is characterized by libration around $\omega _{\rm r}=0{^\circ }$ (or 180°) which is only briefly observed at the end of the backwards integrations (see Fig. 6). The Kozai–Lidov resonance is however in action at some stage in the orbits displayed in Figs 5 and 8. Our calculations show that the orbital evolution followed by 469219 is the result of the dominant secular perturbation of Jupiter as the periodic switching between co-orbital states ceases after about 8 kyr if Jupiter is removed from the calculations. Fig. 7 shows that, without Jupiter, 469219 switches between the Kozai–Lidov domain and that of horseshoe-quasi-satellite orbit transitions and librations (including both −90°and 90°). Jupiter plays a stabilizing role in the dynamics of objects following orbits similar to that of 469219. It is not surprising that Jupiter instead of the Earth or Venus is acting as main secular perturber of 469219. Ito & Tanikawa (1999) have shown that the inner planets share the effect of the secular perturbation from Jupiter; in fact, Venus and our planet exchange angular momentum (Ito & Tanikawa 2002). In their work, these authors argue that the inner planets maintain their stability by sharing and weakening the secular perturbation from Jupiter. Tanikawa & Ito (2007) have extended this analysis to conclude that, regarding the secular perturbation from Jupiter, the terrestrial planets form a collection of loosely connected mutually dynamically dependent massive objects. The existence of such planetary grouping has direct implications on the dynamical situation studied here; if Jupiter is removed from the calculations, the overlapping secular resonances and the recurrent dynamics disappear as well.


We employ two types of kinetic codes, hybrid particle-in-cell (PIC) and full PIC simulations. Both types make use of the P3D family of codes (Zeiler et al. 2002), in hybrid PIC (e.g., Parashar et al. 2011) mode, and fully kinetic PIC mode (e.g., Wu et al. 2013b). All simulations discussed here are performed in the 2.5D geometry (two-dimensional (2D) grid and all three components of field vectors). The hybrid simulation has

 (where

 is the ion inertial length, with c the speed of light and

 the proton plasma frequency),

, 200 particles per cell,

, cold isothermal electrons with

. The simulation is initialized with energy only in wavevectors

 that have

. v and b fluctuations are chosen with a specified initial spectral shape, Gaussian random phases, and only in essentially incompressive modes of the system. This simulation was also used in a recent study of variance anisotropy in kinetic plasmas (Parashar et al. 2016). The first full PIC simulation has

,

, 200 particles per cell,

,

. The initial condition is the Orszag–Tang vortex (OTV) (e.g., Orszag & Tang 1979; Dahlburg & Picone 1989; Parashar et al. 2009; Vasquez & Markovskii 2012). This simulation was performed for a recent study of transition from kinetic to MHD-like behavior (Parashar et al. 2015). The final PIC simulation (Turb812) has

,

, 400 particles per cell,

,

. The initial condition is MHD-like, and more “turbulent,” with v and b fluctuations excited in a band of wave-vectors with

 with a specified initial spectrum. This simulation was done as part of a recent study that discussed the relation of timescales at the proton gyroscale and their relation to relative proton–electron heating (Matthaeus et al. 2016). PIC codes have an inherent noise associated with them due to the finite number of particles per cell. While performing these simulations, the two most important numerical criteria that we paid attention to were: (i) excellent conservation of total energy (less than a few percent change in any fluctuation energy), and (ii) the particle noise in the spectrum was significant only at scales much smaller than the scales of interest (Debye length

 for PIC and di for hybrid PIC). On this basis, the modest number of particles employed here was considered adequate. As an additional measure, we employed filtering (e.g., Wan et al. 2012) to remove particle noise at grid scales prior to computing gradients (e.g., vorticity).


A number of fundamental results have been rigorously proved in the mathematical literature concerning the asymptotic behaviour in time of some of the solutions of the porous medium equation and related equations (e.g. Kamin & Vázquez 1991; Bernis et al. 1993; Hulshof et al. 2001). What is of interest for us here is, primarily, the results that can be applied to the cylindrically symmetric case with diffusion coefficient which is proportional to the square of the dependent variable (n = 2, m = 3 in the notation of Eq. (7)). The most basic result, already mentioned in Sect. 4.4.1, is that initial conditions which have a finite nonzero flux integral (called ‘the mass’ in the mathematical literature for the PME) converge toward the ZKBP solution with the same flux integral (‘mass’) asymptotically in time (Vázquez 2007, Theorem 18.2); here, allowance is made for either a positive or negative flux integral by globally changing the sign of the ZKBP solution; also, ‘convergence’ is meant in the sense that the Lp norm of the difference between the actual solution and the ZKBP function tends to zero as t → ∞ faster than a negative power of the time with an exponent which is a function of n, m, and p (e.g. −1/3 for n = 2 and m = 3 in the L2 norm; see details in the book by Vázquez 2007). A complementary result is the following: when the initial condition has positive net flux and its negative part has compact support, then the whole solution evolves into a positive function after a finite time (Vázquez 2007, Theorem 18.29). Since we are dealing with signed functions which have zero flux integral, these results are of interest mainly because they impose a strict condition on the possible flux imbalance caused by numerical errors (as discussed in Sect. 4.4.1, final paragraph): if it is not small, the numerical solutions will approach the ZKBP solution in a comparatively short time. However, the flux imbalance in all the Bifrost experiments discussed in the present paper is small enough that they have not shown this behaviour even though they have been run until a very long diffusive time.


The CO photodesorption yield reaches its highest value when this ice is deposited at low temperatures (down to 7 K, the lowest temperature studied experimentally) and decreases gradually at higher deposition temperatures (Öberg et al. 2007; Öberg et al. 2009; Muñoz Caro et al. 2010, 2016; Sie et al. 2022). The explanation for this phenomenon motivated further research. It was found that the columnar structure of CO ice samples, grown at incidence angles larger than 45°, increases the effective ice surface exposed to UV photons and therefore the photodesorption efficiency (González Díaz et al. 2019), but ice surface effects cannot account for the large variations observed in the photodesorption of CO ice samples deposited at different temperatures (Muñoz Caro et al. 2016). Absorption band shifts of CO ice in the UV and IR ranges only occurred at deposition temperatures above 20 K (Lasne et al. 2015; Muñoz Caro et al. 2016), suggesting that CO ice grown at lower temperatures is amorphous below 20 K in our experiments, and therefore, the decreasing photodesorption yield is not related to a transition from amorphous to crystalline ice, instead it might be associated to a different degree of molecular disorder in CO ice samples, depending on their deposition temperature. Photon energy transfer via Wannier-Mott excitons between the first photoexcited molecule in the ice and a molecule on the ice surface capable to desorb was proposed (Chen et al. 2017; McCoustra & Thrower 2018). Molecular disorder seems to enhance this energy transfer between neighbour molecules. The colour temperature variations measured at different deposition temperatures could also be the result of molecular disorder (Carrascosa et al. 2021). Urso et al. (2016), Cazaux et al. (2017), and Carrascosa et al. (2021) did not find significant changes in the desorption behaviour or the colour temperature of pure CO ice during controlled warm-up, which points to a low value of the diffusion in the ice. Finally, Sie et al. (2022) investigated the CO photodesorption yield dependence on ice thickness.


Recent MIR studies have provided us with a much more realistic view of the central part of the AGNs. Spitzer studies of nearby Compton-thick AGNs have shown that even Compton-thick AGNs, especially low-luminosity ones, often show only modest to moderate silicate absorption at

 μm (e.g., Hao et al. 2007; Goulding et al. 2012). A classical smooth torus model, such as that of Pier & Krolik (1992), predicts deeper absorption in proportion to the X-ray absorption column density. On the other hand, if the torus is made of a collection of clouds, each cloud is heated to ∼300 K to emit MIR emission while absorbing the background light when the foreground cloud is cooler than the one behind. The radiation transfer effect among the clouds significantly reduces the net silicate absorption even when the torus is seen edge-on (Nenkova et al. 2002, 2008a, 2008b; Hönig et al. 2006; Hönig & Kishimoto 2010; Stalevski et al. 2012, 2016). Meanwhile, recent MIR interferometric studies of nearby AGNs have started to directly reveal the dust distribution in the vicinity of the AGNs at parsec scales. In some best-studied AGNs, extended optically thin dust emission elongated toward the system’s polar direction (e.g., direction of the extended narrow-line region or outflow) is typically found in addition to the compact disk-like component (e.g., Raban et al. 2009; Hönig et al. 2012, 2013; Tristram et al. 2012, 2014; López-Gonzaga et al. 2016; see also Asmus et al. 2016 for the single-dish study; see Netzer 2015 for a review). Such extended polar emission is clearly inconsistent with the classical idea of the dusty torus in the unification theory, and its nature is under debate. Some proposed ideas are that it originates from the inner funnel of an extended dust distribution above and below the torus and/or the dusty outflow within the ionizing cone that is radiatively driven from the inner wall of the compact dusty torus (e.g., Hönig et al. 2012, 2013; Keating et al. 2012; Roth et al. 2012; Tristram et al. 2014).


LoTSS is currently mapping all of the northern sky to a high sensitivity and resolution (S150MHz ~ 0.1 mJy beam−1 and FWHM ~ 6′′) at the relatively unexplored 120–168 MHz frequencies. In parallel with this, LOFAR is also undertaking deep observations of best studied multi-wavelength, degree scale fields in the northern sky, as part of the deep tier of LoTSS: the LoTSS Deep Fields (Tasse et al. 2021 and Sabater et al. 2021; hereafter Paper I and Paper II). The first three LoTSS Deep Fields are the European Large-Area ISO Survey-North 1 (ELAIS-N1; Oliver et al. 2000), Lockman Hole, and Boötes (Jannuzi & Dey 1999); these were chosen to have extensive multi-wavelength coverage from past and ongoing deep, wide-area surveys sampling the X-ray (e.g. Brandt et al. 2001; Hasinger et al. 2001; Manners et al. 2003; Murray et al. 2005), ultra-violet (UV; e.g. Martin et al. 2005; Morrissey et al. 2007) to optical (e.g. Jannuzi & Dey 1999; Cool 2007; Muzzin et al. 2009; Wilson et al. 2009; Chambers et al. 2016; Huber et al. 2017; Aihara et al. 2018) and to infrared (IR; e.g. Lonsdale et al. 2003; Lawrence et al. 2007; Ashby et al. 2009; Whitaker et al. 2011; Mauduit et al. 2012; Oliver et al. 2012) wavelengths; this is ideal for a wide range of our scientific objectives. These fields also benefit from additional radio observations at higher frequencies from the Giant Metrewave Radio Telescope (GMRT; e.g. Garn et al. 2008a,b; Sirothia et al. 2009; Intema et al. 2011; Ocran et al. 2019; Ishwara-Chandra et al. 2020) and the VLA (e.g. Ciliegi et al. 1999; Ibar et al. 2009). The current LoTSS Deep Fields dataset, covering ~ 26 deg2 (including multi-wavelength coverage) and reaching an unprecedented depth of S150MHz ~20 μJy beam−1, is comparable in depth to the deepest existing radio continuum surveys (e.g. VLA-COSMOS) but with more than an order of magnitude larger sky-area coverage. With this combination of deep, high-quality radio and multi-wavelength data over tens of square degrees, and along multiple sight-lines, the LoTSS Deep Fields are now able to probe a cosmological volume large enough to sample all galaxy environments to beyond z ~ 1, minimise the effects of cosmic variance (to an estimated level of ~4% for 0.5  z  1.0; Driver & Robotham 2010), and build statistical radio-selected samples of AGN and star-forming galaxies, even when simultaneously split by various physical parameters.

Background Background Background Background Background


In the framework of the hierarchical formation of structures, clusters of galaxies are continuously accreting galaxies. It has been suggested that in this process of falling, galaxies could undergo different physical processes that could affect the star formation even before they reach the cluster. Consequently, to fully understand what the cluster environment produces in galaxies, it is of key importance to have a throughout characterisation of the population of galaxies in the outskirts of clusters. Several observations have shown that properties of galaxies such as star formation, gas content, and colour are affected by the cluster environment at large clustercentric distances (e.g. Lewis et al. 2002; Solanes et al. 2002; Gómez et al. 2003; Braglia et al. 2009; Hansen et al. 2009; Park & Hwang 2009; von der Linden et al. 2010; Haines et al. 2015; Rhee et al. 2017). In particular, spiral galaxies with low star formation rates were found in the outskirts of clusters in early studies such as Couch et al. (1998) or Dressler et al. (1999). In recent years, a deficit of star-forming galaxies in the infalling region of clusters has been reported (e.g. Wetzel et al. 2013; Haines et al. 2015; Bianconi et al. 2018). This has been reproduced in simulations by Bahé et al. (2013). These results can be explained by the presence of environmental effects accelerating the consumption of the gas reservoir before galaxies enter in a cluster, a process known as pre-processing (e.g. Fujita 2004; Mihos 2004). An important fraction of the cluster galaxies has spent time in groups or filaments before they fall into the cluster (e.g. McGee et al. 2009; De Lucia et al. 2012; Wetzel et al. 2013; Hou, Parker & Harris 2014). The population of galaxies in the outskirts of clusters includes not only galaxies that have not yet entered the cluster but also backsplash galaxies, i.e. galaxies that have passed close to the centre of the cluster since their infall and are now beyond the virial radius (e.g. Mamon et al. 2004; Gill, Knebe & Gibson 2005; Mahajan, Mamon & Raychaudhury 2011). For an adequate characterisation of the properties of galaxies that are falling into clusters, it is important to take into account the contamination by backsplash galaxies, which, having orbited through the inner regions of a cluster, could have been affected by the physical processes present in that extreme environment. The backsplash scenario in the evolution of galaxies has also been explored in Rines & Diaferio (2005), Pimbblet et al. (2006), Aguerri & Sánchez-Janssen (2010), and Muriel & Coenda (2014).


The scenario presented above has been formulated in various flavors to individually explain several of the properties reported here. The main addition of this work, namely the excitation of CO in distant main-sequence and starburst galaxies, fits in the general picture that we sketched. The ensemble of properties and correlations that we reported here can be also used to revisit the definition of what a starburst is. A standard operational classification is based on the distance from the observed empirical M⋆-SFR correlation, the main sequence. This proved to be a useful distinction and an excellent predictor of several trends (e.g., Sargent et al. 2014), but recent results, including our present and previous analysis (Puglisi et al. 2019), show that the demarcation between starburst and main-sequence galaxies is more blurred that we previously considered. We do detect starburst-like behaviors in galaxies on the main sequence (Elbaz et al. 2018), likely linked to the existence of transitional objects (Popping et al. 2017; Barro et al. 2017b; Gómez-Guijarro et al. 2019; Puglisi et al. 2019, and in prep. to limit the references to recent works based on submillimeter observations). Such transition might well imply an imminent increase of the SFR, driving the object in the realm of starbursts (e.g., Barro et al. 2017b), or its cessation, bringing the system back onto or even below the main sequence (Gómez-Guijarro et al. 2019; Puglisi et al. 2019), with the CO properties potentially able to distinguish between these two scenarios. Regardless of these transitional objects, a definition of starburst based on ΣSFR, rather than ΔMS, would naturally better account for the observed molecular gas excitation properties, dust temperatures and opacities, or SFE (see also Elbaz et al. 2011; Rujopakarn et al. 2011; Jiménez-Andrade et al. 2018; Tacconi et al. 2020). As an example, in Fig. 8 we show the mean SLED of the subsample of galaxies with both CO (2 − 1) and CO (5 − 4) coverage, split at its median ΣSFR. While only tentative at this stage, this suggests a trend of increasing CO excitation with ΣSFR, consistently with Fig. 7 and what mentioned above.


In the Local Universe, most of our current knowledge of chemical distributions in disc galaxies comes from studies of the ISM via observations of HII regions or young stellar populations. Current observations are consistent with the metallicity profiles of the ISM having negative metallicity gradients, on average. Metallicity gradients in units of dex kpc-1 determine tight correlations with the global properties of galaxies such as the stellar mass or the size, which are erased when normalised by a characteristics radius such as the half-mass radius (e.g. Zaritsky et al. 1994; Sánchez et al. 2013). There are few indirect estimations of the evolution of the stellar metallicity gradients using planetary nebulae (PN; e.g. Henry et al. 2010; Stanghellini et al. 2010). Maciel et al. (2003) calculated the gradients of SPs with different ages in the Milky Way disc, finding a signal of increasingly negative metallicity gradients for older stars. Recently Magrini et al. (2016) analysed the metallicity gradients determined by PN for four nearby galaxies, finding them to be flatter than those detected using HII regions. Surveys such as CALIFA provide detailed information on the properties of the ISM and the SPs, including their chemical abundances and age distributions on a variety of galaxies (Sánchez-Blázquez et al. 2014; González Delgado et al. 2015). The SDDS-IV MaNGA survey (Bundy et al. 2015) also investigate spatially resolved SPs and radial age and metallicity gradients for nearby galaxies (Li et al. 2015; Wilkinson et al. 2015) and will provide a large statistical sample to confront with models. The available observations of HII regions for high-z galaxies do not allow the formation of a robust conclusion on the evolution of the metallicity gradients (e.g. Yuan et al. 2011; Queyrel et al. 2012; Stott et al. 2014; Jones et al. 2015). In fact, high-redshift observations show a complex situation with gas-phase components showing a variety of metallicity gradients that could respond to the action of different physical processes (e.g. Cresci et al. 2010).


Some of the accretion-powered X-ray pulsars showed additional features in emission between the 10 and 20 keV energy bands and more rarely in absorption between 8 and 10 keV in their respective residuals when fitted with a variety of continuum models (Coburn et al. 2002). Coburn et al. (2002) argued that such features may be caused by inadequacies of the continuum model rather than cyclotron resonance features. For example, it was observed that a single emission line at around 14 keV can fit two features around 10 and 20 keV for Vela X-1 (Kreykenbohm et al. 2002), Her X-1 (Coburn 2001), and Cep X-4 (McBride et al. 2007), and an absorption line between 8 and 10 keV can fit the features for 4U 1907+09, 4U 1538–52, and 4U 0352+309 as in Figure 6 of Coburn et al. (2002). In the case of GRO J2058+42, an introduction of a single Gaussian emission line in this range of energies could not appropriately fit the spectrum. The results described in Section 3.3 using ratios of spectral counts with respect to the Crab spectrum derived for four different phases of the pulsar (Figure 6) clearly indicate the presence of prominent depressions around 10 keV and 20 keV for phase 1 in particular, and its presence in other phases as well. Therefore, it confirms the presence of such absorption features in the spectral data associated with a physical origin and not due to any discrepancies of the continuum model as discussed above. Additionally, it also excludes the possibility of any uncertainty in the response matrix of the detector as the response matrix was not used to deconvolve the spectrum to calculate these ratios. The relative significance of these absorption features that was subsequently estimated after modeling the data and results is shown in Table 2 for the phase-averaged case and in Table 3 for the four different pulse phases. These observations strongly favor the presence and detection of these absorption features in their respective pulsar spectra.


Numerical simulations using the N-body method are the primary instrument used to probe the non-linear regime of structure formation in cosmology and provide the basis for all theoretical predictions for the distribution of dark matter at the corresponding physical scales. Over the last few decades, such simulations have gained in refinement and complexity and have allowed the exploration of an ever larger range of scales (for a review see e.g. Bertschinger 1998; Springel et al. 2005; Dehnen & Reed 2011). Nevertheless, the understanding of their precision and their convergence towards the continuum limit remains, at very least, incomplete, in particular for smaller scales (see e.g. Splinter et al. 1998; Knebe et al. 2000; Romeo et al. 2008; Joyce et al. 2009; Power et al. 2016). In this context ‘scale-free’ cosmological models, in which both the expansion law and the power spectrum characterizing the initial fluctuations are simple power laws, have the advantage of relative simplicity, and they have for this reason been studied quite extensively in the literature (see e.g. Efstathiou et al. 1988; Colombi et al. 1996; Bertschinger 1998; Jain & Bertschinger 1998; Smith et al. 2003; Knollmann et al. 2008; Widrow et al. 2009; Orban 2013; Diemer & Kravtsov 2015). More specifically these models provide a testing ground for the numerical method through the predicted ‘self-similarity’ of the clustering: the temporal evolution of the clustering statistics must be equivalent to a rescaling of the distances. This follows from the fact that there is only one characteristic length scale (derived from the amplitude of the fluctuations) and one characteristic time-scale in the model. Further the exact rescaling function can be determined from the evolution in the linear regime of arbitrarily small fluctuations. However, discreteness and numerical effects typically introduce additional characteristic scales (e.g. force regularization at small scales, particle density, finite box size, etc.) which lead directly to a breaking of such self-similarity. Thus the self-similarity of clustering provides a potentially powerful tool to separate the scales affected by such non-physical effects from the physical results representing the continuum limit. The focus of this study is to exploit self-similar models to better understand the resolution at small scales of N-body simulations. In particular, we will use simulations with a very small force smoothing which allow us to follow carefully the propagation of self-similarity to small scales in the course of a simulation.


The intensity of a geomagnetic storm is the result of the sustained interaction between the solar wind and the magnetosphere during the main phase of a storm. The most outstanding advantage of empirical formulae is their simplicity for space weather forecast: By inputting the solar wind parameters responsible for the main phase of a geomagnetic storm into an empirical formula, one can quickly get the estimated intensity of this geomagnetic storm. Of all empirical formulae, the Burton equation and OM equation have been used mostly to predict extreme geomagnetic storms. For example, the Burton equation was used to estimate the intensity of the storm that occurred on 1859 September 1–2 by Tsurutani et al. (2003), and Liu et al. (2014) used the OM equation to estimate the intensity of the storm on 2014 July 24. Extreme geomagnetic storms can cause widespread interference and damage to technological systems (Love 2021 and references therein) and then lead to significant economic loss (e.g., Council 2008; Schulte in den Bäumen et al. 2014; Eastwood et al. 2017; Riley & Love 2017). Hence, it is very important to ensure the accuracy of extreme geomagnetic storm forecasts. Now the question is whether the Burton equation or the OM equation can estimate the intensities of very large geomagnetic storms correctly. To answer this question, we compare the performance of the three models mentioned above using 15 great geomagnetic storms (ΔSYM-H ≤ −200 nT) that occurred during solar cycle 23. The solar wind parameters responsible for the main phases of the 15 storms are inputted into the three models to get the estimated intensities of the great geomagnetic storms (GGSs), which are compared with the observed intensities. To avoid any possible confusion, we use ΔSYM-H
b
, ΔSYM-Hom, and ΔSYM-H
w
 to indicate the intensities of a geomagnetic storm estimated by the Burton equation, the OM equation, and the WCL equation, respectively, while we use ΔSYM-Hob to represent the observed intensity, namely the real variation of the SYM-H index during the main phase of a geomagnetic storm. The rest of this article is organized as follows. The data source and method are presented in Section 2, the results are presented in Section 3, and the discussion and summary are presented in Section 4.


Finally, we compared the extinction-corrected upper limit on the optical flux of the PSR J0633+0632 PWN (Section 2.1) with its unabsorbed 0.3–10 keV X-ray flux. This is $F_{\rm X}^{{\rm pwn}} = 2.92^{+0.79}_{-0.81} \times 10^{-13}$ erg cm−2 s−1 (Abdo et al. 2013), computed by fitting the PWN area with an ellipse of semimajor and semiminor axis of 0.58 and 0.54 arcmin, respectively, oriented 130° due east (Marelli 2012). We subtracted the flux contribution of the point-like X-ray source south-west of the pulsar position (Fig. 2), which is only spatially coincident with the PWN. The extinction-corrected optical flux of the PWN in the g′ band is $F_{\rm opt}^{{\rm pwn}} \lesssim 9.8 \times 10^{-13}$ erg cm−2 s−1, integrated over the same area as used to compute the PWN X-ray flux. As done for the pulsars, we assumed the most conservative value of the interstellar extinction. This yields an optical-to-X-ray flux ratio of Fopt/Fx ≲ 4.6. PWNe have been detected both in the optical and X-rays around the Crab pulsar, PSR J0205+6449, PSR B0540−69, and PSR J1124−5916. Our upper limit on the Fopt/Fx for the PSR J0633+0632 PWN is above the values obtained for the other PWNe, which are typically ∼ 0.02–0.04, apart from the Crab PWN which has an Fopt/Fx ∼ 2 (Zharikov et al. 2008). This means that, owing to the faintness of the PSR J0633+0632 PWN in the X-rays, much deeper optical observations are needed to set similar constraints on its optical emission. We also compared the extinction-corrected optical spectral flux upper limit on the PWN in the g′ and r′-bands with the extrapolation of its X-ray spectrum in the optical domain. Like in Abdo et al. (2013), we used the best-fitting spectral index of the PWN, $\Gamma _{\rm X}^{{\rm pwn}} = 1.19^{+0.59}_{-0.22}$. The PWN SED is shown in Fig. 5. As seen, we cannot rule the presence of a spectral break between the optical and the X-ray energy range. A break in the optical/X-ray SED has been observed in other PWNe. For instance, the PWN around PSR B0540−69 features a clear break, with the optical fluxes being fainter than expected from the extrapolation of the X-ray PWN spectrum (Mignani et al. 2012). This is also the case for the PSR J1124−5916 PWN (Zharikov et al. 2008). A break in the opposite direction is observed in the SED of the PSR J1833−1034 PWN (Zajczyk et al. 2012), where the infrared fluxes (the PWN is not yet detected in the optical) are about two orders of magnitude above the extrapolation of the PWN X-ray spectrum. Only in the case of the Crab and PSR J0205+6449 PWNe, the PWN spectrum is compatible with a single PL, extending from the X-rays to the optical (Hester 2008; Shibanov et al. 2008). Optical detections of more PWNe through dedicated observing campaigns can allow one to relate the differences in the SEDs to the characteristics of the PWN.

Zharikov et al. 2008
Zharikov et al. 2008


The IGIMF theory (Kroupa et al. 2013) predicts a coupling between some properties of a galaxy (the SFR and the metallicity) and the IMF. Since the IMF in turn strongly affects the dynamical evolution of the galaxy, the feedback between galaxy evolution and IMF is difficult and the fully complexity of a variable IMF has not been yet included in hydrodynamical simulations (but see Bekki 2013; Ploeckinger et al. 2014; Recchi 2014). Even the here treated approach based on the so-called simple model of chemical evolution leads to implicit integral equations that must be solved iteratively. We note in passing that the dependence of the IMF on the metallicity is well established theoretically, as low-metallicity gas cools less efficiently and self-gravitating clumps are more resilient to fragmentation. This leads to the formation of dense cores of higher mass. For this reason, the IMF is supposed to be extremely biased towards massive stars if the metallicity is smaller than ∼10−4 Z⊙ (Schneider et al. 2002). Also the dependence of the IMF on the SFR is nowadays observationally well established (Hoversten & Glazebrook 2008; Meurer et al. 2009; Gunawardhana et al. 2011; Kroupa 2014), and the IGIMF theory is the only existing computable access accounting for these observations (Weidner et al. 2013). Thus, in spite of the inherent complexity, detailed simulations of galaxy evolution based on variable IMFs need to be performed. With this paper, we aimed at showing in a simple setting how to take into account IMF variations in models of the chemical evolution of galaxies (see also Martinelli & Matteucci 2000; Calura et al. 2010). The method outlined here can be used in order to extend analytical studies of the evolution of galaxies based on simple models of chemical evolution (e.g. Spitoni et al. 2010; Lilly et al. 2013; Pipino et al. 2014). We described how the solution of the simple model differs from the standard, textbook analytical solutions of the simple model. We also showed (building on previous results of Köppen et al. 2007) that the IGIMF theory naturally leads to a MZ relation. In fact, low-mass galaxies are characterized on average by smaller SFRs. According to the IGIMF theory, a low SFR leads to a steep, top-light IMF, in which the production of heavy elements by massive stars is extremely limited. More massive galaxies instead produce many more massive stars because of the higher level of SFR, hence the attained present-day metallicity is larger.


Since the manifold spirals arise in a system of reference which corotates with the bar, the manifold theory in its basic form predicts that the spiral arms should have the same pattern speed as the bar. This remark seems to come in conflict with observations both in our Galaxy (as reviewed e.g. in Bland-Hawthorn & Gerhard 2016; see also Antoja et al. 2014; Junqueira et al. 2015 and references therein) and in other galaxies (e.g. Vera-Villamizar et al. 2001; Boonyasait, Patsis & Gottesman 2005; Patsis, Kaufmann & Gottesman 2009; Meidt, Rand & Merrifield 2009; Speights & Westpfahl 2012; Speights & Rooke 2016). Considering again, galactic disc simulations, the leading paradigm over the years refers to simulations showing the coexistence of multiple pattern speeds (Sellwood & Sparke 1988; Little & Carlberg 1991; Rautiainen & Salo 1999; Quillen 2003; Minchev & Quillen 2006; Dubinski, Berentzen & Shlosman 2009; Quillen et al. 2011; Minchev et al. 2012; Baba, Saitoh & Wada 2013; Roca-Fabrega et al. 2013; Font et al. 2014; Baba 2015; but see also a noticeable exception in Roca-Fabrega et al. 2013), possibly connected also to the phenomenon of nonlinear coupling of multiple disc modes (Tagger et al. 1987; Tagger & Athanassoula 1991; Sellwood & Wilkinson 1993; Masset & Tagger 1997). On the other hand, it is well known that even isolated barred galaxies undergo substantial secular evolution (see Athanassoula 2013; Binney 2013; Kormendy 2013 in the tutorial volume Falcon-Barroso & Knapen 2013). The tendency to transfer angular momentum outwards (e.g. towards the halo or across the disc, Tremaine & Weinberg 1984; Debattista & Sellwood 1998; Debattista & Sellwood 2000; Athanassoula 2002; Athanassoula & Misiriotis 2002; Athanassoula 2003; OŃeill & Dubinski 2003; Holley-Bockelmann, Weinberg & Katz 2005; Berentzen, Shlosman & Jogee 2006; Martinez-Valpuesta, Shlosman & Heller 2006) leads the bar to slow down and grow in size at a rate which produces non-negligible change in dynamics at time-scales comparable even to a few bar periods. This process becomes complex, and even partially reversed due to the growth of ‘pseudo-bulges’ or peanuts (Kormendy & Kennicutt 2004), caused by dynamical instabilities such as chaos or the ‘buckling instability’ (Combes & Sanders 1981; Combes et al. 1990; Pfenniger & Friedli 1991; Raha et al. 1991; Bureau & Athanassoula 1999; Martinez-Valpuesta & Shlosman 2004; Bureau & Athanassoula 2005; Debattista et al. 2006). The reduction in size of the bar by the transfer of angular momentum under constant pattern speed is discussed in Weinberg & Katz (2007). Spiral activity acts as an additional factor of outwards transfer of angular momentum (Lynden-Bell & Kalnajs 1972), while a radial re-distribution of matter can take place even under a nearly preserved distribution of angular momentum (Hohl 1971; Sellwood & Binney 2002; Avila-Reese et al. 2005). Radial migration is enhanced by the amplification of chaos due to the overlapping of resonances among the various patterns (Quillen 2003; Minchev & Quillen 2006; Quillen et al. 2011).


Resonant dynamical friction may have applications beyond the relaxation of IMBHs examined in this paper. It may affect all objects in stellar clusters much more massive than the individual constituents of the disk, if present, including massive stars, stellar mass black holes (BHs), or the center of mass of massive binaries. Furthermore, it is also expected to operate in any type of disk with a high number of particles, including active galactic nucleus (AGN) accretion disks. Previously, it has been argued that stars and BHs crossing the disk on low-inclination orbits get captured by Chandrasekhar dynamical friction into the disk (Bartos et al. 2017; Panamarev et al. 2018; Tagawa et al. 2020). An interesting implication is that, if BHs settle into the disk, they interact dynamically and form BH–BH binaries efficiently, and frequent dynamical interactions and gas effects drive the BHs to merger, producing gravitational waves (GWs) detectable by LIGO, VIRGO, and KAGRA (McKernan et al. 2014, 2018; Bartos et al. 2017; Leigh et al. 2018; Yang et al. 2019; Tagawa et al. 2020, 2021; Samsing et al. 2020). Mergers are also facilitated by Lidov–Kozai oscillations in anisotropic systems (Heisler & Tremaine 1986; Petrovich & Antonini 2017; Hamilton & Rafikov 2019). The results in this paper show that resonant dynamical friction may accelerate the capture of objects in the accretion disks by a factor proportional to the SMBH mass over the local disk mass for large orbital inclinations. Pressure and viscosity in a gaseous disk do not inhibit the orbit-averaged torque from the IMBH, which leads to realignment and the warping of the disk (Bregman & Alexander 2012). Thus, RDF may efficiently catalyze the alignment of the orbital planes of BHs even in low-luminosity AGN or Seyfert galaxies with relatively small disk masses, which may not be possible for Chandrasekhar dynamical friction. In fact, this mechanism extends the scope of the “AGN merger channel” for GW source populations even beyond low-luminosity AGN and Seyfert galaxies, as it may organize BHs into disks also in nonactive galaxies with nuclear stellar disks.


This paper presents the results of our study of the effect of a dynamically adapting heat-conduction prescription, based on Kramers opacity law, in conjunction with semi-global MHD simulations. The main aim is to determine the effect of this prescription on the two major transitions reported in numerical studies (e.g., Gastine et al. 2014; Viviani et al. 2018). One concerns the rotation profiles, and is the transition from accelerated poles and decelerated equator to a solar-like profile, with a faster equator. The other involves the large-scale magnetic field, and is the transition from an axisymmetric magnetic field, as in the Sun, to a nonaxisymmetric magnetic field found in more rapid rotators. Previous studies (Viviani et al. 2018) found these transitions to occur at the same rotation rate, in contrast with the current interpretation of observations. The fact that simulations usually produce anti-solar differential rotation for the solar rotation rate could indicate that the Sun is in a transitional regime (e.g., Käpylä et al. 2014; Metcalfe et al. 2016), or could also mean that simulations still cannot fully capture the true rotational influence on turbulent convection in the Sun. Lehtinen et al. (2016) reported on the existence of nonaxisymmetric structures in stars with varying rotation rates, and were therefore able to determine quite a sharp transition point in terms of the rotation period, when fields turn from axi- to nonaxisymmetric configurations. According to dynamo theory, these two modes can compete, and there can be a transition region, where both dynamo modes co-exist, as is also clearly demonstrated by the models presented in this paper and those of Viviani et al. (2018). Therefore, the observational transition point must be regarded as a lower limit for the transition in terms of the rotation period, as it could be that the sensitivity of the current instruments is insufficient to detect the very weak nonaxisymmetric components. However, since active longitudes have not been detected on the Sun (Pelt et al. 2006), these two transitions should not be located at the same, nearly solar rotation rate.


Although each one of the four aforementioned mechanisms has some observational support in certain systems, there is not a single mechanism that can explain all observed polarization in protoplanetary disks. Alignment with respect to the local radiation anisotropy (“k-RAT alignment” thereafter) is best supported by the azimuthal polarization pattern observed at ALMA Band 3 in the HL Tau system (Kataoka et al. 2017). However, it predicts a strong azimuthal variation of polarization and circular pattern (rather than elliptical pattern) (Yang et al. 2019). There is some tentative evidences for alignment with respect to the magnetic field, through either Radiative Alignment Torques (“B-RAT alignment”; Lazarian & Hoang 2007), or recently proposed Mechanical Alignment Torques (Hoang et al. 2018), in, e.g., the IRAS 4A system at cm wavelengths (Cox et al. 2015; Yang et al. 2016b) and BHB07-11 (Alves et al. 2018) at (sub)millimeter wavelengths. But there is no well-resolved system that matches the theoretical expectations (see, e.g., Cho & Lazarian 2007; Yang et al. 2016b; Bertrang et al. 2017) assuming the widely expected disk toroidal magnetic field yet (Flock et al. 2015). Mechanical alignment has recently received some attention. Hoang et al. (2018) claims that under MATs, grains can be aligned with respect to local dust-gas streaming direction, in the case of a weak or zero magnetic field, even if the velocity difference is sub-sonic. Within this picture, Kataoka et al. (2019) investigated the direction of streaming velocities for dust grains with different Stokes numbers, and the resulting polarization orientations. They found that their polarization pattern in the order-of-unity Stokes number case resembles that observed by Alves et al. (2018) in BHB07-11. The BHB07-11, however, is a binary system, and we expect more complicated velocity fields than the simple one assumed in Kataoka et al. (2019). Yang et al. (2019) investigated the observational features of another mechanical alignment mechanism, the Gold mechanism (Gold 1952), to address the circular versus elliptical pattern problem in the ALMA Band 3 polarization observations of HL Tau disk. However, they failed to explain the nonexistence of strong azimuthal variation, and suggested the scattering by dust grains aligned under the Gold mechanism may be the origin of the polarization at ALMA Band 3 in the HL Tau system.


With only six free parameters, the standard Λ cold dark matter (ΛCDM) cosmological model fits no less than 2500 multipoles in the cosmic microwave background (CMB) angular power spectrum (Planck Collaboration XVI 2014), the Hubble diagram of Type Ia supernovae, the large-scale structure matter power spectrum, and even the detailed scale of baryonic acoustic oscillations. It thus provides the current basis for simulations of structure formation, and is extremely successful down to the scale of galaxy clusters and groups. Nevertheless, it still faces numerous challenges on galaxy scales. Among these, the most important ones are the too-big-to-fail problem (Boylan-Kolchin, Bullock & Kaplinghat 2011) and the satellite-plane problem (e.g. Pawlowski, Pflamm-Altenburg & Kroupa 2012; Ibata et al. 2014) for dwarf galaxies, the tightness of the baryonic Tully–Fisher relation (McGaugh 2012; Vogelsberger et al. 2014), or the unexpected diversity of rotation curve shapes at a given mass scale (Oman et al. 2015). The latter problem is actually a subset of a more general problem, i.e. that the shapes of rotation curves indeed do not depend on the Dark Matter (DM) halo mass, contrary to what would be expected in ΛCDM, but rather on the baryonic surface density, as has long been noted (e.g. Zwaan et al. 1995). This makes the problem even worse, since the rotation curve shapes are not only diverse at a given mass scale, but uniform at a given baryonic surface density scale, implying a completely ununderstood fine-tuning of putative feedback mechanisms. On the other hand, this behaviour of rotation curves is an a priori prediction of the formula proposed by Milgrom more than 30 yr ago (Milgrom 1983a,b), relating the total gravitational field to the Newtonian field generated by baryons alone, and which can be interpreted as a modification of Newtonian dynamics on galaxy scales below a characteristic acceleration (Modified Newtonian Dynamics (MOND), for a review see Famaey & McGaugh 2012; Milgrom 2014). With this simple formula, high surface brightness (HSB) galaxies are predicted to have rotation curves that rise steeply before becoming essentially flat, or even falling somewhat to the not-yet-reached asymptotic circular velocity, while low surface brightness (LSB) galaxies are predicted to have rotation curves that rise slowly to the asymptotic velocity. This is precisely what is observed, and was predicted by Milgrom long before LSB galaxies were even known to exist. The formula also predicts the tightness of the baryonic Tully–Fisher relation.


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