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


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.

Compare/Contrast
Compare/Contrast
Future Work


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


Our ideas about which systems may survive spiral-in and produce WR X-ray binaries were triggered by the realization that the peculiar X-ray binary SS433 has avoided going into CE evolution, and that the donor star in this system is transferring mass to the compact star by stable Roche lobe overflow (RLOF; King & Begelman 1999; King, Taam & Begelman 2000). By analysing the properties of this system we realized that it is the high mass of the compact star in this system [4.3(±0.8)  M⊙] in combination with the relatively low mass of its donor star [12.3(±3.3) M⊙] (Hillwig & Gies 2008), which allowed it to avoid CE evolution and enables it to gently spiral in without ever coalescing with its donor. As we consider SS433 to be a ‘keystone’ for understanding the formation of the WR X-ray binaries, we give in Section 2 a brief overview of its properties and evolutionary state. The avoidance of its going into CE evolution is – as we will argue – a consequence of the donor star having a radiative envelope (King et al. 2000), in combination with the donor star and accretor having a mass ratio less than 3.5. In Section 3, we then examine for which donor masses, mass ratios and orbital periods HMXBs will, when they start Roche lobe overflow, avoid going into CE evolution and may survive as WR X-ray binaries with short orbital periods. We also examine under which conditions they may still survive after having gone into CE evolution. In this section, some examples are given on how a number of well-known observed WR+O binaries with relatively short orbital periods are expected to evolve in the future, and are expected to produce WR X-ray binaries and, as a final evolutionary state, close double BHs. This model for producing double BHs is different from the ones proposed by Belczynski et al. (2016), Marchant et al. (2016) and de Mink & Mandel (2016). In Section 4, we attempt to estimate the birth rate of WR X-ray binaries in the Galaxy on the basis of our model, and find it to be still higher than observed and discuss possible ways to minimise this discrepancy. In Section 5, we discuss the results and estimate the possible birth rate of double BHs based on our model.


We calculated the dependence of the width of the profiles on the pulse period, considering the different frequencies separately. We note that the pulse width is not a direct reflection of the beam size or diameter (i.e. 2ρ, where ρ is beam radius). For a visual representation of the geometry see for instance Maciesiak et al. (2011) and Bilous et al. (2014). In fact, only if the observer’s line of sight cuts the emission centrally for magnetic inclination angles, α, that are not too small (i.e. α>  ~ 60°), w ≈ 2ρ. In such a case, when the emission beam is confined by dipolar open field lines, we would expect a P− 1 / 2 dependence, which has indeed been observed when correcting for geometrical effects by transforming the pulse width into a beam radius measurement (see Rankin 1993; Gil & Krawczyk 1996; Maciesiak et al. 2012). For circular beams, profile width and beam radius are related by the relation first derived by Gil et al. (1984): (5)\begin{equation} {\rho_{10}} = 2\sin^{-1} \left[\sin{\alpha}\sin{(\alpha+\beta)}\sin^2\left(\frac{w_{10}}{4}\right)+\sin^2\left(\frac{\beta}{2}\right)\right]^{1/2}\cdot \end{equation}ρ10=2sin-1sinαsin(α+β)sin2w104+sin2β21/2·The angle β is the impact angle, measured at the fiducial phase, φ, which describes the closest approach of our line of sight to the magnetic axis. This equation is derived under the assumption that the beam is symmetric relative to the fiducial phase. Typically, widths are measured at a certain intensity level (e.g. 50% or 10%, as here), and ρ values are derived accordingly. In many cases, profiles are indeed often asymmetric relative to the chosen midpoint, or become so as they evolve with frequency. We note that for a central cut of the beam (β = 0) and for an orthogonal rotator (α ~ 90°) the equation reduces to ρ = w/ 2 as expected, while in a more general case, where β = 0 and α ≫ ρ the relation reduces to ρ = (w/ 2)sinα. In principle, it is possible to determine α and β with polarisation measurements. However, in reality the duty cycle of the pulse is often too small to obtain reliable estimates (see Lorimer & Kramer 2004). Alternatively, at least for α, the relation reported by Rankin (1993) can be used: (6)\begin{equation} \label{eqn:w50} w_{50,{ \rm core}}(1~{\rm GHz}) = 2.45^\circ \cdot P^{-0.5\pm 0.2}/\sin(\alpha), \end{equation}w50,core(1GHz)=2.45◦·P−0.5±0.2/sin(α),calculated from the observed width dependency on period for the core components of pulsars (see Sect. 5.1), which is intrinsically related to the polar cap geometry. Equation (6) is valid at 1 GHz, but can be applied at LOFAR frequencies, maintaining the same dependence, if the impact angle β ≪ ρcore; sinα should be ignored for orthogonal rotators. Additionally, Rankin (1993), Gil et al. (1993), Kramer et al. (1994), Gould & Lyne (1998) suggested that “parallel” ρ − P relations are found if the radio emission of the pulsar can be classified and separated into emission from “inner” and “outer” cones, which seem to show different spectral properties (see Sect. 5.1 for details).


It is well known that there exists an anticorrelation between the cyclic variations of GCR intensity and SSN (Forbush 1954), and the time lag in this relationship has also been reported by Forbush (1958). The time lag in solar modulation of GCRs should be closely related to the transport of solar wind plasma with its embedded HMF through the modulation region. This effect has been considered in numerical models of GCR modulation to study the long-term modulation mechanism (e.g., Le Roux & Potgieter 1990; Ferreira & Potgieter 2004; Bobik et al. 2012; Potgieter et al. 2014; Qin & Shen 2017). Moreover, the delay time in odd solar cycles was found to be longer than that in even ones (e.g., Nagashima & Morishita 1980; Mavromichalaki & Petropoulos 1984; Usoskin et al. 1998; Mavromichalaki et al. 2007; Ross & Chaplin 2019). Drift theory has predicted that positively charged particles mainly drift inward through the polar region of the heliosphere during the A > 0 solar magnetic cycle, while they predominantly participate in the heliosphere along the wavy heliospheric current sheet when A  0 (Jokipii et al. 1977; Jokipii & Thomas 1981). Thus, positively charged particles will take a longer time to reach Earth when A  0, and such modulation mechanism may cause a longer delay time in odd cycles (Van Allen 2000; Cliver & Ling 2001). In addition, the time lag varies with the energy/rigidity of the particle, which is easy to understand: the higher the particle’s energy is, the shorter its propagation time in the modulation region. Such phenomenon is implied from several theoretical (O’Gallagher 1975; Strauss et al. 2011) and observational (Burger & Swanenburg 1973; Nymmik & Suslov 1995) studies. Meanwhile, the difference in the energy dependence of the time lag in odd and even solar cycles was also shown by Nymmik & Suslov (1995). However, in the correlation studies of Ross & Chaplin (2019), an obvious rigidity dependence on the delay time between SSN and GCR intensity recorded by NMs was not found. Thus, we focus on the GCR data from spacecraft rather than those from NMs in this work.


Information about fundamental parameters of stars – like their mass, luminosity, surface temperature and chemical composition – comes primarily from matching observations to synthetic spectra computed using models of stellar atmospheres. For massive stars with hot surfaces, scattering and absorption in spectral lines further transfer momentum from the star’s intense radiation field to the plasma, and so provides a force that overcomes gravity and drives a wind-outflow directly from the stellar surface (Castor et al. 1975). These starlight-powered winds are very strong and fast, and can dramatically affect the star’s atmospheric structure (review by Puls et al. 2008) as well as the evolution of its mass and luminosity, chemical surface abundances, rotational velocity, and nuclear burning life-times (review by Smith 2014). Atmospheric models of such hot, massive stars must thus generally be constructed using a unified, or global, approach, wherein the basic structural equations for the quasi-static photosphere and the outflowing stellar wind are solved simultaneously (Gabler et al. 1989). In addition, the expanding atmospheres of these stars are characterized by their large departures from local thermodynamic equilibrium (LTE), meaning the full number density rate equations (typically reduced to statistical equilibrium, and often simply called non-LTE or NLTE) must be solved to obtain the atmospheric radiation field and the excitation and ionization balance. As such, quite intricate numerical solution techniques are normally required to compute synthetic observables, like spectral lines and energy distributions, for these objects (for details, see book by Hubeny & Mihalas 2014). Over the past decades, much effort has been devoted toward constructing such global NLTE, steady-state model atmospheres of hot stars with winds; several numerical computer codes meanwhile exist on the market, for example CMFGEN (Hillier & Miller 1998), POWR (Gräfener et al. 2002; Sander et al. 2015), PHOENIX (Hauschildt 1992), WM-BASIC (Pauldrach et al. 2001), and the subject of this paper, FASTWIND (Santolaya-Rey et al. 1997; Puls et al. 2005; Rivero González et al. 2011; Carneiro et al. 2016). FASTWIND is routinely applied for both photospheric and wind analyses of hot stars, and used for detailed studies of individual objects as well as in large spectroscopic surveys (like within the recent VLT-FLAMES survey of massive stars in the Tarantula giant star-forming region in the Large Magellanic Cloud, Evans et al. 2011). A critical component of all these codes regards their practical treatment of the stellar wind; traditionally this has been to assume a parametrized steady-state and smooth outflow, without any clumps or shocks. However, it has been known for quite many years now, that these line-radiation driven winds are in fact inhomogeneous and highly structured on small spatial scales (see overviews in Puls et al. 2008, 2015; Hamann et al. 2008; Sundqvist et al. 2012b). Such wind clumping arises naturally from the strong line-deshadowing instability, the LDI, a fundamental and inherent property of line driving (e.g., Owocki & Rybicki 1984, 1985). Radiation-hydrodynamic, time-dependent wind models (Owocki et al. 1988; Feldmeier et al. 1997; Owocki & Puls 1999; Dessart & Owocki 2003; Sundqvist & Owocki 2013, 2015; Sundqvist et al. 2018) following the non-linear evolution of this LDI show a characteristic two-component-like structure consisting of spatially small and dense clumps separated by large regions of very rarified material, accompanied by strong thermal shocks and a highly non-monotonic velocity field. Such clumpy winds then affect both the atmospheric structure and the radiative transfer needed to derive synthetic observables; as just one example of this, neglecting clumping typically leads to observationally inferred mass-loss rates that might differ by more than an order of magnitude for the same star, depending on which spectral diagnostic is used to estimate this mass loss (Fullerton et al. 2006). Global model atmospheres nowadays normally account for such wind inhomogeneities by simply assuming a two-component medium consisting of overdense, optically thin clumps of a certain volume filling factor, following a smooth, parametrized velocity law, and an inter-clump medium that is effectively void (e.g., Hillier 1991; Puls et al. 2006). However, if clumps become optically thick, it leads to an additional leakage of light – not accounted for in the filling factor approach – through porous channels in between the clumps. Such porosity can occur either spatially (e.g., Feldmeier et al. 2003; Owocki et al. 2004; Sundqvist et al. 2012a), or for spectral lines in velocity-space due to Doppler shifts in the rapidly accelerating wind (sometimes thus called velocity-porosity, or “vorosity”, Owocki 2008). Regarding spatial porosity, several studies over the past years have focused on examining potential effects on the bound-free absorption of X-ray photons by the bulk wind (e.g., Oskinova et al. 2006; Owocki & Cohen 2006; Sundqvist et al. 2012a; Leutenegger et al. 2013; Hervé et al. 2013). Regarding velocity-space porosity, similar studies (Oskinova et al. 2007; Hillier 2008; Sundqvist et al. 2010, 2011, 2014; Šurlan et al. 2012, 2013) have shown that clumps indeed very easily become optically thick in especially the strong UV wind-lines of hot stars (the so-called P-Cygni lines), and that the associated additional leakage of line-photons leads to weaker line profiles than predicted by smooth or volume filling factor models1. But constructing realistic, multi-dimensional ab-initio radiation-hydrodynamic wind simulations that account naturally for (time-dependent) spatial and velocity-field porosity is an extremely challenging and time-consuming task (Sundqvist et al. 2018). Thus there has also been a big need for developing simplified, parameterized models that can be more routinely applied to diagnostic work on samples of hot stars with winds. Building on their prior studies Sundqvist et al. (2010; 2011; 2012a; 2014, hereafter SPO14) developed and benchmarked such a method, using effective quantities to simulate the reduction in opacity associated with optically thick clumps. In contrast to some other models mentioned above, this “effective opacity” approach has the great advantage that it can be quite readily implemented into the already existing (time-independent) global NLTE atmosphere models discussed above.


Otherwise (i.e. if there is insufficient mass left in the sub-grid gas reservoir), the mass deficit $m_\mathrm{BH} + \Delta m - m_\mathrm{BH}^\mathrm{dynamical}$ (the last term denotes the dynamical mass of the SMBH) is drawn from the surrounding gas particles. In eagle, this was done by stochastically swallowing individual gas neighbours. This is not an ideal approach: the momentum imparted on the SMBH from the swallowed gas particle may artificially dislodge it from its position, particularly without instantaneous repositioning (as also discussed by Steinborn et al. 2015). The mass of a gas particle is also typically much greater than Δm, so that the dynamical mass of SMBH particles remains systematically above its sub-grid mass. Both issues become more severe when individual gas particles have been enriched to masses well above their initial value due to stellar outflows, which is particularly common in massive, gas-poor galaxies. Instead of swallowing entire particles, we therefore transfer a (typically very) small fraction of mass from all gas neighbours to the SMBH simultaneously, with the mass δmi ‘nibbled’ from each neighbour i weighted in analogy to their contribution to the gas density at the location of the SMBH,
(4)$$\begin{eqnarray}
\delta m_i = (1-\epsilon _\mathrm{r}) \Delta m \left[\frac{w_i m_i}{\sum _j (w_j m_j)}\right],
\end{eqnarray}$$where wi is the kernel weight of particle i, mi its mass, and the sum is over all neighbours; as above, the factor of (1 − ϵr) accounts for the mass converted to energy. In addition to mass, a fraction δmi/mi of the momentum of neighbour i is also transferred to the SMBH. To prevent individual gas particles from becoming too light, we exclude any neighbour that would be reduced to less than half its initial mass and accept that the dynamical mass of the SMBH grows slightly less than desired in this case. In practice, we have found that this limit is never reached in the simulations presented here, because stars typically inject far more mass into gas particles than is drained by SMBHs.


Lenticular galaxies seems to have a wider range of properties compared to ellipticals that resemble more the old definition of ETGs. However, even in ellipticals, large differences prevail. Recent observations of elliptical galaxies with Spitzer and Herschel (Temi et al. 2005, 2007a, 2007b, 2009; Smith et al. 2012; Agius et al. 2013; Mathews et al. 2013) have revealed that the far-infrared (FIR) luminosity LFIR from these galaxies can vary by ∼100 among galaxies with similar optical luminosity. The 70 μm band luminosities (from Temi et al. 2007a, 2009), is a good example of such a huge scatter in the FIR luminosity of elliptical galaxies. Some of the high L70 galaxies are members of a small subset of ellipticals having radio detections of neutral and molecular gas. A few others may be S0 galaxies which, because of their rotationally supported disks, often contain large masses of cold gas and dust. Ellipticals containing large excess masses of dust and cold gas probably result from significant galaxy mergers in the past. However a fraction of elliptical galaxies appear to be completely normal but L70 in these galaxies still ranges over a factor of ∼30, far larger than can be explained by uncertainties in the estimate of the FIR spectral energy distribution (SED) due to local stellar mass loss. While a significant fraction of the cold gas mass in low- to intermediate-mass ETGs is thought to have an external, merger-related origin (e.g., Davis et al. 2011), in the most massive ETGs the cold gas phases are presumably generated internally (Davis et al. 2011; David et al. 2014; Werner et al. 2014). Mergers with gas- and dust-rich galaxies have often been suggested for the origin of dust in all elliptical galaxies (e.g., Forbes 1991). Although the merger explanation is almost certainly correct in some cases, mergers cannot explain most of the observed scatter in L70. A crucial element in our understanding of the evolution of galaxies toward ETGs is the mutual role played by the major merging of galaxies and the secular star formation quenching. Neither of these scenarios yet accounts for all the observational evidence, and one could assume both contributing to some extent.


Surveys of radio bursts in decimetric wavelengths is presented in papers by Isliker & Benz (1994) and Jirička et al. (2001), within 1–3 GHz and 0.8–2.0 GHz frequency ranges, respectively. Some of these bursts are still not well understood. This is a case of the slowly positively drifting bursts (SPDBs). They appear in groups or as single bursts, with a duration of an individual burst from 1 to several seconds and their frequency drift is lower than about 100 MHz s−1 (Jirička et al. 2001). The SPDBs seem to be similar to the reverse type III bursts (Aschwanden 2002) but their frequency drift is much smaller. The majority of observed SPDBs are connected to solar flares (Jirička et al. 2001), and they appear many times at the very beginning of the flares (Benz & Simnett 1986; Kotrč et al. 1999; Kaltman et al. 2000; Karlický et al. 2018). Kaltman et al. (2000) reported on several SPDBs observed during three solar flares in the 0.8–2 GHz frequency range. They found frequency drifts of the observed SPDBs to be within the 20–180 MHz s−1 range. Kotrč et al. (1999) studied one of those flares. By combining the radio and spectral plus imaging Hα observations, they explained the observed SPDBs as radio emission generated by downwards propagating shock waves. Based on numerical simulations of the formation of thermal fronts in solar flares, Karlický (2015) proposed that SPDBs observed in the 1–2 GHz range could be a signature of a thermal front. Furthermore, Karlický et al. (2018) reported the observation of an SPDB (1.3–2.0 GHz) observed during the impulsive phase of an eruptive flare. They found time coincidence between the SPDB occurrence, an appearance of an ultraviolet (UV)/EUV multithermal plasma blob moving down along the dark Hα loop at approximately 280 km s−1, and the observed change of Hα profile at the footpoint of that dark loop. Combining these observations they concluded that observed SPDB was likely generated by the thermal front formed in front of the falling EUV blob.


Type II supernovae (SNe II) are believed to originate from the core collapse of massive stars with initial masses larger than 8 M⊙ (Heger et al. 2003). They are characterized by prominent P-Cygni profiles of Balmer series in their spectra (Filippenko 1997). Photometrically, they are classified as SNe IIP if their light curves show extended plateau features (∼100 d), and SNe IIL if their light curves display post-peak linear declines (Barbon, Ciatti & Rosino 1979). Such a two-type classification is favoured by some statistical studies of SNe II (e.g. Faran et al. 2014a, b). However, Anderson et al. (2014) pointed out that if the sample is sufficiently large, one will find that SNe IIP and SNe IIL belong to a continuous distribution. Such a distribution is believed to be related to the mass of the hydrogen envelope maintained by the progenitor stars, as evidenced by the results that SNe having larger envelope masses produce light curves with shallower plateau slopes and longer plateau durations (Barbon et al. 1979; Swartz, Wheeler & Harkness 1991; Blinnikov & Bartunov 1993). In spite of the variety of envelope masses, the initial masses of the progenitor stars of SNe II are restricted to a certain range. Stellar evolution theory predicts an upper limit of 25 M⊙ for SN-II progenitors (Heger et al. 2003). Based on analyses of pre-explosion images (e.g. Smartt 2009), the progenitors of most SNe II are found to be red supergiants (RSGs), but their masses lie in a narrow range (i.e. ∼9–17 M⊙). This inconsistency is known as the ‘RSG problem’ and can be partially explained by the ‘failed SNe’ theory (Lovegrove & Woosley 2013). As SNe II can also be used to determine distances, thus they are intriguing to the cosmology community. The measurement methods include the Expanding Photosphere Method (EPM; Kirshner & Kwan 1974; Hamuy 2001) and the Standard Candle Method (SCM; Hamuy & Pinto 2002). The basic idea of EPM is to derive the intrinsic luminosity from the photospheric radius and the temperature, and then compare the intrinsic luminosity with the apparent value to obtain the distance, while the SCM is based on the correlation between the expansion velocity and the luminosity at a specific epoch.


With the advent of the Parker Solar Probe (PSP) we are able to directly measure properties of the solar wind closer to the Sun than ever before (Fox et al. 2016). One of the early highlight discoveries of PSP is the omnipresence of strong local deflections of the magnetic field in the solar wind, mostly referred to as switchbacks (Kasper et al. 2019; Horbury et al. 2020). These structures, also called folds, jets, or spikes, are not necessarily full reversals of the local magnetic field, unlike some names suggest. In fact, the measured distribution of deflections resembles a power law, with most of the deflections at small angles relative to the Parker spiral (Dudok de Wit et al. 2020). There is evidence that switchbacks are localized kinks in the magnetic field and not polarity reversals or closed loops (McManus et al. 2020; Whittlesey et al. 2020). However, switchbacks are not a new finding. They have already been observed for several decades, by, e.g., Helios (e.g., Horbury et al. 2018), out to 1.3 au by Ulysses (e.g., Balogh et al. 1999; Neugebauer & Goldstein 2013). The novelty in the PSP observations is their sharpness and omnipresence (among other features; see Dudok de Wit et al. 2020), indicating that switchbacks are a more frequent feature closer to the Sun. This observation lends the possibility that switchbacks may originate lower in the solar atmosphere. The formation mechanism(s) of switchbacks, and whether they represent large-amplitude Alfvén waves or structures advected by the solar wind, is as of yet not known. Several explanations about their origin have been put forth. Among these theories, interchange reconnection is the most focused upon (Yamauchi et al. 2004; Fisk 2005; Fisk & Kasper 2020). In this scenario, switchbacks are generated in the solar corona, and form at the reconnection sites between open and closed magnetic fluxes. In some studies, it is argued that the interchange reconnection results in magnetic flux ropes, which are ejected by the reconnection outflow, and are advected by the wind (Drake et al. 2020). In other studies, reconnection is thought to generate either Alfvénic (He et al. 2020) or fast magnetosonic (Zank et al. 2020) wave pulses. Alternatively, as the distribution of deflections appears to be featureless and monotone in switchbacks (Dudok de Wit et al. 2020), they may not be a distinct feature but a manifestation of the ensuing turbulent dynamics in the solar wind (Squire et al. 2020). Thus, it is still not clear whether switchbacks originate in the lower solar atmosphere, or represent dynamic features of solar wind turbulence. Additionally, it is not clear whether they are wavelike perturbations, propagating at the Alfvén or some other characteristic speed, or structures that are advected by the wind, such as flux ropes. However, some observations offer good constraints on the nature of switchbacks. Given that switchbacks are characterized by a strong Alfvénic correlation of their velocity and magnetic field perturbations, a nearly constant magnetic pressure, and velocity enhancements along the propagation direction, an interpretation in terms of propagating nonlinear Alfvén waves is a plausible scenario (Matteini et al. 2014). Alternatively, their localization in the perpendicular direction and the kink-like geometry may indicate their kink fast magnetoacoustic nature (e.g., Van Doorsselaere et al. 2008). An additional option is the association of the switchbacks with kink solitons, which keep their shape because of the balance between nonlinear and dispersive effects (see, e.g., Ruderman et al. 2010), i.e., a stationary nonlinear kink wave pulse. Other observations, such as a sharp rise in ion temperature at the boundaries of switchbacks are more compatible with an origin by reconnection (Farrell et al. 2020; Mozer et al. 2020).


With regard to Ni isotopes in the metal phase of iron meteorites, multiple studies have analyzed samples belonging to the same iron groups (e.g., IIAB, IIIAB, IVA, IVB) using broadly similar techniques (i.e., wet chemical separation of Ni followed by mass spectrometry). The initial studies reported no nucleosynthetic anomalies (Cook et al. 2006; Quitté et al. 2006). As analytical precision improved, anomalies were reported in some subsequent studies (e.g., Bizzarro et al. 2007; Regelous et al. 2008; Steele et al. 2011) but not in others (e.g., Dauphas et al. 2008; Chen et al. 2009), and no clear picture has emerged. Moreover, the interpretation of Ni isotopic data is hampered by the omission of data for 64Ni, the least abundant Ni isotope, from multiple studies. For Fe isotopes, initial studies pointed to a high degree of homogenization among various meteorite classes (e.g., Dauphas et al. 2008; Tang & Dauphas 2012). However, more recent studies (Cook & Schönbächler 2017; Schiller et al. 2020) have revealed small non-mass-dependent variations in Fe isotopes. A related issue, also without consensus, concerns the magnitude of the initial abundance of the radionuclide 60Fe in the early solar system. A wide variety of sample types have been analyzed in an attempt to constrain the solar system initial 60Fe/56Fe ratio including CAIs (e.g., Quitté et al. 2007), chondrules (e.g., Tachibana et al. 2006; Telus et al. 2018), chondritic metal (Cook et al. 2006), and differentiated meteorites, such as angrites and eucrites (e.g., Tang & Dauphas 2012, 2015). These studies have broadly used one of two analytical approaches: wet chemical separation of Ni followed by mass spectrometry or in situ analyses using ion microprobe (aka SIMS). Among these studies, estimates of 60Fe/56Fe span more than a factor of 100 (e.g., Quitté et al. 2007; Tang & Dauphas 2012, 2015) from ≈2 × 10−6 to ≈1 × 10−8. Determining the initial 60Fe/56Fe ratio in the protoplanetary disk is important for studies of early solar system chronology. Furthermore, radioactive decay of 60Fe may have been an important heat source on early-formed bodies, but this depends on its abundance (Kohman & Robison 1980; Yoshino et al. 2003).


For over a decade, a tight correlation between metallicity and galaxy stellar mass (

), i.e., the mass–metallicity relation (MZR), has been quantitatively established, from the vast database of local galaxies observed by the Sloan Digital Sky Survey (SDSS; Tremonti et al. 2004; Zahid et al. 2012; Andrews & Martini 2013). This relation has been further extended to high redshifts, using deep near-infrared (IR) spectroscopy facilitated by large ground-based and space-based telescopes (Erb et al. 2006; Maiolino et al. 2008; Zahid et al. 2011; Henry et al. 2013; Steidel et al. 2014; Sanders et al. 2015; Guo et al. 2016). The measurements of the MZR as a function of redshift can cast useful constraints on various galaxy evolution models, since the slope of the MZR is sensitive to the properties of outflows, such as the mass loading factor and the outflow speed (see, e.g., Davé et al. 2012; Lu et al. 2015a). This slope can also be explained by variations of star-formation efficiency and gas mass fraction in galaxies with different stellar masses (see, e.g., Baldry et al. 2008; Zahid et al. 2014). The normalization of the MZR can shed light upon the stellar chemical yield across cosmic time (Finlator & Davé 2008). Mannucci et al. (2010) first suggested that there exists a so-called fundamental metallicity relation (FMR) in the 3D parameter space spanned by

, star-formation rate (SFR), and metallicity, such that the MZR is merely a 2D projection of this more fundamental 3D manifold (see also Hunt et al. 2016). This 3D scaling relation shows a tight scatter (∼0.05 dex) in metallicity and is speculated to not evolve with z. In this context, the apparent redshift evolution of the MZR normalization originates primarily from sampling the FMR in terms of galaxies with different SFR. This concept of the FMR is in accord with the gas regulator model proposed by Lilly et al. (2013), even though mergers can also play a subtle role in shaping the form of the FMR by increasing the scatter (Michel-Dansac et al. 2008). However, at high redshifts, the validity of the FMR is still under investigation (see, e.g., Wuyts et al. 2014; Sanders et al. 2015).


Afterglows of gamma-ray bursts (GRBs) are generally believed to be produced by a relativistic jet interacting with the surrounding medium (e.g., Mészáros & Rees 1997; Sari et al. 1998; Kumar & Zhang 2015). Very early multi-wavelength afterglows are critical to reveal the properties of the radiating fireball and its environment as well as the central engine of GRBs. Using the prompt slewing and precise locating capacity of the X-ray telescope (XRT) on board the Swift mission, very early X-ray and optical afterglows were obtained with the XRT and ground-based optical telescopes. The early X-ray afterglows are usually dominated by erratic X-ray flares and the tail emission of prompt gamma-rays are due to the arrival time delay of photons in the high latitude of the radiating fireball (Liang et al. 2006; O’Brien et al. 2006; Zhang et al. 2006, 2007a). The flares and prompt tail emission are usually not seen in the early optical afterglow data (Li et al. 2012; Wang et al. 2013). About one-third of well-sampled optical afterglow light curves show a clear smooth bump (Li et al. 2012). It may be attributed to deceleration of the fireball by the ambient medium (see Rees & Mészáros 1992; Mészáros & Rees 1993 and Sari & Piran 1999 for the thin shell case; Kobayashi et al. 1999 and Kobayashi & Zhang 2007 for the thick shell case). This may give the most robust estimate for the initial Lorentz factor (

) of the fireball since the deceleration time weakly depends on other model parameters than

 (e.g., Molinari et al. 2007; Melandri et al. 2010; Xin et al. 2015). With a sample of GRBs with a detected optical afterglow onset bump, Liang et al. (2010) derived their

 and found a tight

 relation (see also a

 relation in Lu et al. 2012). Furthermore, by incorporating the peak energy of the

 spectrum in the burst frame (

) into the

 relation, a tighter

 relation is found (Liang et al. 2015). This relation places strong constraints on the composition of GRB fireballs.


Unlike the CMB, the 21 cm signal is highly non-Gaussian, because patchy, bubble-like structures of ionized hydrogen (H ii) regions are produced surrounding the ionizing sources. Thus, there is potentially a wealth of information in the 21 cm signal that is not contained in the 21 cm power spectrum, a two-point statistics of 21 cm brightness temperature fluctuations that is traditionally well studied in the literature. It is therefore essential to develop new methods that maximally exploit the full information in the 3D 21 cm images obtained by the SKA. Toward this goal, conventionally, new summary statistics that can only be measured with imaging have been proposed. These include the three-point correlation function (Hoffmann et al. 2019; Jennings et al. 2020), bispectrum (Yoshiura et al. 2015; Shimabukuro et al. 2016, 2017; Majumdar et al. 2018, 2020; Hutter et al. 2020; Saxena et al. 2020; Kamran et al. 2021), one-point statistics (Harker et al. 2009; Shimabukuro et al. 2015; Gorce et al. 2021), topological quantities such as the Minkowski functionals (Gleser et al. 2006; Chen et al. 2019; Kapahtia et al. 2021) and Betti numbers (Giri & Mellema 2021), the cross correlation between the 21 cm line and other probes, such as the CO line (Gong et al. 2011; Lidz et al. 2011), the C ii line (Gong et al. 2012; Beane & Lidz 2018), the kinetic Sunyaev–Zel’dovich (kSZ) effect (Ma et al. 2018; La Plante et al. 2020), and novel techniques such as the antisymmetric cross correlation between the 21 cm line and CO line (Zhou et al. 2021). Since those summary statistics are fully determined by the parameters in the reionization models (hereafter “reionization parameters”), in principle, Monte Carlo Markov Chain (MCMC) methods can be employed to constrain the reionization parameters from measurements of those statistics with futuristic 21 cm experiments (see, e.g., Watkinson et al. 2022), just as the MCMC analysis with the 21 cm power spectrum (Greig & Mesinger 2015, 2017, 2018).


Owing to their brightness at rest-frame FIR wavelengths, the ionized and neutral species of Carbon, Nitrogen, and Oxygen are powerful diagnostic lines for tracing the ISM of nearby and distant galaxies. When combined with photodissociation region (PDR) models (Tielens & Hollenbach 1985), measurement of the emission from different lines provide a means to constrain quantities such as the ionization rate and metallicity of the ISM of galaxies. Multilevel FIR transition lines have now been widely surveyed in local galaxies, originally by ISO (e.g. Luhman et al. 1998; Malhotra et al. 2001) and more recently using the PACS spectrometer (Poglitsch et al. 2010) on the ESA Herschel Space Observatory (Pilbratt et al. 2010). The [C ii]158 μm line is typically the brightest in star-forming galaxies, arising from ionized, and even neutral gas where it is the main coolant (Wolfire et al. 2003). Another commonly observed FIR line tracer of the ionized ISM is [N ii]122 μm. It has the advantage that it can be found associated with lower excitation gas, close to that observed in our own Galaxy (e.g. Goldsmith et al. 2015; Herrera-Camus et al. 2016). Another major coolant of the ISM is [O i]63 μm (Wolfire et al. 2003). Owing to its high excitation temperature and critical density, it can dominate the cooling in regions of starburst activity (Kaufman et al. 1999; Kaufman, Wolfire & Hollenbach 2006; Brauher, Dale & Helou 2008; Croxall et al. 2012; Narayanan & Krumholz 2017). When combined with measurements of the [C ii]158 μm line intensity and FIR luminosity, the [O i]63 μm line intensity can constrain the FUV field, G, and the gas density using PDR models. The luminosity in these FIR lines generally exhibits a deficit in the most FIR luminous galaxies compared to the trend expected from lower luminosity galaxies (e.g. Malhotra et al. 2001; Graciá-Carpio et al. 2011; Díaz-Santos et al. 2017). This has made the emission from lines like [O i]63 μm more challenging to detect at high-redshifts.


Globular clusters are of particular dynamical interest because of the phenomena of core collapse and binary burning. Stellar interactions in dense globular clusters tend to drive the central core towards a collapse to a state of extremely small radius and high density. Primordial binary populations may delay the onset of this core collapse by serving as dynamical energy sources, but eventually become depleted by various destruction mechanisms (e.g. Verbunt & Freire 2014), allowing core collapse to proceed (e.g. Fregeau et al. 2003, and references therein). Several studies suggest that black hole binaries, rather than main-sequence (MS) binaries, are critical for delaying core collapse (e.g. Breen & Heggie 2013; Wang et al. 2016; Kremer et al. 2019). In addition, an intermediate-mass black hole (IMBH) in a cluster core will act as a strong central energy source able to delay, or even prevent, core collapse (e.g. Baumgardt, Makino & Ebisuzaki 2004; Gill et al. 2008; Lützgendorf, Baumgardt & Kruijssen 2013). In any case, after an initial collapse, the cluster core will undergo gravothermal oscillations of expansion and contraction, as first demonstrated by Sugimoto & Bettwieser (1983), during which the core radius remains quite small. About 20–25 globular clusters, including NGC 6397 and NGC 6752, have very compact (rc ≲ 10 arcsec), high-density cores that appear to be post-collapse. The post-collapse oscillations of these cores should produce episodic bursts of strongly enhanced dynamical binary formation and ejection during the densest phases, as noted by Lugger et al. (2007). Their reasoning is based on the scaling of the encounter rate Γ, which is given by the integral of ρ2/v over the cluster volume, where ρ is spatial mass density and v is the velocity dispersion (Verbunt & Hut 1987; Bahramian et al. 2013). The encounter rate can be approximated by the simplified expression $\Gamma \propto \rho _0^2 r_c^3/v_0$ (Pooley et al. 2003), where ρ0 is central density, rc is the core radius, and v0 is the central velocity dispersion. This results in $\Gamma \propto r_c^{-1.4}$ for a simple homologous model for core collapse, in which $\rho _0 \propto r_c^{-2.2}$ and $v_0 \propto r_c^{-0.05}$ (Cohn 1980).


However, it is not straightforward to explain H2 formation in astronomical sources even when the catalytic roles of dust grains are introduced into models. Interstellar species are believed to be formed on cold grain surfaces via the so called Langmuir–Hinshelwood mechanism (Watson & Salpeter 1972; Pickles & Williams 1977; Hasegawa, Herbst & Leung 1992). To form H2, H atoms accrete on dust grains and then bind weakly with surfaces, which is known as physisorption. They can overcome the diffusion barrier and move on the grain surfaces via quantum tunnelling or thermal hopping. However, laboratory and theorectical studies showed that quantum tunnelling does not contribute much to the mobility of H atoms on silicate, carbonaceous or solid amorphous water (ASW) surfaces (Pirronello et al. 1997, 1999; Katz et al. 1999; Nyman 2021). If H atoms encounter other H atoms, then H2 molecules are formed. But H atoms can also desorb and leave grain surfaces. A hydrogen atom must reside on a grain long enough to find a partner H atom to form H2. As the dust temperature increases, the H atom desorption and diffusion rates also increase. So the temperature of grain surfaces must be sufficiently low so that an H atom can encounter another one before it desorbs. On the other hand, the temperature of grain surfaces must be high enough so that H atoms can diffuse on the grain surface. The parameter that measures how strongly species are to bound to grain surfaces is called desorption energy. It was found that if we assume a single H desorption energy in models, the dust temperature range over which efficient H2 formation occurs is narrow (6–10 K for olivine grains) (Katz et al. 1999). Moreover, it was found that the highest dust temperature at which H2 can be formed efficiently is less than 17 K (Katz et al. 1999). However, the grain surface temperature in the unshielded diffuse clouds, where hydrogen molecules are believed to be efficiently formed, is around 20 K (Li & Draine 2001).


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


Magnetic fields are actively searched for at the surface of all kinds of stars throughout the Hertzsprung-Russell diagram (HRD), as they probably impact stellar evolution from birth to death in various ways (see e.g., Donati & Landstreet 2009 for a general review; and Wade et al. 2016; Alecian et al. 2013; Vidotto et al. 2014; Folsom et al. 2016 for recent spectropolarimetric surveys on massive, intermediate-mass, and low-mass stars). Recently, magnetic fields have been unambiguously detected via Zeeman signatures in a large sample of single G-K giants observed with the spectropolatimeters TBL/Narval and CFHT/ESPaDOnS (Konstantinova-Antova et al. 2013; Aurière et al. 2015; Borisova et al. 2016; Tsvetkova et al. 2017). Interestingly, the cool intermediate-mass evolved stars with surface magnetic fields are found to cluster in certain regions of the HRD that correspond to precise moments of their evolution where convective envelopes make up a significant fraction of the stellar mass. These observations are of particular importance for stellar-evolution modeling, since magnetic fields may play a crucial role in the angular momentum evolution of different types of stars. For instance, it is well established that magnetic fields affect the rotation rate of solar-type stars through the torque applied to stellar surfaces by magnetically coupled stellar winds (e.g., Schatzman 1962; Matt et al. 2015; Réville et al. 2015; Amard et al. 2016). However, the efficiency and the impact of magnetic braking for evolved stars are not well studied yet. In addition, because of the angular momentum they transport (e.g., Spruit 1999; Mathis & Zahn 2005), magnetic fields may play an important role in explaining the properties of core and surface rotation in giants as seen by asteroseismology (e.g., Beck et al. 2012; Mosser et al. 2012b,a; Deheuvels et al. 2012, 2014; Cantiello et al. 2014; Di Mauro et al. 2016), as well as the rotation rate of white dwarf remnants (Suijs et al. 2008). By comparing the observed rotational and magnetic properties of stars at different evolutionary phases with the predictions of rotating stellar models, one may thus obtain strong constraints on the input physics of the stellar models. Conversely, it is important to know whether the possible presence and the global properties of the magnetic field of a given star can be anticipated from its position in the Hertzsprung-Russell diagram (see Gregory et al. 2012 for the case of pre-main sequence stars).


The search for observational evidence of dark matter substructure in galaxies is on-going, as traditional methods for in-directly detecting dark matter sub-haloes (e.g. modelling tidal streams and gravitational lensing) have yet to agree on either the Milky Way’s or an external galaxies’ current substructure composition. Gravitational lensing allows for constraints to be placed on the dark matter substructure content of external galaxies, as orbiting sub-haloes will result in anomalies in strong gravitational lenses (Mao & Schneider 1998; Dalal & Kochanek 2002; Vegetti et al. 2012). The disruption of stellar streams by dark matter sub-haloes in the Milky Way has also been well studied (e.g. Johnston, Spergel & Haydn 2002; Ibata et al. 2002; Carlberg 2009; Erkal et al. 2016; Sanders, Bovy & Erkal 2016; Bovy, Erkal & Sanders 2017; Carlberg 2017), with gaps in stellar streams believed to be a tell-tale sign that a stream has recently encountered a sub-halo. Hence the presence of gaps in a tidal stream, or lack thereof, can be used to constrain the dark-matter substructure properties of the Milky Way (Yoon, Johnston & Hogg 2011; Carlberg 2012; Erkal & Belokurov 2015a,b; Bovy 2016; Carlberg 2016; Banik et al. 2018; Bonaca et al. 2019). However gaps in tidal streams, as well as overdensities and asymmetry, can also be produced as stars are tidally stripped from a star cluster along its orbit (Küpper et al. 2010), disc shocking (Odenkirchen et al. 2003), spiral arms (Dehnen et al. 2004), a tri-axial halo (Küpper et al. 2015), the Galactic bar (Pearson, Price-Whelan & Johnston 2017), interactions with giant molecular clouds (Amorisco et al. 2016), the stream’s progenitor cluster (Webb & Bovy 2018), and complex dynamical histories (i.e a time-dependent tidal field due to galaxy growth via mergers or accretion) (Carlberg 2018). Banik & Bovy (2018) recently studied these effects in detail for the Pal 5 stream and found that the bar and molecular clouds can each individually explain the observed structure of the Pal 5 stream. Hence new methods are required in order to help search for dark matter substructure in the Milky Way and constrain its properties.


This dynamical limit on planetesimal sizes could suggest that these may exist in the belt a factor of 103 larger than the ${\sim }1\,$km sized lower limit predicted by collisional replenishment. However, if the assumed α = 3.5 Dohnanyi (1969) size distribution continued up to planetesimals of this size, then the disc mass would be $M_{\rm {disc}}{\sim }220\, M_{\oplus }$, a factor of ∼3 higher than the prediction of Schüppler et al. (2016) and over an order of magnitude larger than the lower limit derived from the collisional lifetime and age of the system. This would not violate our earlier calculation since these ≫1 km planetesimals could be abundant in the disc without having collided within the age of the system. Whilst this higher total disc mass is still consistent with the dust mass measurements of protoplanetary discs (for example, see Andrews & Williams 2005; Ansdell et al. 2016; Cieza et al. 2019), high debris disc masses, i.e. those in the range of $100\!-\!1000\, M_{\oplus }$, become problematic since these would require a very high efficiency of primordial dust being incorporated into these larger planetesimals (an example of the so-called ‘disc mass problem’, see Krivov et al. 2018; Krivov & Wyatt 2021). Nevertheless, it might still be possible to explain the observed level of stirring by embedded bodies while retaining a lower disc mass (i.e. if the largest bodies are less frequent than the α = 3.5 size distribution would predict). If instead the size distribution had a slope of α = 3.7, then even with these 1200 km bodies, the total disc mass estimate would be reduced from ${\sim }220\, M_\oplus$ to ${\sim }6\, M_\oplus$, since the total number of these would be greatly reduced. On the other hand, the size distribution could be truncated, being much steeper for planetesimals larger than a few kilometres, and shallower in other regions. We estimate the effect that this can have on the derived disc mass using equation (9) of Krivov & Wyatt (2021), and find that the total mass can be reduced by an order of magnitude from ${\sim }220\, M_\oplus$ to ${\sim }17\, M_\oplus$, if based on a triple power law size distribution, with qmed = 4, qbig = 3 and q = 3.5. Alternatively the measured vertical scale height could be due to other dynamical interactions (e.g. stirring by a planet internal or external to the belt, or a recent stellar fly-by) or even be a remnant of the primordial disc (e.g. if this disc was born stirred, Booth & Clarke 2016). In summary, whilst q1 Eri at an age of ${\sim }1.4\, \rm {Gyr}$ is an outlier in terms of its brightness, it need not be an outlier in terms of its disc mass unless many much larger planetesimals are present.


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.


The nonaxisymmetric potential of a bar induces large-scale streaming motions in stars and gas into the central part of the galaxy (e.g., Athanassoula 1992a, 1992b; Sellwood & Wilkinson 1993). Being dissipative, the gas loses angular momentum and energy and flows inward toward the galactic center (Knapen etÂ al. 1995; Regan etÂ al. 1999; Sheth etÂ al. 2000, 2002), accumulating in the central â¼1Â kpc of galaxies (e.g., Sakamoto etÂ al. 1999; Sheth etÂ al. 2005). The accumulation of gas in the central parts leads to high levels of circumnuclear star formation activity (SÃ©rsic & Pastoriza 1965; Hawarden etÂ al. 1986; Devereux 1987; Martin 1995; Ho etÂ al. 1997; Sheth etÂ al. 2000, 2005; Gadotti & dos Anjos 2001; Ellison etÂ al. 2011; Coelho & Gadotti 2011; Wang etÂ al. 2012); this circumnuclear star formation is often in the shape of nuclear rings (Knapen etÂ al. 2002; ComerÃ³n etÂ al. 2010; Kim etÂ al. 2012; Seo & Kim 2013) and nuclear star clusters (BÃ¶ker etÂ al. 2002, 2004, 2011). Such star formation activities may help to create disky pseudobulges (Kormendy & Kennicutt 2004; Sheth etÂ al. 2005; Athanassoula 2005; Debattista etÂ al. 2006). Bars are the primary mechanism for transporting gas from a few kiloparsec scale to the central kiloparsec. However, there have been mixed answers to the question of whether the presence of a bar and active galactic nucleus (AGN) activity are connected. Some studies find weak statistical links among AGN activity and the presence of bars (e.g., Arsenault 1989; Knapen etÂ al. 2000; Laine etÂ al. 2002; Laurikainen etÂ al. 2004a; Coelho & Gadotti 2011), whereas others find little or no link (e.g., Moles etÂ al. 1995; McLeod & Rieke 1995; Mulchaey & Regan 1997; Ho etÂ al. 1997; Hunt & Malkan 1999; Martini etÂ al. 2003; Lee etÂ al. 2012; Cisternas etÂ al. 2013). While bar torques drive gas inside the bar corotation inward, they push the gas between the corotation and outer Lindblad resonance (OLR) outward (Combes 2008; Kubryk etÂ al. 2013).


As can be seen from Fig. 1, in both the optical and the NIR band, several predominant flares appearing in the whole period considered are usually surrounded by other smaller subflares. In addition, it seems that the NIR light curves follow a similar flaring activity, lasting for several days or weeks, to the optical bands, although the NIR flux is more variable compared than the optical one, increasing by about 7 times in the J band, from 9.68 to 67.85 mJy (for an example, see Table 1). An exponential rise/decay model can appropriately fit the blazar light curve, which generally consists of superpositions of a steady background flux density and a number of flare components caused by events in the jet or the accretion disc/corona region (e.g. Valtaoja et al. 1999; Chatterjee et al. 2008; Abdo et al. 2010b; Chatterjee et al. 2012; Guo et al. 2016; Li et al. 2017, 2018, and references therein). Following Abdo et al. (2010b), we define the multipeaked model to analyse the temporal flare profiles during the interval of interest:
(3)
\begin{eqnarray*}
F(t) = {F_{\rm c}} + \sum _{i}\left[{F_i}{\left({{{\rm e}^{\frac{{{T_{0,i}} - t}}{{{T_{r,i}}}}}} + {{\rm e}^{\frac{{{\rm t} - {T_{0,i}}}}{{{T_{{\rm d},i}}}}}}} \right)^{ - 1}}\right],
\end{eqnarray*}
where Fc is the assumed constant background flux level underlying the flare components and is constrained to be less than or equal to the lowest value of flux, and the sum runs over all of the individual flares being fitted. For any one of the individual flares, Fi is the variability amplitude, T0, i is the epoch of the peak, and Tr, i and Td, i are the time-scales of rise and decay, respectively. Equation (3) represents flares within a limited time interval, because the observational gaps exist regularly or occasionally. In order to ensure the accuracy of the fitting model, the divided observational segments in different bands mentioned in Section 2 were used to analyse the temporal flare profiles. Each segment of the light curves was first interpolated by means of cubic spline interpolations through the 1-d binned light curves, then smoothed by a five-point moving-average filter to reduce the impact of the short-term variabilities.


Outflows from the central regions of active galactic nuclei (AGNs) are thought to be the main agents that regulate the evolution of both the central supermassive black holes as well as the host galaxies (Silk & Rees 1998; Di Matteo, Springel & Hernquist 2005). The presence of high-velocity outflows from AGNs can be established from the evidence provided by the blueshifted broad absorption lines (BALs) seen in the spectra of 10–20 per cent of quasi-stellar objects (QSOs)1 (Weymann et al. 1991). BALQSOs are classified into three sub-classes based on the ionization state of the absorbing gas: (a) high-ionization BALQSOs (HiBALs) consist of absorption from high-ionization lines such as C iv, Si iv, and N v (Gibson et al. 2008; Filiz Ak et al. 2013; Vivek, Srianand & Gupta 2016; Vivek 2019; Mishra et al. 2021) (b) low-ionization BALQSOs (LoBALs) show absorption from low-ionization lines such as Mg ii and Al iii along with the high-ionization lines (Voit, Weymann & Korista 1993; Vivek et al. 2014; Vivek, Srianand & Dawson 2018; Yi et al. 2019), and (c) iron-LoBALs (FeLoBALs) are LoBALs with excited fine-structure Fe ii and/or Fe iii absorption lines (Vivek et al. 2012; McGraw et al. 2015). The observed BALQSO fraction is explained either by an orientation model, where the line of sight intersects with the BAL absorbing clouds in 10–20 per cent QSOs (Weymann et al. 1991; Elvis 2000), or an evolutionary model, where the QSO spends 10–20 per cent of its lifetime in the BALQSO phase (Farrah et al. 2007; Lipari et al. 2009). Although the similarity in the optical/NIR properties of BAL and non-BALQSOs, higher reddening and polarization features in BALQSOs support the orientation model, the observed radio spectral indices of BALQSOs and the discovery of polar winds in BALQSOs challenge this scenario (Reichard et al. 2003; Zhou et al. 2006; Wang, Wang & Wang 2007; Montenegro-Montes et al. 2008). On the other hand, the anticorrelation between the radio loudness parameter and balnicity index, Compact Steep Spectrum (CSS) nature of BALQSOs, and the redshift dependence of BALQSO fraction favour the evolutionary model (Gregg, Becker & de Vries 2006; Farrah et al. 2007; Allen et al. 2011).


In this paper, following the method proposed by Ofek et al. (2003), we use the differential optical depth to lensing with respect to the lens redshift zl as the probability density. For a statistical sample that contains Nl strong lensing systems, the log-likelihood of observing the lens at redshift zl is given by
(9)$$\begin{eqnarray*}
{\rm ln}\mathcal {L}({\bf p})=\sum _{i=1}^{N_l} {\rm ln} \delta p_i({\bf p}),
\end{eqnarray*}$$where p represents the set of the VDF parameters (α, β) and the galaxy evolution parameters (νn, νv). Now one can perform Monte Carlo simulations of the posterior likelihood ${\cal L} \sim \exp {(- \chi ^2 / 2)}$, where the χ2 function is defined as
(10)$$\begin{eqnarray*}
\chi ^2=-2{\rm ln}\mathcal {L}.
\end{eqnarray*}$$in our statistical analysis of lens redshift distribution. The sample used in this paper is primarily drawn from Sloan Lens ACS Survey (SLACS) and recent large-scale observations of galaxies, which is compiled and summarized in Cao et al. (2015) and Shu et al. (2017). The combined sample includes 91 lenses from SLACS (Bolton et al. 2008; Auger et al. 2009; Shu et al. 2017) and an extension of the SLACS survey known as ‘SLACS for the Masses’ (S4TM) (Shu et al. 2015, 2017), 35 lenses from the BOSS emission-line lens survey (BELLS) (Brownstein et al. 2012) and BELLS for GALaxy-Lyα EmitteR sYstemsGALLERY (BELLS GALLERY) (Shu et al. 2016a,b), 26 lenses from the Strong Lensing Legacy Survey (SL2S) (Sonnenfeld et al. 2013a,b), and five lenses from Lenses Structure and Dynamic (LSD) (Treu & Koopmans 2002; Koopmans & Treu 2003; Treu & Koopmans 2004). The advantage of this recently assembled lens sample, the detailed information of which is described and listed in Chen et al. (2019), lies in its well-defined observational selection criteria satisfying the assumption of spherical lens mass model. Fig. 1 shows the redshift distributions of the lensing systems used in our analysis. However, a statistical analysis requires a sample that is complete and has well-characterized, homogeneous selection criteria. Note that the lensing systems collected in this analysis are selected in very different manners. For instance, the SLACS, S4TM, and BELLS surveys, respectively, selected candidates from the spectroscopic observations of ETGs and look for the presence of higher redshift emission lines in Sloan Digital Sky Survey I (Eisenstein et al. 2001) and Sloan Digital Sky Survey-III (Eisenstein et al. 2011). These lens candidates were followed up with HST ACS snapshot imaging and after image processing. Therefore, in order to verify the completeness of the full early-type lens sample (hereafter Sample A), one additional subsample will also be applied to discuss its utility for the redshift test: 126 deflector-selected lenses from SLACS, S4TM, BELLS, and BELLS GALLERY (hereafter Sample B). Such choice is also motivated by the fact that the SLACS and BELLS lenses could be moderately suffered from the finite Sloan fibre size (Brownstein et al. 2012).


In this context, MWC 758 (HD 36112) offers a unique environment to probe the existence of planetary companions and to explore the connection between disk structures and planet formation. MWC 758 is a young stellar object (3.5 ± 2 Myr, Meeus et al. 2012) at a distance of 151
$^{+9}_{-8}$

151

−9

+8

4

 pc (Gaia Collaboration 2016) close to the edge of the Taurus star forming region (stellar properties are given in Table 1). Measurements of resolved CO emission around the star determined the stellar mass to be 2.0 ± 0.2 M⊙ and the disk to have an inclination of 21° ± 2° and a position angle of the semi-major axis of 65° ± 7° (Isella et al. 2010). The mass and age estimates were based on the previously adopted hipparcos distances of 200 pc (van den Ancker et al. 1998) and 279 pc (van Leeuwen 2007). Given the revised Gaia distance, the star could be older and lighter than previously thought. In this paper, we assume a stellar mass of 1.5 ±0.2 M⊙, reflecting the scaling of the dynamical mass estimate to the new Gaia distance. Based on its SED, MWC 758 has been classified as a pre-transition disk (Grady et al. 2013). Although a cavity of 55 astronomical units (au) in radius has been inferred from dust millimeter emission (Andrews et al. 2011), infrared polarized intensity observations have found no clear evidence for a cavity in scattered light (Grady et al. 2013; Benisty et al. 2015). Using Ks-band (2.15 μm) direct imaging andH-band (1.65 μm) polarimetric imaging with the High-Contrast Instrument with Adaptive Optics (HiCIAO) at the Subaru Telescope, Grady et al. (2013) detected two spiral arms and polarized light down to 0.′′ 1 (15 au) from the star. Recent VLT Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) observations in the Y band (1.04 μm) have confirmed the presence of scattered light at least down to 14 au (Benisty et al. 2015). The asymmetries observed by Isella et al. (2010) in the mm-dust distribution and in CO emission suggest that the disk may be gravitationally perturbed by a low-mass companion orbiting within a radius of 23 au (assuming a distance of 151 pc). The asymmetric cm-dust distribution was shown to follow the location of the mm-dust (Marino et al. 2015a), hinting towards the hypothesis of a dust trap, which could also be created by a companion in the gap through the Rossby wave instability (e.g., Pinilla et al. 2012b). Hydrodynamical simulations of the disk indicate that the observed spirals could instead be launched by a massive planet or brown dwarf at larger separations (~ 100 au based on the revised Gaia distance, Dong et al. 2015b). The presence of stellar companions down to a mass limit of 12 MJup at 0.′′ 25 and of planets outside 0.′′5 (5 MJup at 0.′′ 5, and 3 MJup at 1′′ , according to the BT-SETTL models; Allard et al. 2012) has been ruled out based on a combination of sparse aperture masking observations at L′ band and angular differential imaging at K′ and Ks bands (Grady et al. 2013).


The formation of the approximately 40% of sdB stars that appear to be single has been a mystery for decades. In the absence of a companion, it is hard to explain how the star can expel most of its envelope on the RGB and still achieve core-He burning ignition. Recently, Pelisoli et al. (2020) suggested that all sdB stars might originate from binary evolution. Merger scenarios involving two low-mass white dwarfs have also been investigated (Webbink 1984; Han et al. 2002, 2003; Zhang & Jeffery 2012), but several facts challenge this hypothesis. First, compact low-mass white dwarf binaries are quite rare, even though some candidates are identified (Ratzloff et al. 2019). Second, the mass distributions of single and binary sdB stars are indistinguishable (Fontaine et al. 2012, Table 3 in particular). This mass distribution is mainly obtained from asteroseismology (some sdB stars exhibit oscillations, which allow the precise and accurate determination of the stellar parameters, including total mass; Van Grootel et al. 2013) and also from binary light-curve modeling for hot subdwarfs in eclipsing binary systems. Single and binary mass distributions peak at ~ 0.47 M⊙, which is the minimum core mass required to ignite He through a He-flash at the tip of RGB (stars of ≳ 2.3 M⊙ are able to ignite He quietly at lower core masses, down to ~0.33 M⊙, but the more massive the stars, the rarer they are). A mass distribution of single sdB stars from mergers, in contrast, would be much broader (0.4−0.7 M⊙; Han et al. 2002). With the DR2 release of Gaia (Gaia Collaboration 2018) and precise distances for many hot subdwarfs (Geier 2020), it is now also possible to build a spectrophotometric mass distribution for a much larger sample than what was achieved with the hot subdwarf pulsators or those in eclipsing binaries. Individual masses are much less precise than those obtained by asteroseismology or binary light-curve modeling (Schneider et al. 2019). However, single and binary spectrophotometric mass distributions share the same properties here as well, which tends to disprove the hypothesis of different origins for single and binary sdB stars. The third piece of evidence against merger scenarios (which would most likely result in fast-rotating objects) is the very slow rotation of almost all single sdB stars, as obtained through v sin i measurements (Geier & Heber 2012) or from asteroseismology (Charpinet et al. 2018). Moreover, their rotation rates are in direct line with the core rotation rates observed in RC stars (Mosser et al. 2012), which is another strong indication that these stars and the single sdB stars do share a same origin, that is, that they are post-RGB stars.


The present HST-COS data were taken 20 days after the last XMM-Newton pointing (Kaastra et al. 2011) as the closing measurements of the campaign, which lasted in total about 100 days. Spectral coverage simultaneous to HST-COS was provided instead by both Chandra-LETGS (Ebrero et al. 2011) and Swift-XRT (Mehdipour et al. 2011). We used the average SED recorded by the XMM-Newton instruments 20–60 days before the HST-COS observation. The choice of SED is very important in the BLR modeling, as different lines respond to the continuum variations on different time scales (Korista & Goad 2000; Peterson et al. 2004). Reverberation mapping studies of Mrk 509 report that the delay of the Hβ with respect to the continuum is very long (about 80 days for Hβ, Carone et al. 1996; Peterson et al. 2004). However, higher ionization lines respond more quickly to the continuum variations. Taking as a reference the average Hβ/C iv delay ratio for NGC 5548 (Peterson et al. 2004), for which – contrary to Mrk 509 – a large set of line measurements is available, we obtain that the C iv line in Mrk 509 should respond in approximately 40 days. A similar (but shorter) time delay should apply to the Lyα line (Korista & Goad 2000). This delay falls in the time interval covered by the XMM-Newton data. Therefore, our choice of SED should be appropriate for the modeling of at least the main UV lines. Variability of the X-ray broad lines has been reported on time scales of years (Costantini et al. 2010); however, no short-term studies are available. We expect that the X-ray broad lines should respond promptly to the continuum variations, as they may be located up to three times closer to the black hole with respect to the UV lines (C07). During the XMM-Newton campaign the flux changed by 30% at most, with a minimal change in spectral shape (Sect. 3.1). The used SED should therefore represent what the BLR gas sees for the X-ray band. However, for the optical lines the used SED might be too luminous as we observed an increase in luminosity of about 30% during the XMM-Newton campaign and, as seen above, the time-delay of the optical lines may be large.


More recently, García-Bernete et al. (2022) found that the PAH molecules responsible for the 11.3 μm PAH emission band are more resilient in the hard environments often present in AGN. In particular, the authors found larger 11.3/7.7 μm and 11.3/6.2 μm PAH ratios in AGN-dominated systems compared to SF galaxies, indicating a larger fraction of neutral PAH molecules (as noted by Smith et al. 2007 using a sample of relatively weak AGN). However, these studies were limited by the spatial resolution (∼4″) and the low spectral resolution (R ∼ 60–130) of Spitzer/InfraRed Spectrograph (IRS). Previous sub-arcsecond angular resolution N-band (∼8–13 μm) ground-based spectroscopic studies investigated the 11.3 μm PAH feature in the nuclear and circumnuclear regions of AGN (e.g., Hönig et al. 2010; González-Martín et al. 2013; Alonso-Herrero et al. 2014, 2016; Ramos et al. 2014; Esquej et al. 2014; García-Bernete et al. 2015; Jensen et al. 2017; Esparza-Arredondo et al. 2018). However, these works were unable to provide definitive details regarding the effect of the AGN on the PAH molecules due to limited wavelength coverage and sensitivity. The changes in the PAH properties due to the presence of the AGN might be more prominent in their innermost regions of galaxies. Therefore, the unprecedented combination of high angular and spectral resolution (R ∼ 1500 − 3500) in the entire mid-IR range (4.9–28.1 μm) afforded by the James Webb Space Telescope (JWST)/Mid-Infrared Instrument (MIRI; Rieke et al. 2015; Wells et al. 2015; Wright et al. 2015) is key to investigating PAH properties. In this Letter we report on the first investigation of PAH emission in the nuclear regions of three luminous Seyfert (Sy) galaxies and compare them with emission from SF regions using JWST/MIRI Medium Resolution Spectrograph (MRS) data. This enables us, for the first time, to characterise the PAH properties of local luminous Sy galaxies (log (Lbol)> 44.46 erg s−1)1 at sub-arcsecond scales (∼0.45″, ∼142–245 pc).


It is also possible that these clusters have a smaller extent and can just be missed by our extent selection as our detection algorithm sets the extent to zero if it is smaller than 6 (Brunner et al. 2022). Following the method presented in Ghirardini et al. (2021a), we estimated several dynamical properties of the clusters in the point source sample and compared them with the extent-selected sample presented in Ghirardini et al. (2021a). In Fig. 5 we compare the distributions of the core radii (Rcore) constrained by the V06 model and the concentration parameter (cSB) between these two samples. The concentration parameter is defined as the ratio of the surface brightness within 0.1 R500 to the surface brightness within R500 (Ghirardini et al. 2021a; Santos et al. 2008; Maughan et al. 2012). Intuitively, the expectation is that the smaller the core radius, the more compact the cluster. The left panel of Fig. 5 clearly shows that the clusters in the point source sample have relatively smaller core radii, hence the emission is more concentrated in a smaller area. Consistently, the concentration of the point source sample shows a clear excess in higher values than the extent-selected sample, indicating that a significantly larger fraction of cool-core clusters and clusters host a central AGN. We performed the same experiment by applying cuts in flux 1.5 × 10−14 ergs s−1 cm−2 and in detection likelihood to test whether the clusters are missed by the extent selection because they are fainter and/or more compact than the extent-selected clusters. The distribution of number density, core radius, and concentration parameter remains the same, indicating that the population of clusters in the point source catalog is more compact than the extent-selected sample. The extent-selected sample does not show a clear bias toward cool-core clusters or clusters with a central AGN, but contains the fraction of cool-cores is similar to that of SZ surveys (Ghirardini et al. 2021a). In this sample, we observe the opposite trend.


We appear to live in a flat, homogeneous and isotropic expanding Universe (at scales >100 Mpc) well described by the Friedmann–Lemaître–Robertson–Walker (FLRW) metric where the scalefactor, a(t), describes the time dependence of the Universe geometry: a(t) ∝ t1/2 for radiation domination, a(t) ∝ t2/3 for matter domination, and $a(t)\propto \exp (\scriptstyle\sqrt{\frac{\Lambda }{3}}ct)$ for dark energy domination, where Λ = 3H0ΩΛc−2 is the cosmological constant (e.g. Beringer et al. 2012) – see Table 1. A common normalization of the FLRW metric defines the scalefactor equal to unity at the present time (a(t0) = 1; e.g. Liddle & Lyth 1993), yielding, for a Universe dominated by a positive cosmological constant (cf. Table 1)

(5)

\begin{eqnarray}
a_{\Lambda }(t)=\exp \left(c\sqrt{\frac{\Lambda }{3}}(t-t_{0})\right),& t_{\Lambda }\le t\le t_{0} \:.
\end{eqnarray}

For the matter-dominated Universe, we have

(6)

\begin{eqnarray}
a_{\text{m}}(t)=a_{\Lambda }(t_{\Lambda })\left(\frac{t}{t_{\Lambda }}\right)^{2/3}, \:\: t_{\text{eq}}\le t\le t_{\Lambda } \:.
\end{eqnarray}

Between the end of inflation at t = te ∼ 10−33 s; (e.g. Narlikar & Padmanabhan 1991) and t = teq = 2.37 × 1012 s, the Universe was radiation-dominated since at the latter instant a radiation-matter equality is reached (Table 1). Exceptions to radiation-domination in the te ≤ t ≤ teq time interval might have taken place during cosmological phase transitions such as the QCD (when the Universe might have been dust-like). We, then, split the radiation-domination epoch into three parts. For the interval between the end of the QCD phase transition (t+) and teq, we define

(7)

\begin{equation}
a_{\text{rl}}(t)=a_{\text{m}}(t_{\text{eq}})\left(\frac{t}{t_{\text{eq}}}\right)^{1/2}, \:\: t_{+}\le t\le t_{\text{eq}} \:.
\end{equation}

During the QCD phase transition, we define

(8)

\begin{eqnarray}
a_{\text{QCD}}(t)=a_{\text{rl}}(t_{+})\left(\frac{t}{t_{+}}\right)^{n_{\text{QCD}}}, \:\: t_{-}\le t\le t_{+},
\end{eqnarray}

where nQCD = 2/3 if the Universe experiences a QCD dust-like phase or nQCD = 1/2 if the Universe continues to be radiation-dominated during that epoch. Finally, between the end of inflation (te) and the beginning of the QCD phase transition (t−), we define

(9)

\begin{equation}
a_{\text{rm}}(t)=a_{\text{QCD}}(t_{-})\left(\frac{t}{t_{-}}\right)^{1/2}, \:\: t_{\text{e}}\le t\le t_{-} \:.
\end{equation}


Detections of ionic, atomic, and molecular species in exoplanetary atmospheres serve as a unique and strong diagnostic of those chemical and dynamical processes driving their formation and evolution. Their detection and abundance measurements could act as indicators of planetary formation scenarios and reveal connections to the primordial protoplanetary disc and the host star (Williams & Cieza 2011; Mordasini et al. 2016; Madhusudhan et al. 2017). Furthermore, discoveries of atmospheric chemical species allow us to better understand various thermodynamical processes and chemistry, winds in the upper atmosphere (Goodman 2009; Snellen et al. 2010; Brogi et al. 2016; Madhusudhan et al. 2016; Wyttenbach et al. 2020), and to probe planetary interiors and various bulk properties through their abundances (Kite et al. 2016; Thorngren & Fortney 2019; Madhusudhan et al. 2020). A whole host of ions, atoms, and molecules have been detected through a variety of, often complementary, techniques, such as differential spectrophotometry using low-to-mid resolution spectroscopy (e.g. Gibson et al. 2012, 2017; Deming et al. 2013; Kreidberg et al. 2014; Kirk et al. 2016; Nortmann et al. 2016), and high resolution spectroscopic techniques (e.g. Redfield et al. 2008; Snellen et al. 2008; Rodler, Lopez-Morales & Ribas 2012; Birkby et al. 2013; Hoeijmakers et al. 2015, 2018, 2020; Brogi et al. 2016; Birkby et al. 2017; Žák et al. 2019; Ehrenreich et al. 2020). To date, ionic species such as Fe ii and Ti ii (Hoeijmakers et al. 2019), atomic absorption from Na, K, H α, and He (e.g. Redfield et al. 2008; Sedaghati et al. 2016; Casasayas-Barris et al. 2017; Spake et al. 2018; Chen et al. 2020; Seidel et al. 2020), and molecules such as H2O, CH4, and CO (e.g. Konopacky et al. 2013; Brogi et al. 2014; Fraine et al. 2014; Barman et al. 2015; Sing et al. 2016) have been detected through the aforementioned techniques. Needless to say that this list of detected constituents is by no means exhaustive, nor that of methods employed to detect exoplanetary atmospheres. For instance, high-resolution imaging instruments such as SPHERE (Beuzit et al. 2019) and GRAVITY (Gravity Collaboration et al. 2017), both at the VLT (ESO’s Very Large Telescope), through combination with low-dispersion spectroscopy, have facilitated direct measurements of exoplanetary atmospheres (Samland et al. 2017; Gravity Collaboration et al. 2020).


Observations of the polarized dust emission of nine low-mass protostars at 0.87 mm were obtained using the SMA (Projects 2013A-S034 and 2013B-S027, PI: A. Maury) in the compact and subcompact configuration. To increase our statistics, we also included SMA observations from three additional sources from Perseus (NGC 1333 IRAS4A and IRAS4B) and Ophiuchus (IRAS16293) observed in 2004 and 2006 (Projects 2004-142 and 2006-09-A026, PI: R. Rao; Project 2005-09-S061, PI: D.P. Marrone). The observations of NGC 1333 IRAS4A and IRAS16293 are presented in Girart et al. (2006) and Rao et al. (2009), respectively. Marrone (2006) and Marrone & Rao (2008) provide a detailed description of the SMA polarimeter system, but we provide a few details on the SMA and the polarization design below. The SMA has eight antennas. Each optical path is equipped with a quarter-wave plate (QWP), an optical element that adds a 90° phase delay between orthogonal linear polarizations and is used to convert the linear into circular polarization. The antennas are switched between polarizations (QWP are rotated at various angles) in a coordinated temporal sequence to sample the various combinations of circular polarizations on each baseline. The 230, 345, and 400 band receivers are installed in all eight SMA antennas. Polarization can be measured in single-receiver polarization mode and in dual-receiver mode when two receivers with orthogonal linear polarizations are tuned simultaneously. In this dual-receiver mode, all correlations (the parallel-polarized RR and LL and the cross-polarized RL and LR; with R and L for right circular and left circular, respectively) are measured at the same time. Both polarization modes were used in our observations. This campaign was used to partly commission the dual-receiver full polarization mode for the SMA. A fraction of the data was lost during this period owing to issues with the correlator software. Frequent observations of various calibrators were interspersed to ensure that such issues were detected as early as possible to minimize data loss.


Here we demonstrate that, over a fixed time interval, the planar three-body problem can be solved by means of a multilayered deep artificial neural network (ANN; e.g. see LeCun, Bengio & Hinto 2015). These networks are designed for high-quality pattern recognition by mirroring the function of our brains (McCulloch & Pitts 1943; Rosenblatt 1985) and have been successfully applied to a wide variety of pattern recognition problems in science and industry, even mastering the game of Go (Silver et al. 2016). The abundance of real-world applications of ANNs is largely a consequence of two properties: (i) an ANN is capable of closely approximating any continuous function that describes the relationship between an outcome and a set of covariates, known as the universal approximation theorem (Cybenko 1989; Hornik 1991); and (ii) once trained, an ANN has a predictable and a fixed computational burden. Together, these properties lead to the result that an ANN can be trained to provide accurate and practical solutions to Newton’s laws of motion, resulting in major improvements in computational economy (Lee, Sode-Yome & Park 1991) relative to modern technologies. Our proof-of-principle method shows that an ANN can accurately match the results of converged solutions found using the arbitrary precision numerical integrator that, for computationally challenging scenarios, e.g. during multiple close encounters, can offer numerical solutions at a fraction of the time cost and CO2 expense. We demonstrate the importance of training an ANN on converged solutions. This enables the trained ANN to accurately predict particle locations even when a conventional ‘double-precision’ numerical integrator fails dramatically. By training an ANN that can accurately compute particle trajectories during close encounters, our work extends previous work training neural networks on an n-body-type problem (e.g. Quito, Monterola & Saloma 2001; Battaglia et al. 2016). Our findings also add to the growing body of literature that supports machine learning technologies being developed to enrich the assessment of chaotic systems (Pathak et al. 2018; Stinis 2019) and providing alternative approaches to classical numerical solvers more broadly (Hennig, Osborne & Girolami 2015).


Magnetic flux ropes are frequently observed magnetic structures with helical magnetic field lines and a strong core field. In spacecraft observations, flux ropes are often identified from bipolar variations in one magnetic field component and the enhancement of magnetic strength at the center. There are various observations of flux ropes in the magnetosphere (e.g., Khurana et al. 1995; Slavin 2003; Yang et al. 2013; Poh et al. 2019; Sun et al. 2019), boundary of magnetosphere (e.g., Rijnbeek et al. 1984; Kawano & Russell 1997; Fear et al. 2008, 2009; Akhavan-Tafti et al. 2018; Hwang et al. 2018; Yao et al. 2020), and solar wind (e.g., Zheng & Hu 2018; Blanco-Cano et al. 2019; Bai et al. 2020). Flux ropes are also observed in the magnetospheres of Mercury (Zhong et al. 2020a), Mars (Briggs et al. 2011), Jupiter (Sarkango et al. 2021), and Saturn (Jasinski et al. 2016). Flux ropes are widely believed to result from magnetic reconnection. In earlier studies, some flux ropes near the magnetopause are referred to as flux transfer events (FTEs; Russell & Elphic 1978), which allow plasma transportation across the magnetopause. Various mechanisms for FTE generation have been proposed, such as single X-line reconnection (Scholer 1988; Southwood et al. 1988) and multiple X-line reconnection (Lee & Fu 1985). Recent simulations show that reconnection can generate not only fluid-scale flux ropes but also those with ion or even electron scales (Daughton et al. 2011; Hoilijoki et al. 2019; Lu et al. 2020). These kinetic-scale flux ropes may interact with one another to form larger-scale flux ropes (Daughton et al. 2011), which could be manifested in spacecraft observations as entangled flux ropes (Wang et al. 2017; Øieroset et al. 2019; Qi et al. 2020). There are also observations of ion-scale flux ropes near the ion/electron diffusion region (Wang et al. 2016; Hwang et al. 2018; Poh et al. 2019; Dong et al. 2020). The flux ropes can change in size while moving through convection, often expanding (Dong et al. 2017; Akhavan-Tafti et al. 2018, 2019) and sometimes contracting (Hasegawa et al. 2016). Eastwood et al. (2012) investigated that the flux ropes in the day side and in the distant-tail magnetopause have similar orientations and comparable magnetic flux content, indicating that the flux ropes may be in quasi-equilibrium as they are convected tailwards along the magnetopause. Moreover, ion-scale flux ropes are believed to be responsible for exciting waves (Huang et al. 2016; Wang et al. 2019) or accelerating particles (Zhu et al. 2019; Zhong et al. 2020b), implying that they are actively involved in magnetospheric physics.


The projected position angle (PA) of the jet gradually rotates counterclockwise with increasing distance from the jet base. In the 2.3 GHz VLBA image the PA is 50° ± 5° east of north at about 20 mas from the core and the jet bends toward the north–south direction closer to the core, consistently with the jet orientation in the nonsimultaneous 1.6 GHz image at 5–10 mas from the core (Shen et al. 1999). At 8.7 GHz we find a PA of 25° ± 5° at about 5 mas from the core, consistent with the archival VLBA monitoring results at 15 GHz, showing a persistent jet orientation at a PA of about 30° in the epochs from 1995 to 2013 at angular scales ∼5 mas (Kellermann et al. 1998; Pushkarev et al. 2017). The same MOJAVE observations hint at more variability of the jet PA on the smallest resolved scales ∼1 mas. Observations by Shen et al. (2002) with the VLBA between 1994 and 2000 across four frequencies (5, 12, 15, and 43 GHz) showed a consistent PA orientation of 30° at 5 GHz with a clockwise shift of about 51°–67° at 43 GHz. At 86 GHz a possible bent jet structure is seen, with the inner jet oriented with a PA of about −40° less than 0.3 mas from the core, and an apparent transition to a northeast direction further out. The −40° PA with respect to the core is consistent with the PA of the single jet component located ∼400 μas from the core, imaged from 2018 April GMVA observations (see Figure 4 of Issaoun et al. 2021). 2018 images at 86 GHz do not indicate jet bending. At 230 GHz, the component C1 is located at a PA of −45° and C2 at a PA of −35° with respect to the core C0. This morphology can potentially be explained by a helical structure in the jet (Conway & Murphy 1993; Steffen et al. 1995). Such a helical jet structure can be caused by an orbiting lower-mass secondary black hole around a stable primary central black hole, as also proposed for 4C 73.18 (Roos et al. 1993) and OJ 287 (e.g., Dey et al. 2021; Gómez et al. 2022), precession caused by a wobbling disk (Britzen et al. 2018), or a large-scale accretion flow that is tilted with respect to the black hole spin axis (e.g., as in M81; Martí-Vidal et al. 2011).


Investigations of the turbulent nature of solar wind fluctuations have been ongoing for more than half a century (see, e.g., Bruno & Carbone 2016). Advances have been made consistently thanks to the increasingly accurate measurements of several dedicated space mission as well as to the enormous improvement of numerical calculation, new detailed models and theoretical frameworks, and the development of specific data analysis techniques. Nevertheless, the extremely complex nature of the system and the coexistence of multiple actors, scales, and dynamical regimes have led to a number of questions that remain open (Viall & Borovsky 2020). Among these, the very nature of the turbulent cascade of the solar wind flow and its relationship with the small-scale processes still need to be described in full (Tu & Marsch 1995; Bruno & Carbone 2013; Matthaeus & Velli 2011; Chen 2016). Magnetic field fluctuations have been characterized with great detail at magnetohydrodynamic and kinetic scales, for example, through spectral and high-order moments analysis (Tu & Marsch 1995; Bruno & Carbone 2013). The anisotropic nature of magnetic turbulence has also been addressed, and is still being debated, due to the limited access to three-dimensional measurements in space (see, e.g., Horbury et al. 2008, 2012; Sorriso-Valvo et al. 2010; Yordanova et al. 2015; Verdini et al. 2018; Telloni et al. 2019a; Oughton & Matthaeus 2020). Velocity fluctuations have been studied thoroughly (see, e.g., Sorriso-Valvo et al. 1999; Bruno & Carbone 2013), although the kinetic scales still remain quite unexplored for instrumental limitations, most notably in the sampling time resolution. Both the velocity and magnetic field show highly variable turbulence properties, with well developed spectra, strong intermittency (Sorriso-Valvo et al. 1999), anisotropy, and linear third-order moments scaling (Sorriso-Valvo et al. 2007; Carbone et al. 2011). The level of Alfvénic fluctuations (mostly but not exclusively found in fast streams, see e.g., D’Amicis et al. 2011; Bruno et al. 2019) are believed to be associated with the state of the turbulence. In particular, solar wind samples containing more Alfvénic fluctuations are typically associated with less developed turbulence, as inferred from both shallower spectra and reduced intermittency (see Bruno & Carbone 2013, and references therein). This is consistent with the expectation that uncorrelated Alfvénic fluctuations contribute to reduce the nonlinear cascade by sweeping away the interacting structures (Dobrowolny et al. 1980), as also confirmed by the observed anticorrelation between the turbulent energy cascade rate and the cross-helicity (Smith et al. 2009; Marino et al. 2011a,b).