The WSN/ISN series is based on the counts of both sunspot groups and individual sunspots, with the former being weighted with a factor of ten: (1)\begin{equation} R = k\cdot(10\cdot G + S), \end{equation}R=k·(10·G+S),where G and S are the numbers of sunspot groups and individual sunspots, respectively, and k is a correction factor, characterizing each observer. However, resolving individual spots may be imprecise with poor instrumentations, and a new series, based only on sunspot groups, was proposed, called the group sunspot number, GSN (Hoyt et al. 1994; Hoyt & Schatten 1998). The GSN is more robust than WSN regarding observational conditions (e.g., Usoskin 2017). There is still a potential problem related to the grouping of individual spots, which may have been considered by earlier observers in a different manner to that currently accepted (Clette et al. 2014). This uncertainty is related to both WSN/ISN and GSN but can be fixed by redefining groups in historical sunspot drawings (Arlt et al. 2013). The GSN series produced by Hoyt & Schatten (1998) also uses the linear scaling and daisy-chaining method to reduce different data to the same reference observer, for which the RGO was chosen. The GSN is constantly scaled up by a factor 12.08 to make it comparable with the WSN series. The main advantage of the GSN series is that Hoyt & Schatten (1998) had collected and published the original database of raw data, including all the records of individual observers. This makes it possible to revise the entire series if needed. Since some corrections and additions have been recently made to this dataset, a revised database of the sunspot group numbers, separate for each observer, is published (Vaquero et al. 2016, referred to as V16 hereafter). The GSN series was revised by Svalgaard & Schatten (2016) who performed a full re-calibration of the observers using a modified daisy-chaining method with a reduced number of links (the “backbone” method). The revised backbone GSN series suggests that the level of solar activity was relatively high in the 18th and 19th centuries, much higher than that implied by the original GSN series by Hoyt & Schatten (1998) and by WSN.


We find that, even though the physical parameters such as kTe and Ïe are very well constrained by the data, it is still impossible to formally distinguish the geometry. The slab (disk-like) and the spherical geometries, as parameterized by the compTT and compPS models used here, both describe the MCGâ05-23-016 spectrum equally well. We note that a similar result was found in observations of the Seyfert 1.2 ICÂ 4329a and the narrow-line Seyfert 1 SWIFT J2127.4+5654 with NuSTAR (Brenneman etÂ al. 2014a, 2014b; Marinucci etÂ al. 2014). Both of these AGNs and MCGâ05-23-016 are radio-quiet, however, they differ in other properties. With a mass of the super-massive black hole of â¼5 Ã 107Â M (Wandel & Mushotzky 1986), the mean intrinsic 2â10âkeV luminosity of 1.66 Ã 1043 ergÂ sâ1 (see TableÂ 1) and a bolometric correction from Marconi etÂ al. (2004), MCGâ05-23-016 is accreting at approximately 5% of the Eddington rate. This is almost an order of magnitude less than the key other two AGNs. Interestingly, SWIFT J2127.4+5654 has the lowest black hole mass and the lowest cut-off, followed by MCGâ05-23-016 in the middle, and ICÂ 4329a with highest mass and cut-off energy. In a number of other AGNs, a stringent lower limit on the cut-off energy was placed using the NuSTAR data, indicating a generally higher coronal temperature and lower optical depths, e.g., Ecut > 190âkeV in 3C 382 (Ballantyne etÂ al. 2014) and in Ark 120 (Matt etÂ al. 2014), and Ecut > 210âkeV in NGCÂ 2110 (Marinucci etÂ al. 2015). Using long-term averaged data from INTEGRAL, Malizia etÂ al. (2014) constrained cut-off energies for 26 AGNs in the range between 50 and 200âkeV, some of which have been or will be observed with NuSTAR. With more high-quality measurements in the near future, covering a wide range of physical properties, it will be possible to directly probe the physics of the AGN corona. In order to distinguish the fine differences due to the coronal geometry, longer observations of sources with a weaker reflection continuum will be needed.


The comparison between Ulysses and Pamela overlapping measurements revealed that the proton flux in the rigidity interval 1.6–1.8 GV (0.92–1.09 GeV, corresponding approximately to the median energy of the GCR spectrum at solar minimum) has a radial intensity variation of 2.7 ± 0.2% AU−1, and a latitudinal gradient of −0.024 ± 0.005% degree−1 (De Simone et al. 2011). Positive (negative) latitudinal gradients are observed during positive (negative) polarity periods. In addition, Experiment 6 (E6) on board Helios-A and Helios-B provided ion data from four to several hundreds of MeV n−1 (Winkler 1976; Marquardt & Heber 2019). The Helios-A and Helios-B S/C were launched on December 10, 1974 and January 15, 1976 during a positive polarity epoch and were sent into ecliptic orbits of 190-day and 185-day periods around the Sun. The orbits perihelia were 0.3095 AU and 0.290 AU, respectively. The aphelia were approximately 1 AU. As a result, the Helios data are representative of the cosmic-ray bulk variations that are to be experienced by Solar Orbiter, which will also reach maximum distances from the Sun of about 1 AU. In the recent paper by Marquardt & Heber (2019), the Helios proton data radial gradients of the GCR flux were found to be 6.6 ± 4% above 50 MeV and 2 ± 2.5% between 250 and 700 MeV between 0.4 and 1 AU. These results are in agreement with those from Pamela/Ulysses (within the statistical and systematic errors). In conclusion, variations in the GCR proton-dominated flux along the Solar Orbiter orbit are expected to be of a few % at most; consequently, it is plausible to assume that models for cosmic-ray modulation developed on the basis of observations gathered near Earth will also apply to Solar Orbiter. On the other hand, the Metis data will allow us to verify this assumption in the unexplored region of tens of degrees above the solar equator. Analogously, even though no SEP data were gathered up to present time, it is likely that a study of the evolution of SEP events near the Sun above the solar equator will be possible for the first time also with Metis, in addition to the dedicated instruments flown on board Solar Orbiter.


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


As described in the introduction, spectroscopically confirmed Lyα emitters at high redshift (and the nonconfirmations from follow-up campaigns) have proven very valuable for studying the early universe and the environment at the epoch of reionization (Pentericci et al. 2011, 2014; Caruana et al. 2012, 2014; Treu et al. 2012, 2013; Faisst et al. 2014; Tilvi et al. 2014). In particular, confirmed Lyα emitters fix the redshift of the object, resulting in improved prediction power from fitting stellar population synthesis models to the photometry. Assuming a set of stellar population models (e.g., Bruzual & Charlot 2003; Maraston 2005) to generate spectral energy distributions for galaxies at the emission-line redshift, and fitting them to the available photometry, can give estimates of physical quantities of the galaxies like total stellar mass (the normalization between the observed flux and best-fit model), the star formation rate, metallicity, and the age of the stellar populations, i.e., the galaxy (e.g., Labbé et al. 2006; Vanzella et al. 2011; Coe et al. 2013, 2014; Finkelstein et al. 2013; Huang et al. 2015; Oesch et al. 2015; Zitrin et al. 2015b). When performing the spectral energy distribution fitting, assuming a dust law can furthermore predict the dust content of the galaxy. This can be directly compared to the measured UV spectral slope, if available from the data (e.g., Bouwens et al. 2015; Finkelstein et al. 2015b; Oesch et al. 2015). Another direct comparison can be obtained from independently determining the star formation rate from scaling relations with the UV photometry (Kennicutt 1998; Madau et al. 1998). As part of our study of IRAC-detected high-redshift galaxies presented by Huang et al. (2015), we estimated the physical properties of the confirmed Lyα emitter presented in Section 7.1. An important aspect of this study was the availability of ancillary Spitzer photometry from SURFS-UP (Bradač et al. 2014). Photometry in the rest-frame optical falling in the Spitzer IRAC infrared bands for high-redshift galaxies has proven to be an important part of reliably predicting the physical properties of (high-redshift) galaxies through spectral energy distribution fitting (e.g., Schaerer & de Barros 2010; Labbé et al. 2013; Smit et al. 2014a, 2014b; Finkelstein et al. 2015a; Huang et al. 2015; Wilkins et al. 2015). Furthermore, fixing the redshift of the spectral energy distributions when fitting to photometry can also be used as a test of the validity of potential low-redshift contaminants. If, for instance, the best-fit low-redshift model predicts a dusty red and old stellar population, it would be very unlikely to see strong [O ii] emission, therefore making a high-redshift Lyα scenario more likely (Coe et al. 2013; Finkelstein et al. 2013). Similar arguments can be used to rule out other line-emitting low-redshift contaminants. Fixing the redshift of high-redshift sources behind massive clusters, like the ones presented in the current study behind the GLASS clusters, is not only important for the study of individual sources and high-redshift galaxy populations. Knowing the redshift, i.e., the luminosity distance to any object, precisely, especially if it is multiply lensed, is also very valuable for lens modeling of the foreground clusters (e.g., Coe et al. 2013, 2014; Zitrin et al. 2014). Lastly, the sizes of high-redshift galaxies have also been shown to provide useful information about the environment and epoch they inhabit (Ono et al. 2013; Curtis-Lake et al. 2014; Holwerda et al. 2015).


As displayed in Fig. 1 and Supplementary Movie 1, the control torque τ, applied to the lander at rest, actuates it to pivot over the leading edge, and then the bottom side is dragged downwards in contact with the granular regolith, yielding a reaction force on to the lander (Allen et al. 2013). Given sufficient acceleration impulsive moment, the lander will leave the surface, hopping forwards in a ballistic trajectory. Hockman et al. (2017) stated that the key mechanism of this internally actuated mobility is the transmission of rotational energy to translation energy, indicating that the acceleration duration T of the control torque could determine the hopping outcomes. To elucidate the fundamental dynamics that governs surface locomotion on asteroids, we adopt 12 different acceleration durations ranging from 20 to 800 $\rm {ms}$ in this section, in which μ is set to 0.5, β is set to 1.0, and c is set to 0 Pa. Two typical dynamics data, corresponding to 20 and 600 $\rm {ms}$, are displayed in the insets of Figs 2(a) and (b), which shows instantaneous velocity $v$ and angle θ (relative to horizon), versus time t. Generally, during the hopping process, the acceleration first shows a gradual increase, and then decreases rapidly at the end of control torque, during which the reaction force is highly fluctuating due to intermittent transmissions of acoustic energy along force-chain-like networks (Clark, Kondic & Behringer 2012; Cheng et al. 2018), as illustrated in Fig 3. In this collisional scenario, the acceleration torque excites strong force chains which exert sporadic impacts on the bottom of the lander, while after the end of acceleration, the force networks become sparse and fragmented immediately, leading to the rapid decrease of the reaction force as evidenced by Fig. 2(c). The work done by the lander to impact with regolith surface generates the contact force, and then increase its velocity and height before the lander loses contact with the regolith at time tesc. After that, the lander behaves as free projectile motion under only gravity, which corresponds to a gradual decrease of the vertical velocity, forming a peak value in the velocity curve and a turning point in the angle curve. Hereafter, we define these two values as hopping velocity V and hopping angle ϑ, respectively. Note that the lowercase $v$ and θ represent the instantaneous velocity and angle, while the uppercase V and ϑ represent hopping outcomes. The hopping distance can be deduced from V and ϑ, given as 2V2cos (ϑ)sin (ϑ)/g. Thus in the case of T = 600 ms, the lander hops about 57 m under the gravity of 1.0 × 10−4$\rm {m\, s^{-2}}$, corresponding to a large surface coverage on small asteroids. And in a lower acceleration duration like T = 40 ms, the lander only moves about 45 cm, which gives a much more precise form of surface relocation. The results presented here provide strong evidence on the feasibility of the hopping landers for the exploration of low-gravity bodies. Additionally, our simulations show the lander takes about 1–17 min to complete the hop, which is far less than the battery life of MASCOT (16 h, Ho et al. 2017). This information is crucial for the design of landers equipped without solar batteries.


Radio astronomy is recognized as one of the most effective techniques to search for interstellar molecules. By comparing the spectra of candidate molecules in the laboratory with the spectra observed in astronomical surveys, we can determine whether these molecules exist in interstellar space. Therefore, it is necessary to provide rotational spectra of candidates for astronomical detection. Radio astronomy has helped to detect several sulfur-containing molecules in the ISM in recent years: in particular, thiols, the sulfur analogs of alcohols. Methanethiol (or methyl mercaptan, CH3SH) was detected in the Sagittarius B2 (Sgr B2) region of the center of our Galaxy (Linke et al. 1979; Gibb et al. 2000; Müller et al. 2016; Rodríguez-Almeida et al. 2021) and in the protostar IRAS 16293-2422 (Majumdar et al. 2016). Two groups reported to have detected several signs of ethanethiol (C2H5SH) in Sgr B2 (Müller et al. 2016) and Orion (Kolesniková et al. 2014). Most recently, Rodriguez-Almeida reported the first unambiguous detection of ethanethiol in the ISM, toward the G+0.603-0.027 molecular cloud (Rodríguez-Almeida et al. 2021). Moreover, several sulfur-containing species have been observed in comets (Altwegg et al. 2017). Some recent efforts, both from spectroscopy and astronomical searches, to detect S-stitutes of other classes of compounds have also been reported. For instance, thioformic acid (HC(O)SH) was very recently detected in G+0.693–0.027. Its trans-isomer has an abundance of ~1 × 10–10 (Rodríguez-Almeida et al. 2021). Conversely, thioformamide (NH2CHS), the counterpart of for-mamide (NH2CHO), was characterized in the laboratory up to 660 GHz, and its transitions were searched for toward the hot cores Sgr B2(N1S) and Sgr B2(N2), but it was not detected (Motiyenko et al. 2020). The rotational spectrum of thioac-etamide was recently analyzed in the 59.6–110.0 GHz frequency region (5.03–2.72 mm). Its emission was searched for in regions associated with star formation using the IRAM 30 m ASAI observations toward the prestellar core L1544 and the outflow shock L1157–B1. The molecule was not detected, but the study allowed placing constraints on the thioacetamide abundances (Maris et al. 2019; Remijan et al. 2022).


Outflows are ubiquitous in both luminous AGN and in local Seyfert galaxies, and occur on a wide range of physical scales, from highly ionised semi-relativistic winds and jets in the nuclear region at subparsec scales to galactic scale outflows seen in mildly ionised, molecular, and neutral gas (Morganti et al. 2016; Fiore et al. 2017; Fluetsch et al. 2019; Lutz et al. 2020; Veilleux et al. 2020, and references therein). In some cases molecular and ionised winds have similar velocities and are nearly co-spatial, suggesting a cooling sequence scenario where molecular gas forms from the cooling of the gas in the ionised wind (Richings & Faucher-Giguere 2017; Menci et al. 2019). Other AGN show ionised winds that are faster than the molecular winds, suggesting a different origin of the two phases (Veilleux et al. 2020, and references therein). The molecular phase is a crucial element of the feeding and feedback cycle of AGN because it constitutes the bulk of the total gas mass and it is the site of star formation activity. On galactic scales massive molecular winds are common in local Seyfert galaxies (e.g. Feruglio et al. 2010; Cicone et al. 2014; Dasyra et al. 2014; Morganti et al. 2015; García-Burillo et al. 2014, 2017, 2019); these winds likely suppress star formation (i.e. negative feedback) as they reduce the molecular gas reservoir by heating or expelling gas from the host-galaxy ISM. In late-type AGN-host galaxies, the gas kinematics appears complex at all scales, showing several components such as bars, rings, and (warped) discs, with high velocity dispersion regions (e.g. Shimizu et al. 2019; Feruglio et al. 2020; Fernández-Ontiveros et al. 2020; Alonso-Herrero et al. 2020; Aalto et al. 2020; Audibert et al. 2020). Accurate dynamical modelling of the molecular gas kinematics reveals kinematically decoupled nuclear structures, high velocity dispersion at nuclei, trailing spirals, and evidence of inflows and AGN-driven outflows. (e.g. Combes et al. 2019; Combes 2019, 2021). The outflow driving mechanism (wind shock, radiation pressure, or jet), their multiphase nature, and their relative weights and impact on the galaxy ISM are still open problems (Faucher-Giguère & Quataert 2012; Zubovas & King 2012; Richings & Faucher-Giguere 2017; Menci et al. 2019; Ishibashi et al. 2021). To date, far different outflow phases have been observed only for a handful of sources. Atomic, cold, and warm molecular outflows have been observed in radio galaxies (e.g. Morganti et al. 2007; Dasyra & Combes 2012; Dasyra et al. 2014; Tadhunter et al. 2014; Oosterloo et al. 2017). The nuclear semi-relativistic phase and the galaxy-scale molecular phase have been observed simultaneously in less than a dozen sources, with varied results: in some cases data suggest energy driven flows (Feruglio et al. 2015; Tombesi et al. 2015; Longinotti et al. 2018; Smith et al. 2019), in other cases data suggest momentum driven flows (e.g. García-Burillo et al. 2014; Feruglio et al. 2017; Fluetsch et al. 2019; Bischetti et al. 2019; Marasco et al. 2020). Fiore et al. (2017), using a compilation of local and high redshift winds, showed that there is a broad distribution of the momentum boost, suggesting that both energy- and momentum-conserving expansion may occur. Enlarging the sample of local AGN-host galaxies with outflows detected in different gas phases is important to understand the nature and driving mechanisms of galaxy-scale outflows.


Studies aiming at measuring and modeling solar radiation and its variability are strongly motivated by the impact that solar irradiance (that is, the electromagnetic energy emitted by the Sun received at the top of Earth’s atmosphere in units of area and time), especially in the UV, has on the chemistry and physical properties of Earth’s atmosphere and climate (e.g., Gray et al. 2010; Matthes et al. 2017). Studies of solar variability have been recently also driven by the necessity of improving our understanding of stellar variability (see Fabbian et al. 2017, for a recent review), which, in turn, is essential to characterize the habitable zones of stars and the atmospheres of their exoplanets. As for Earth, modeling of exoplanet atmospheres requires as fundamental input the spectral energy distribution of the hosting star, especially UV and shorter wavelengths (e.g., Tian et al. 2014; Ranjan et al. 2017; Rugheimer & Kaltenegger 2018). Unfortunately, measurements of UV radiation are strongly hampered by the interstellar medium absorption (up to 70%–90%), which is significant even for relatively close stars, so that estimates of stellar UV radiation strongly rely on modeling (see Linsky 2017, for a recent review). Moreover, because there is no mission scheduled in the near future to observe stellar spectra in the UV, after the Hubble Space Telescope ceases operations, the characterization of UV spectra of stars hosting exoplanets that will be discovered by current and future missions (e.g., TESS or James Webb Space Telescope) will necessarily rely on indirect estimates, performed, for instance, through the use of semi-empirical models (e.g., Mauas et al. 1997; Fontenla et al. 2016; Busá et al. 2017) or proxies (e.g., Stelzer et al. 2013; Shkolnik et al. 2014). Stellar irradiance variability also affects the detectability of exoplanets (see, e.g., the recent review by Oshagh 2018). The passage over the disk of spots and faculae may induce photometric variations of amplitude similar to or larger than photometric variations induced by planetary transits. Moreover, the presence of active regions may alter spectral line profiles, thus hindering exoplanet detections performed through radial velocity measurements. Similarly, spectroscopic techniques that allow us to estimate the physical properties of exoplanet atmospheres (see, e.g., Kreidberg 2017, for a recent view) require as fundamental input the spectra synthetized through models representing quiet and active regions (faculae and sunspots). Finally, stellar irradiance variability observed at different spectral ranges, especially in the UV, is a fundamental observable for the characterization of the magnetic activity of a star, and therefore for the understanding of dynamo processes in stellar objects (e.g., Reinhold et al. 2013; Basri 2016; Salabert et al. 2016). Because stellar photometric and spectral variability can be modeled using the semi-empirical approaches developed for the Sun described above (see, e.g., Shapiro et al. 2016; Witzke et al. 2018), understanding the limitations of current irradiance models is fundamental to improving our capability of modeling stellar variability.


Magnetic fields observed in various astrophysical systems, such as the Earth, the Sun, disk galaxies, accretion disks, etc., possess large-scale magnetic fields in addition to a fluctuating component. The magnetic field survives for timescales much larger than the diffusion timescales in those systems, and therefore are thought to be self-sustained by turbulent dynamo action. The standard model of such a turbulent dynamo producing a large-scale magnetic field involves the amplification of seed magnetic fields due to the usual α effect, where α is a measure of the net kinetic helicity in the flow (see, e.g., Moffatt 1978; Parker 1979; Krause & Rädler 1980; Brandenburg & Subramanian 2005; Brandenburg et al. 2012). Since it is not necessary for the turbulent flow always to be helical, it is interesting to study the dynamo action in non-helically forced shear flows. Dynamo action due to shear and turbulence in the absence of the α effect received some attention in the astrophysical contexts of accretion disks (Vishniac & Brandenburg 1997) and galactic disks (Blackman 1998; Sur & Subramanian 2009). The presence of large-scale shear in turbulent flows is expected to have significant effects on transport properties (Rädler & Stepanov 2006; Rüdiger & Kitchatinov 2006; Leprovost & Kim 2009; Sridhar & Singh 2010; Singh & Sridhar 2011). It has also been demonstrated that the mean shear in conjunction with rotating turbulent convection gives rise to the growth of large-scale magnetic fields (Käpylä et al. 2008; Hughes & Proctor 2009). The problem we are interested in may be stated as follows: in the absence of the α effect, will it be possible to generate a large-scale magnetic field solely through the action of non-helical turbulence in the background shear flow on the seed magnetic field? This question was recently numerically studied by Brandenburg et al. (2008), Yousef et al. (2008a, 2008b). These works clearly demonstrated the growth of large-scale magnetic fields due to non-helical stirring at small scales in the background linear shear flow.


Moreover, if mixing is effective over kiloparsec scales, then we would expect the neutral gas observed toward the QSO and the ionized gas seen toward the central H ii region to have the same metallicity. In which case, in order to find

, a significant fraction of the neutral gas must be many kiloparsecs away from the star-forming regions in order to not be contaminated. Such an explanation was adopted by Cannon et al. (2005), who postulated the existence of a low-metallicity halo beyond the inner ISM to explain the discrepancy between

 and

 toward star-forming regions in NGC 625. Our results are consistent with this idea and provide additional evidence for IGM gas feeding into galaxies through streams from the cosmic web (e.g., Sánchez Almeida et al. 2014a, and references therein). Dwarf galaxy pairs in particular are thought to have enhanced star formation because they are fed by significant reservoirs of neutral gas in which they reside, or because of their mutual interactions (Lelli et al. 2014; Stierwalt et al. 2015; Pearson et al. 2016). As noted in Section 2.4, UGC 5282 does lie near a galaxy of similar mass (UGC 5287 in Figure 3) and interactions between the two galaxies may be the source of gas flowing into UGC 5282. For example, Pearson et al. (2018) have suggested that multiple encounters between dwarf galaxies can “park” gas at significant distances from the protagonists, which can then return over several Gyr. It remains unknown whether the metallicity of such returning debris would be low enough to cause the decrease in metallicity in either UGC 5282 or UGC 5287, but it may reflect whatever buildup of metals occurred in the dwarfs at much earlier times. Alternative tidal models that cause strong metallicity gradients and the removal of low-metallicity gas at the edges of dwarf galaxies (Williamson et al. 2016) seem less well supported by our results. Indeed, the situation for UGC 5282 may be even more complicated, depending on whether it has entered the halo of NGC 3003 (Figure 3) and has begun to feel any effects from ram pressure stripping by gas in the host’s halo. The effects on the metallicity of the dwarf galaxy may, however, be less significant than any effects from tidal stripping (Williamson & Martel 2018).


Similarly to the [α/Fe] ratio, the ratio of the slow (s-) neutron capture process elements to iron can be regarded as a cosmic clock. Ba, Sr, La, and Y are mainly s-process elements produced on long timescales by low mass AGB stars (Matteucci 2012). Since a low mass star must evolve to the AGB phase before the s-process can occur, the s-process elements are characterized by a delay in the production, much like the delay of iron production by SNe Ia relative to the α elements production by core collapse SNe. Among the four s-process elements mentioned above, GES provides the abundances of Y II (the first s-process peak element) and Ba II (the second s-process peak element) for all our sample stars. Their abundances behave differently in the Galactic thick and thin discs (Bensby et al. 2005, 2014; Israelian et al. 2014; Bisterzo et al. 2017; Delgado Mena et al. 2017). Unlike the Galactic thick disc stars, which show an almost constant [Ba/Fe] abundance close to the solar value, the Galactic thin disc stars have their [Ba/Fe] abundances increasing with [Fe/H] and reaching their maximum values around solar metallicity, after which a clear decline is seen (see also Cristallo et al. 2015a,b, for the most recent s-process calculation in AGB yields). The same trend is observed in our sample. In Fig. 13 we display the Li-[Ba/Fe], [Ba/Fe] as a function of [Fe/H], and the evolution of absolute Ba abundance A(Ba), as derived from Ba II lines. Similar figures are also plotted for yttrium (Y II). [Ba/Fe] and [Y/Fe] values here are derived from MCMC simulations, taking into account the measurement uncertainties of A(Ba II)/A(Y II) and [Fe/H]. By applying the same MCMC setups used for [α/Fe] (see Sect. 3.1), we calculate the mean values of [Ba/Fe] and [Y/Fe] for each star. These values, together with their corresponding 1σ uncertainties, are listed in Table 1. In the literature there are several theoretical works on the evolution of [Ba/Fe] and [Y/Fe] in the Galactic thin disc (e.g. Pagel & Tautvaisiene 1997; Travaglio et al. 1999, 2004; Cescutti et al. 2006; Maiorca et al. 2012; Bisterzo et al. 2017). For comparison, we show in Fig. 13 the predictions of the most recent one (Bisterzo et al. 2017) where the updated nuclear reaction network was used.


In this paper we extend previous work based on cosmological simulations by analysing the general magnetic field properties and the diffuse radio halo emission in galaxy clusters in the IllustrisTNG project, a set of cosmological magnetohydrodynamics simulations run with the moving-mesh code arepo (Springel 2010) that include a comprehensive module for galaxy formation physics. The main and novel aspect of our work is the analysis of the diffuse radio emission resulting from radio haloes in galaxy clusters (Feretti & Giovannini 1996; Murgia et al. 2009; Vacca et al. 2011; Feretti et al. 2012). We investigate radio emission from clusters by a detailed comparison with observations, trying to match the current observational constraints and to make predictions for the upcoming radio surveys that will be performed with the new generation of radio instruments such as SKA and LOFAR. The analysis of simulated radio haloes gives us a complementary view on the spatial extent and energy content of magnetic fields in galaxy clusters, since the radio emission is proportional to their strength. As such, the study of radio halo scaling relations (Giovannini et al. 2009; Cassano et al. 2013; Zandanel, Pfrommer & Prada 2014) with the total X-ray power and halo mass may yield important information about the amplification mechanisms of magnetic fields in clusters and the level of turbulence in the ICM. The modelling of radio emission makes it also possible to study the transport of charged particles and their re-acceleration to relativistic speeds, and it constrains the probability of detecting extended radio-emitting structures in a statistical sample of realistic simulated clusters. The comparison of the simulated radio emission with actual observations might also be employed as a useful check for the implementation of the galaxy formation physics modules used to perform the simulations, although our modelling of relativistic particles is rather preliminary and might have a non-negligible impact on the results.


These observations have identified a large reservoir of baryons surrounding galaxies. This circumgalactic gas extends to roughly the virial radius (Shull 2014) and contains a substantial fraction of the baryons (Werk et al. 2014; Bregman et al. 2018) and metals (Peeples et al. 2014) associated with the dark matter halo. The larger column densities of the O+5 ion in the CGM of star-forming galaxies compared to passive galaxies (Tumlinson et al. 2011) has generated great interest in the CGM, because the processes producing this dichotomy may explain why star formation is quenched in massive halos (Blanton et al. 2003; Kauffmann et al. 2003; Schawinski et al. 2014). In cosmological hydrodynamical simulations, the O vi absorbing gas lies behind the halo accretion shock and is maximal in L* galaxies because their virial temperature is close to the temperature T ≈ 105.5 K where the O+5 ionization fraction peaks (Oppenheimer et al. 2016). Feedback from supermassive black holes may suppress the O+5 fraction in the halos of red galaxies relative to the halos of blue galaxies of similar stellar mass (Nelson et al. 2018). The nucleus would not typically still be active by the time its outflow impacted the gas properties at half the virial radius, so differentiating between nuclear activity and halo mass is challenging observationally (Berg et al. 2018). Simulations that zoom in on individual galaxies include more physics than cosmological simulations (Hummels et al. 2013; Su et al. 2018). They qualitatively agree that enhanced star formation feedback increases the strength of high-ionization absorption lines, as Heckman et al. (2017) observed. Quantitatively, however, the star formation feedback does not produce enough O vi absorption, nor does it permanently quench star formation. A solution may require a completely different schema for the CGM. Stern et al. (2018) argue, for example, that the O vi absorption occurs beyond the accretion shock, where O vi would be photoionized by the UV background, a low-pressure scenario.


The year 2020 marks the 350 yr anniversary of the discovery of the eruption of Nova 1670 (or CK Vul) made by European astronomers (Shara et al. 1985). Their observations, predominantly performed with a naked eye, traced the object’s evolution on the sky in 1670−1672. From the archive records, we know that the eruption was rather unusual, in particular it was very much unlike classical novae. The light curve of CK Vul displayed three peaks and the star was described as reddish in the later stages of the eruption (Hevelius 1671; Shara et al. 1985). These characteristics resemble closest the behavior often observed in (luminous) red novae (Kato 2003; Tylenda et al. 2013), a modern category of eruptive stars known from our and other galaxies (e.g. Pastorello et al. 2019). Red novae are recognized as manifestations of on-going mergers of non-compact stars such as main-sequence dwarfs, sub-giants, or red giants (Soker & Tylenda 2003; Tylenda & Soker 2006; Tylenda et al. 2011; Pastorello et al. 2019). While the number of known red novae, mainly extragalactic ones, is quickly rising (e.g., Stritzinger et al. 2020), we know only a few red-nova remnants that are decades old (Kamiński et al. 2018a). The remnant of the 1670 eruption of CK Vul, as a candidate post-merger site, could be the oldest (counting from the onset of the eruption) known object of this type and as such offers the opportunity to investigate a merger aftermath centuries after the stellar coalescence. The nature of the progenitor system of CK Vul has been debated. Eyres et al. (2018) proposed that the seventeenth-century merger took place between a white dwarf and a brown dwarf, but there is little quantitative evidence to support this. Based on the analysis of the source’s chemical and isotopic composition, including the unique presence of the radioactive isotope of 26Al, Kamiński et al. (2018b) found that the progenitor system of CK Vul included at least one red-giant-branch (RGB) star with a fully developed helium core.


A widely used statistical property of the sky brightness distribution is its power spectrum (Lazarian 1995; Bharadwaj & Sethi 2001, and others). As the redshifted 21-cm signal is expected to be faint and hard to detect with imaging, estimating its power spectrum or equivalently intensity mapping gives a possible probe of the evolution of the baryonic matter distribution over cosmic time. Bharadwaj & Sethi (2001) show that visibility correlation directly measures the power spectrum. This method and its variants (Datta, Choudhury & Bharadwaj 2007; Choudhuri et al. 2014; Choudhuri et al. 2016; Bharadwaj et al. 2019; Choudhuri et al.2019, and others) have been used to estimate the angular power spectrum of the diffused galactic foreground (Ghosh et al. 2012; Choudhuri et al. 2017b; Chakraborty et al. 2019a; Choudhuri et al. 2020) as well as the power spectrum of H i distribution in nearby galaxies (Dutta et al. 2009; Dutta & Bharadwaj 2013; Nandakumar & Dutta 2020). These works propagate the uncertainties in each visibility estimate and combine that with the sample variance error in measuring the power spectrum to quote uncertainties in the power spectrum estimates. In this work, we use the estimator discussed in Choudhuri et al. (2014), where visibilities are gridded before estimating the power spectrum. Given an angular field of view of θ0 to which the telescope is sensitive, it has been shown (Bharadwaj & Sethi 2001; Bharadwaj & Ali 2005; Choudhuri et al. 2014) that the visibilities in the nearby baselines remain correlated to a baseline separation of $\Delta U \lt \frac{1}{\pi \theta _0}$. The size of the uv-grids is chosen such that they are large enough to include a sufficient number of baselines in a given uv-grid and small enough to have all visibilities in the uv-grid correlated. In each uv-grid, they estimate the power spectrum by correlating visibilities only in nearby baselines, omitting the visibility autocorrelations. This drastically reduces the noise bias in estimates of the power spectrum in uv-grids. The contribution from each uv-grid within a given annulus in $U = \mid \vec{U} \mid$ is then combined, and the real part of it is used to quote the value of the isotropic power spectrum for the baseline separation U. We may schematically write it as
(4)$$\begin{eqnarray}
\mathcal {E} \lbrace P(U)\rbrace = \mathcal {R} [\langle \tilde{V}(\vec{U})^{*} \tilde{V}(\vec{U}+\Delta \vec{U}) \rangle].
\end{eqnarray}$$Here, the average is taken over the uv-grid first and then within the annulus, as explained above. Note that the power spectrum estimator here assumes that a perfect calibration is done and the gains are all unity. In such a case, the power spectrum estimate has no bias arising from instrumental noise, and its uncertainties can be written as (Ali et al. 2008; Dutta 2011)
(5)$$\begin{eqnarray}
\sigma _P^2 = \frac{P^2(U)}{N_\mathrm{ G}} + 2\frac{P(U)\sigma _N^2}{N_\mathrm{ B}} + 2\frac{\sigma _N^4}{N_\mathrm{ B}},
\end{eqnarray}$$where NG is the number of independent estimates of the power spectrum in a given annulus bin at U, NB is the total number of visibility pairs in the bin.


The magnetic field assumed in our models is normalized either to β = 100, which means thermally dominated accretion flows, or to β = 1, which means actually quite strong magnetization and equilibrium ratio of the magnetic and gas pressures. The gas pressure is set by the solution of the Bondi transonic accretion flow, which is our initial condition for the simulation. Only if the magnetic pressure does not add a high contribution to this flow structure can we safely assume that the solution holds, and the gas falls supersonically to the black hole downstream of the sonic point, ultimately reaching the speed of light at the black hole horizon. We perturb this flow in time, by adding a slow rotation to the gas; hence, our sonic point is moving, and the shape of the sonic surface is disturbed. However, when the magnetic pressure is substantially large, the initial solution for the transonic accretion may not be a good approximation. Already at the beginning, multiple critical points might exist in the flow. The possible existence of shocks in low angular momentum flows connected with the presence of multiple critical points in the phase space has been studied from different points of view during the past 30 yr. However, the theoretical works that describe the fundamental properties of the low angular momentum accretion and that usually treat the steady solution of the equations have so far been carried out only for nonmagnetized and usually also nonviscous flows (Abramowicz & Zurek 1981; Abramowicz & Chakrabarti 1990; Das 2002; Das & Czerny 2012). Hydrodynamical models of the low angular momentum accretion flows have been studied already in two and three dimensions, e.g., by Proga & Begelman (2003) and Janiuk et al. (2008, 2009). In those simulations, a single, constant value of the specific angular momentum was assumed, while the variability of the flows occurred owing to, e.g., nonspherical or nonaxisymmetric distribution of the matter. The level of this variability was also dependent on the adiabatic index (see also Palit et al. 2019). However, these studies considered nonmagnetized flow only, which limits the applicability of these models to observational data and to the stellar evolution and presupernova studies (Heger et al. 2005). The range of strength of the magnetic field varies from very low values in the interstellar medium to extremely high values of ∼ 1015 G in the magnetars, which are extremely magnetized neutron stars. During the accretion process, the magnetic field in the star is likely to be amplified in the innermost region of the black hole, so a negligible amount of magnetic field in those regions, where the shock and the sonic point could be located, is thus not anticipated. The only method, however, to describe the effect of strong magnetic fields in the context of transonic accretion with low angular momentum is via numerical simulations, because no analytic solution of this problem exists, to the best of our knowledge. Hence, setting up the initial condition with strong magnetic fields overimposed on the slowly rotating transonic Bondi flow is a simple but working approach that we make here.


Using the RADEX3 non local thermodynamic equilibrium (LTE) modeling program (van der Tak et al. 2007) with collisional rate coefficients from Wiesenfeld & Faure (2013), we modeled the relation between the gas kinetic temperature and the measured average of para-H2CO 0.5 × [(322–221 + 321–220)/303–202] ratios, adopting a 2.73 K background temperature, an average observational linewidth of 4.0 km s−1, and column densities N(para-H2CO) = 2.7 × 1012 and 3.7 × 1012 cm−2 for N113 and N159W, respectively. The results are shown in Fig. 5. The values of the para-H2CO column density were obtained with APEX data (beam size ~30″; Tang et al. 2017b), which cover similar regions. Different column densities of para-H2CO only weakly affect derived kinetic temperatures (see Fig. 3 in Tang et al. 2017b or Fig. 4 in Tang et al. 2018a; this was also shown in Fig. 13 and discussed in Sect. 4.3.1 of Mangum & Wootten 1993) as long as all lines are optically thin. Considering that the relation between the gas temperature and the para-H2CO line ratio may vary at different spatial densities (see Fig. 2 in Tang et al. 2017b), we modeled it at spatial densities 104, 105, and 106 cm−3 in Fig. 5. It appears that Tkin at n(H2) = 105 cm−3 is consistently lower than values at 104 and 106 cm−3 by ≲23% and ≲34%, respectively, for Tkin ≲ 100 K. Local thermodynamic equilibrium (LTE) is a good approximation for the H2CO level populations under optically thin and high-density conditions (Mangum & Wootten 1993; Tang et al. 2017a,b, 2018b). Following the method applied by Tang et al. (2017b) in their Eq. (2), we plot the relation between the LTE kinetic temperature, TLTE, and the para-H2CO (3–2) line ratio in Fig. 5. Apparently, TLTE agrees well with Tnon-LTE at volume densities n(H2) ~ 105 cm−3 as long as Tkin ≲ 100 K. Previous observations show that para-H2CO (3–2) is sensitive to gas temperature at density 105 cm−3 (Ginsburg et al. 2016; Immer et al. 2016; Tang et al. 2017b). The spatial density measured with para-H2CO (303–202) and C18O (2–1) in N113 and N159W is n(H2) ~ 105 cm−3 on a size of ~30″ (Tang et al. 2017b). Therefore, here we adopt 105 cm−3 as an averaged spatial gas density in the N113 and N159W regions.


Here, we present a revised calculation of the emissivity of ionizing photons at z = 2.85 based on the analysis of the HST data in the HS1549 field. We estimate the comoving specific emissivity as
3

following the assumptions of M13 and Nestor et al. (2013). In this expression, L is the non-ionizing UV luminosity, Φ is the non-ionizing UV luminosity function, and (FUV/FLyC)corr is the average flux-density ratio of non-ionizing to ionizing UV radiation for the entire galaxy sample, corrected for the mean IGM attenuation in the LyC spectral region.19

19
To correct for absorption of LyC photons by neutral hydrogen in the IGM, we use the sample-averaged transmission values calculated in M13: tLAE = 0.44 ± 0.03 and tLBG = 0.35 ± 0.04.
 We perform this emissivity calculation separately for the main sample of spectroscopically confirmed LBGs and LAEs from M13 (using the UV luminosity functions from Reddy et al. 2008 for LBGs and Ouchi et al. 2008 for LAEs), and combine the LBG and LAE emissivities to obtain a total emissivity for star-forming galaxies. As in M13, we use the LRIS V-band to represent non-ionizing UV flux and NB3420 to represent LyC flux. The difference between our calculation and that of M13 lies in our estimation of the average flux-density ratio. Rather than estimating the average amount of foreground contamination from simulations, we instead know exactly which galaxies are contaminated based on the HST data. There were only two NB3420-detected galaxies in the M13 spectroscopic sample for which we were unable to acquire U336V606J125H160 imaging (D24 and lae4680), and for these objects we could not evaluate whether or not the NB3420 detections are due to foreground contamination. We thus calculate the emissivity twice in order to quote the full range of possible values: in one calculation we assume that MD5 is the only true LyC detection, and in the other calculation we assume that MD5, D24, and lae4680 are all true LyC-emitters. In addition to using the HST data to remove the NB3420 flux of foreground contaminants, we also use these measurements to estimate the percentage of contaminated flux in the non-ionizing UV. All objects with foreground contaminants identified through the HST imaging are blended in the LRIS V imaging, and it is impossible to isolate the uncontaminated z ∼ 2.85 flux in the LRIS V image. Thus, for each contaminated object, we decrease its LRIS V-band flux to match the fraction of uncontaminated V606 flux in the HST imaging. For objects that do not have HST U336V606J125H160imaging and are undetected in NB3420, we decrease their LRIS V-band flux to match the average fraction of uncontaminated V606 flux in the full sample of HST-imaged galaxies without NB3420 detections (99% for LBGs, 91% for LAEs). Finally, we use the same sample-averaged IGM correction to compute (FUV/FLyC)corr as described in M13, employing statistics of H i  absorbers from Rudie et al. (2013). We note that the clustering of Lyman limit systems is not taken into account in these absorber statistics, and thus the true mean IGM transmission may be slightly higher than the values presented in M13 (see, e.g., Prochaska et al. 2014).


Ikarashi et al. (2015) discussed that if both the radio and FIR continuum are tracers of star-forming regions, then the z ≳ 3 SMGs are more compact than the lower-redshift SMGs typically observed in radio continuum emission (e.g. Biggs & Ivison 2008). As shown in Fig. 7, our present VLA 3 GHz data do not suggest such a trend, and, as mentioned earlier, there is actually a hint of larger radio sizes at z ~ 2.5–5 compared to lower redshifts. However, the highest-redshift SMG in our sample, AzTEC3 at z ≃ 5.3, shows the most compact size among our sources, consistent with the rest-frame FIR sizes from Ikarashi et al. (2015). We note that Capak et al. (2011) found that AzTEC3 belongs to a spectroscopically confirmed protocluster containing eight galaxies within a 1 arcmin2 area, and therefore the environment might also play a role in the galaxy size evolution (see also Smolčić et al. 2015b). However, it is currently unclear whether the environmental effects in a galaxy overdensity will lead to a more compact or more extended radio-emitting size than field galaxies. On one side, a protocluster environment is expected to show an elevated merger rate (e.g. Hine et al. 2015), and, as discussed above, mergers are expected to pull the galactic magnetic fields to larger spatial scales, and hence lead to a more extended radio synchrotron emission. On the other side, the ram and/or thermal pressures of the intracluster medium could compress the ISM of the galaxy, increase the magnetic field strength, and hence cause an excess in radio emission (consistent with a low IR-radio q parameter of ≲2 for AzTEC3; Miettinen et al., in prep.). The aforementioned pressure forces can drive shock waves into the ISM, and hence accelerate the CR particles (Murphy 2009). Consequently, the cooling time and diffusion length-scale of CR electrons can decrease (see Appendix E), resulting in a compact radio-emitting area. More detailed environmental analysis of SMGs is needed to understand this further.


Among the main proposed formation channels for merging binary COs, we find: pairing of primordial BHs (e.g. Carr & Hawking 1974; Bird et al. 2016; Carr et al. 2016; Scelfo et al. 2018; De Luca et al. 2021); isolated binary evolution via common envelope (e.g. Tutukov & Yungelson 1973; Bethe & Brown 1998; Portegies Zwart & Yungelson 1998; Belczynski, Kalogera & Bulik 2002; Belczynski et al. 2008; Dominik et al. 2013; Belczynski et al. 2016; Eldridge & Stanway 2016; Mapelli et al. 2017; Stevenson, Berry & Mandel 2017; Ablimit & Maeda 2018; Klencki et al. 2018; Kruckow et al. 2018; Mapelli & Giacobbo 2018; Eldridge, Stanway & Tang 2019; Mapelli et al. 2019; Neijssel et al. 2019; Spera et al. 2019), via stable mass transfer (e.g. Kinugawa et al. 2014; Inayoshi et al. 2017; van den Heuvel, Portegies Zwart & de Mink 2017; Kinugawa, Nakamura & Nakano 2020; Tanikawa et al. 2021a,b), or via chemically homogeneous mixing (e.g. de Mink & Mandel 2016; Mandel & de Mink 2016; Marchant et al. 2016; du Buisson et al. 2020); dynamical perturbations in the field (Michaely & Perets 2019, 2020); dynamical formation in young star clusters (YSCs, e.g. Banerjee, Baumgardt & Kroupa 2010; Ziosi et al. 2014; Mapelli 2016; Askar et al. 2017; Banerjee 2017; Banerjee 2018; Rastello et al. 2018; Di Carlo et al. 2019, 2020a,b; Kumamoto, Fujii & Tanikawa 2019, 2020; Rastello et al. 2020; Banerjee 2021; Rastello et al. 2021; Trani et al. 2021); globular clusters (GCs, e.g. Portegies Zwart & McMillan 2000; Downing et al. 2010; Tanikawa 2013; Samsing, MacLeod & Ramirez-Ruiz 2014; Rodriguez et al. 2015; Rodriguez, Chatterjee & Rasio 2016; Rodriguez & Antonini 2018; Samsing, Askar & Giersz 2018; Zevin et al. 2019; Antonini & Gieles 2020); nuclear star clusters (NSCs, e.g. Miller & Lauburg 2009; O’Leary, Kocsis & Loeb 2009; Antonini & Perets 2012; Prodan, Antonini & Perets 2015; Antonini & Rasio 2016; Petrovich & Antonini 2017; Arca-Sedda & Gualandris 2018; Gondán et al. 2018; Arca-Sedda & Capuzzo-Dolcetta 2019; Rasskazov & Kocsis 2019; Arca Sedda 2020; Arca Sedda et al. 2020); and AGN discs (e.g. McKernan et al. 2012; Bartos et al. 2017; Stone, Küpper & Ostriker 2017; McKernan et al. 2018; Yang et al. 2019; Tagawa, Haiman & Kocsis 2020).


As the H ii regions S235 A and S235 C are deeply embedded in the molecular cloud, we cannot use published predictions from standard plane-parallel PDR models without foreground absorption (e.g. Kaufman et al. 1999). In order to understand how the observational view by SOFIA is matched by a ’classical’ model of expanding H ii regions, described analytically and numerically by Spitzer (1978), Elmegreen & Lada (1977), Hosokawa & Inutsuka (2006), Raga et al. (2012), Kirsanova et al. (2009), and Bisbas et al. (2015), we make simulations with the MARION model (Kirsanova et al. 2009; Akimkin et al. 2015). The gas-phase chemical network from Röllig et al. (2007) (mainly based on the UMIST99 ratefile; Le Teuff, Millar & Markwick 2000) allows us to reproduce the C+, CO, and HCO+ abundances in PDRs (see Kirsanova & Wiebe 2019), so we use this network together with the ionization of the atomic species and corresponding recombinations in the H ii regions. The cross-sections for most of photoreactions are taken from the Leiden data base of ‘Photodissociation and photoionization of astrophysically relevant molecules’ (Heays, Bosman & van Dishoeck 2017). We implement the formation of H2 on grain surfaces and accretion and desorption processes of other neutral species, but other chemical reactions on dust surfaces are not considered in the calculations to save computation time. The rates of accretion and desorption processes are based on the work by Hasegawa & Herbst (1993), with updated desorption energies from Garrod, Wakelam & Herbst (2007). We use the ‘high-metallicity’ initial elemental abundances based on the ‘EA2’ set from Wakelam & Herbst (2008). The initial conditions are cold, molecular, and solid. This means that we start with all carbon and oxygen in CO and H2O on dust surfaces. Fifty two chemical species are included: H, H+, H2, H$_2^+$, H$_3^+$, O, O+, O++, OH+, OH, O2, O2:d, O$_2^+$, H2O, H2O+, H3O+, C, C+, C++, CH, CH+, CH2, CH$_2^+$, CH3, CH$_3^+$, CH4, CH$_4^+$, CH$_5^+$, CO, CO:d, CO+, HCO+, He, He+, S, S+, S++, Si, Si+, H:d, H2:d, O:d, OH:d, H2O:d, C:d, CH:d, CH2:d, CH3:d, CH4:d, S:d, Si:d, and e−, where the postfix ‘:d’ indicates species on dust grain ices. Chemical species containing Si and S are included only to obtain correct gas temperature in ionized region. We recognize that the chemical network is far from complete, but our choise was motivated by limited computation time. The heating and cooling processes included in the model are listed in Akimkin et al. (2015) and Kirsanova & Wiebe (2019).


A realistic EoS that is able to reproduce the properties of compact astrophysical objects has to fulfill several requirements. The possibility of including many particle species, which is known as multicomponent character, is of crucial importance for modeling the NS interiors, which in even the simplest treatment include neutrons, protons, and electrons, while more advanced descriptions have to account for the presence of hyperons (Schaffner-Bielich et al. 2002). Therefore, the grand canonical ensemble is the natural choice for the formulation of such an EoS. Another element of the realistic phenomenological hadronic EoS corresponds to the short-range repulsive interaction of the hard core nature between particles  (Andronic et al. 2006; Bugaev et al. 2016). Analysis of the particle yields produced in relativistic A+A collisions within statistical (thermal) models, i.e., the Hadron Resonance Gas (HRG) model (Bugaev et al. 2016), shows the importance of the particle hard core repulsion. In this approach every particle species is defined as a rigid sphere with a fixed radius estimated from experimental data analysis. These radii do not exceed 0.5 fm  (Andronic et al. 2017; Sagun et al. 2017a). Note that the hard core of hadrons in phenomenological EoSs is important in order to suppress thermal excitations of the hadronic spectrum and provide deconfinement of the color degrees of freedom expected at high temperatures/densities  (Satz 2012). Another requirement to the phenomenological EoS is related to its causal behavior when the speed of sound cannot exceed the speed of light. At sufficiently high densities this condition is violated by the hard core repulsion. As was shown by Sagun et al. (2017a), introducing the induced surface tension (IST) of particles to the model with the hard core repulsion between an arbitrary number of hadron species makes the EoS significantly softer and extends its causality range up to 7.5 normal nuclear densities, where formation of the quark-gluon plasma is expected. The IST is the key element of this approach (Sagun et al. 2014), as it allows us to account for the hard core repulsion between constituents in the most accurate way, and to properly reproduce the virial expansion of the multicomponent EoS. Recently, the IST EoS was used to describe the experimental data of hadron multiplicities measured at AGS, SPS, RHIC, and LHC energies of nuclear collisions (Sagun et al. 2017b), as well as the nuclear matter properties (Sagun et al. 2014). In this work the focus is on the application of IST EoS to the study of NS properties.


HCOOH is the simplest carboxylic acid and has been observed toward high-mass and low-mass star-forming regions (e.g., Woods et al. 1983; Liu et al. 2001, 2002; Bisschop et al. 2007; Lefloch et al. 2017; Oya et al. 2017; Csengeri et al. 2019), protoplanetary disks (e.g., Favre et al. 2018), pre-stellar sources (e.g., Irvine et al. 1990; Vastel et al. 2014; Jiménez-Serra et al. 2016), and comets of the solar system (Biver et al. 2014). Although the production of HCOOH has also been investigated experimentally (Ioppolo et al. 2011) and theoretically (Tielens & Hagen 1982; Garrod & Herbst 2006; Aikawa et al. 2008; Garrod et al. 2008; Vasyunin et al. 2017), its formation process and chemical link to nitrogen-bearing species are puzzling. Indeed, the chemical network calculation tracing a pre-stellar/protostellar core by Aikawa et al. (2020) indicates that nitrogen-bearing COMs and HCOOH appear in the same region (i.e., a hot core) as oxygen-bearing COMs: no differentiation is found. It should be noted that the differentiation is not ascribed to the desorption temperature of these molecules formed on grain mantles. As described in Section 4.2, the temperature of the outer envelope traced by CH3OH is 150–165 K, which is higher than that of the inner envelope traced by HCOOH and NH2CHO, 75–112 K. Hence, ice mantles containing various COMs should have already been liberated from dust grains in the outer envelope. However, the results of PCA-3D suggest that HCOOH and the nitrogen-bearing species, NH2CHO, HNCO, and HC3N, do not appear in the gas phase outside the radius of ∼0.″06, even though these desorption temperatures are comparable to those of CH3OH (e.g., Oya et al. 2019). In other words, other factors rather than the desorption temperature should be responsible for these molecules to be observed in the gas phase. It may be the high-density condition, protostellar radiation, or both of them. The gas-phase production of nitrogen-bearing COMs and HCOOH should be considered seriously.


N-body simulations represent the most widely used and convenient method of exploring the highly non-linear regime of cosmic structure formation. Starting from a set of initial conditions, the numerical simulations follow the formation and evolution of structures from an early epoch down to present day. Motivated by the fact that DM represents most of the matter in the Universe and because of the relatively simple physics of collisionless DM particles, DM-only simulations represent the most widely used category of numerical simulations. When designing a cosmological N-body experiment, one is concerned by two major factors. Ideally, one would like to simulate a region of the universe that is as large as possible to get a representative census of the structures encompassed within it. On the other hand, one would also want very high mass resolution, to be able to resolve accurately even the smallest cosmologically relevant objects. Unfortunately, due to limited computational resources, these two requirements are in conflict, which implies that various compromises need to be made when designing a numerical simulation. So far, the biggest efforts were focused into two, somewhat complementary approaches. The first is represented by simulations like Millennium (ms; Springel et al. 2005), Millennium II (ms-II; Boylan-Kolchin et al. 2009), Millennium XXL (MXXL; Angulo et al. 2012), Bolshoi (Klypin et al. 2011), MultiDark (Prada et al. 2012), Horizon Run I-III (Kim et al. 2009, 2011), Horizon-4π (Prunet et al. 2008; Teyssier et al. 2009), MareNostrum Universe (Gottloeber et al. 2006), Jubilee project (Watson et al. 2014), Coyote Universe (Heitmann et al. 2010), DEUS simulation (Alimi et al. 2012; Rasera et al. 2014) or MICE suite (Fosalba et al. 2015). These follow structure formation in a large cosmological volume at the expense of having a medium or a low-mass resolution. Such simulations provide the formation histories for a very large number of medium- and high-mass DM haloes, but do not necessary resolve all the details relevant for galaxy formation. On the other side we have N-body simulations like the aquarius project (Springel et al. 2008), the Via Lactea (Diemand, Kuhlen & Madau 2007), the Phoenix project (Gao et al. 2012), CLUES (Gottloeber, Hoffman & Yepes 2010) and the ELVIS suite (Garrison-Kimmel et al. 2014b) that are characterized by a very high mass and force resolution but are limited to very small cosmic volumes. These give a very detailed picture of galaxy- and cluster-size haloes, but do so only for a very limited number of objects, which makes their results sensitive to small number statistics, and are unable to capture the full interconnection between small (DM haloes) and large (the cosmic web) cosmic scales.


The Juno spacecraft has measured Jupiter’s gravitational field to high precision through precise Doppler tracking in its polar orbit around Jupiter, compared with the previous values detected by Pioneer 10 and 11 and by Voyager 1 and 2 (Folkner et al. 2017; Bolton et al. 2017; Iess et al. 2018). These new gravity data have improved our knowledge of Jupiter’s interior. The even gravity harmonics are affected by the shape and internal structure of Jupiter in its hydrostatic equilibrium under the effect of rotational distortion. To accurately describe the shape and internal structure of Jupiter, various interior models with new ingredients, such as two-layer and three-layer structure models, have been established by several groups (Guillot & Morel 1995; Guillot 1999; Hubbard 1999, 2013; Anderson & Schubert 2007; Kaspi et al. 2010; Nettelmann et al. 2012; Helled et al. 2015; Vazan et al. 2015; Kong et al. 2016; Wahl et al. 2017; Ni 2018; Guillot et al. 2018; Debras & Chabrier 2019). Most of these models describe the internal structure of Jupiter via the physical laws of nature given an empirical or simulated equation of state (EOS), such as polytropic EOSs, EOSs obtained using the free-energy minimization method (Saumon et al. 1995), and ab initio EOSs (Nettelmann et al. 2008, 2012; French et al. 2012; Becker et al. 2014; Militzer et al. 2008; Militzer & Hubbard 2013; Chabrier et al. 2019). The EOSs describe the microscopic properties of planetary matter and play an important role in calculating the structure and evolution of planets, in spite of uncertainties in the hydrogen–helium phase separation (Hubbard et al. 2002; Saumon & Guillot 2004; Fortney & Nettelmann 2010; Miguel et al. 2016, 2018; Militzer et al. 2016; Debras & Chabrier 2019). Juno’s gravity measurements have demonstrated small values for high-order even gravitational harmonics with respect to the heavy-element abundance measured by the Galileo entry probe (Wahl et al. 2017; Debras & Chabrier 2019). In order to reconcile the calculated gravitational harmonics with these small values of J4 to J8, Wahl et al. (2017) proposed a dilute core model where heavy elements are dissolved in a hydrogen–helium mixture and expanded outward through a portion of Jupiter. Alternatively, these latter authors modified the abundances of helium and heavy elements in the outer molecular envelope to be lower than those measured by the Galileo entry probe. Stimulated by dilute cores, the three-layer structure models for Jupiter have been generalized into four-layer structure models by introducing a dilute core region above central compact cores. Guillot et al. (2018) compared the effective even harmonics

$J_{2i}^{\mathrm{eff}}(H,m)\;{=}\;J_{2i}^{\mathrm{Juno}}-\bigtriangleup J_{2i}(H,m)$
J2ieff(H,m) = J2iJuno−△J2i(H,m)
 with the ones obtained from interior models assuming rigid rotation to explore the rotation of Jupiter’s deep interior. It is found that Jupiter’s deep interior exhibits an almost rigid-body rotation and Jupiter’s atmospheric zonal flow extends to a depth H of 2000−3500 km. Debras & Chabrier (2019) established new models of Jupiter which satisfy both Juno’s gravity data and the outer helium and heavy element abundances from Galileo, showing a considerable entropy increase between the outer and inner envelopes and an inward decreasing abundance of heavy elements in the inner envelope.


Strong controversies are however still present regarding the way stars form in gravitationally unstable cores, in particular high-mass stars. Whether it happens on approximately a free-fall time, as suggested in the competitive accretion scenario by Bonnell et al. (2001), or rather slowly, implying at least several free-fall times, in the core accretion model by McKee & Tan (2003), which assumes that turbulence and/or magnetic fields provide a major stabilizing contribution. It is therefore of central importance to obtain independent constraints on the time-scale of star formation. A potentially powerful tool that was suggested in the literature is the measurement of deuteration fractions, which may be translated into time-scales via chemical models (Caselli et al. 2002; Fontani et al. 2011; Pagani et al. 2011a; Kong et al. 2015; Barnes et al. 2016; Lackington et al. 2016). In relation to filaments, a time-scale estimate has recently been achieved by Lackington et al. (2016) for the infrared dark cloud L332. They found deuteration ratios N2D+/N2H+ in the range 0.003–0.14. Based on the chemical models by Kong et al. (2015), the authors deduced time-scales for various cores within L332 of the order of several free-fall times to match the observed deuteration fractions, indicating rather old cores. The free-fall time of their best-fitting model was tff = 1.39 × 105 yr at a density of nH = 105 cm−3. However, the authors emphasize that a change in the CO depletion factor reduces the time-scale to only one free-fall time, which points towards (dynamically) young objects. In addition, Barnes et al. (2016) deduce a chemical age of about eight free-fall times (defined for spherical systems at a density of n = 104 cm−3, giving tff = 3.4 × 105 yr) for the dark cloud G035.39-00.33 to fit the observed average deuteration fraction of 0.04 ± 0.01, which they attribute to support of the filament by magnetic fields and turbulence. Furthermore, these authors find that deuteration is widespread over the filament rather than concentrated in individual cores, in agreement with recent findings by Pillai et al. (2012) who report widespread H2D+ emission in Cygnus X.


As described in Köhler et al. (2015)2, we assume that the dust properties change with increasing local density through accretion and coagulation. First, in the transition between the diffuse ISM and dense clouds, a second mantle can form on the surface of the CM grains that is due to the coagulation of the small aromatic-rich carbon grains on top of the bigger grains, which might be subsequently hydrogenated (a-C → a-C:H) and/or to the accretion of a-C:H material from the gas phase. Such carbonaceous mantles are efficiently processed by UV photons (Alata et al. 2014), but can stay H-rich as long as the radiation field is attenuated (Jones et al. 2014) or if the rehydrogenation process is efficient enough. This leads to grains with two mantles (core/mantle/mantle grains, CMM). Second, inside dense clouds, the CMM grains can coagulate into aggregates (AMM). On average, regarding the material abundance, one aggregate is composed of three CMM grains with amorphous silicate cores and one CMM grain with an amorphous carbon core. The formation of ice mantles on the surface of the aggregates (AMMI) can also occur in the densest regions, where the shielding from energetic photons is efficient enough to allow either gas molecules to form and to freeze out on the grains or surface chemistry to proceed effectively. The three types of evolved grains (CMM, AMM, and AMMI) contain 406 ppm of C in agreement with Parvathi et al. (2012), who found that 355 ± 64 ppm of C are enclosed within grains for lines of sights where NH ≳ 2 × 1021 H/cm2 (equivalently where E(B − V) ≳ 0.4 or AV ≳ 2). For each grain type, a size distribution consistent with grain growth is considered as explained in Köhler et al. (2015) and shown in Fig. 2. For the CMM grains, ~65% of the dust mass is in grains with \hbox{$40~{\rm nm} \leqslant a \leqslant 0.25$}40 nm ⩽ a⩽ 0.25μm, ~25% in grains with \hbox{$0.25 \leqslant a \leqslant 0.5$}0.25 ⩽ a⩽ 0.5μm, and ~10% in grains with \hbox{$0.5 \leqslant a \leqslant 0.7$}0.5 ⩽ a⩽ 0.7μm. For the AMM (AMMI) aggregates, ~50% of the dust mass is in grains with \hbox{$48~(91)~{\rm nm} \leqslant a \leqslant 0.25$}48 (91) nm ⩽ a⩽ 0.25μm, ~40% in grains with \hbox{$0.25 \leqslant a \leqslant 0.5$}0.25 ⩽ a⩽ 0.5μm, and ~10% in grains with \hbox{$0.5 \leqslant a \leqslant 0.7$}0.5 ⩽ a⩽ 0.7μm. The optical properties of all grains and a detailed description of the calculation method can also be found in Köhler et al. (2015), while a more specific description of the grain scattering properties and efficiencies are given in Paper I. A schematic view of the dust composition and stratification from the diffuse ISM to dense molecular clouds is shown in Fig. 1.


Analyzing optical emission lines, emanating from within the northern lobe, Tylenda et al. (2019) found a reddening with EB − V ≈ 0.9 mag or AV ≈ 2.8 mag, which we assume is mainly circumstellar in origin. Hajduk et al. (2013) observed two stars shining through the southern lobe and found AV = 3.3 − 4.4 mag with unknown contribution from the interstellar component. We assume here that those observations quantify the amount of circumstellar dust that is the main actor in shielding molecules from the central source. We recalculated the lifetimes of molecules assuming AV = 3 mag, and with (1) standard dust properties (i.e. with composition and size distribution as of interstellar dust) or (2) with larger and less opaque grains, at the gas-to-dust mass ratio of 124 (see Heays et al. 2017, for more details on the assumed dust properties). We used shielding functions from Heays et al., which include effects in lines. Results are shown in Cols. (3) and (4) of Table 3. The presence of ISM grains makes it possible for the observed molecules to survive for a very long time, longer than 350 yr. The lifetimes in the presence of the large grains considered by Heays et al. are typically a few times shorter than the age of the remnant. It is uncertain what kind of grains populate the dusty remnant of CK Vul, but given its anomalous elemental and molecular compositions and eruptive history, dust may have a peculiar chemical composition and size distribution. In such a case, the total to selective extinction law would also be different and the assumed AV may not be adequate. Nevertheless, if the molecules formed 350 yr ago and are shielded by big grains, with the calculated lifetimes a considerable fraction of molecular species would survive, except perhaps for a few most fragile ones which indeed are almost absent in the lobes. We conclude that the lifetimes in Table 3 that were calculated with an attenuated ISRF are consistent with the molecule formation 350 yr ago or more recently.

We used shielding functions from
which include effects in lines.


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


In Equations (24) and (25) the cumulative effect of all ions with Zi ≥ 2 is included in the term ζ(T, f), where a (rather weak) dependence on frequency f appears due to the Gaunt factor. The ζ(T, f) function depends both on the elemental abundances and on each element’s ionization state, which are different in equilibrium and nonequilibrium conditions. In this work, we will provide the ζ(T, f) function calculated under the assumption of ionization equilibrium using the CHIANTI spectral code (Dere et al. 1997, 2019), as detailed below. In this framework it is straightforward to users to replace the CHIANTI values for the equilibrium ion fractions by their own values calculated under nonequilibrium conditions, depending on the physical process they model. We carried out the calculations for the plasma element abundances typical of the solar corona (Feldman 1992), as well as for two abundance models obtained for the solar photosphere (Caffau et al. 2011; Scott et al. 2015). The main difference between these models is that in the solar corona all elements with low first ionization potential (FIP) are overabundant by a factor of about four over their photospheric abundances. However, this overabundance factor is somewhat uncertain—while it has been extensively used in the field, its value has been suggested to vary with time (Widing & Feldman 2001) and also within the same active region; also, the absolute correction of the abundances has been disputed, as some studies suggest that the FIP effect affects both low-FIP and high-FIP ions (Schmelz et al. 2012). Furthermore, solar abundances can be different from those of other stars, both in the photosphere and in the corona, even to the point that some stars exhibit an inverse FIP effect (Laming 2015). So, the software we implemented to carry out the calculations allows the user to interactively select an abundance data set that is best suited for the star or the solar region under consideration.


The effectiveness of an IRX-β relation depends on its validity for different types of galaxies across cosmic time. While the original MHC99 IRX-β relation applies to majority of galaxies, large scatters around this relation have been observed. Theoretical studies have shown that the IRX-β scatter may depend on the type of dust, gas metallicity, star formation history (SFH), dust-star geometry, and stellar population age (Popping et al. 2017; Safarzadeh et al. 2017; Narayanan et al. 2018; Schulz et al. 2020). Observations have shown that the IRX-β relation varies with stellar mass (Bouwens et al. 2016, 2020; Reddy et al. 2018; Fudamoto et al. 2020), infrared (IR) luminosity (Buat et al. 2012; Casey et al. 2014), age (Siana et al. 2009; Reddy et al. 2010; Shivaei et al. 2015), redshift (Capak et al. 2015; Pannella et al. 2015), and intrinsic β0 (β for a dust-free system; Boquien et al. 2012; Reddy et al. 2018; Schulz et al. 2020). These variations are linked to the diversity of galaxies’ attenuation curves, seen in previous studies (e.g., Kriek & Conroy 2013; Scoville et al. 2015; Battisti et al. 2020). The attenuation curve variations stem from two main sources: (a) different geometrical distributions of dust with respect to stars (and different dust optical depths), and (b) different dust grain properties, which affect the shape of the underlying extinction curve irrespective of the dust-star geometry (see the review by Salim & Narayanan 2020). While scenario (a) is extensively studied by comparing the attenuation curves of galaxies with different dust optical depths (references above), scenario (b) is less explored. Dust compositions are related to gas-phase element depletions and abundances (Jenkins 2009). Following this relation, Shivaei et al. (2020, hereafter S20) studied scenario (b) by deriving the attenuation curve of z ∼ 2 galaxies in two different metallicity (

) bins, while the dust optical depth distributions were kept the same. They found a steep SMC-like curve for galaxies with

, and a shallower Calzetti et al. (2000, hereafter C00)-like curve at

.


The lifetime of molecular clouds (MCs) remains an active research topic in the study of the interstellar medium and star formation, and most recent studies, both observational and theoretical, place this lifetime at a few times 107 yr for clouds in the 105–106M⊙ mass range (e.g. Blitz & Shu 1980; Kawamura et al. 2009; Zamora-Avilés, Vázquez-Semadeni & Colín 2012; Zamora-Avilés & Vázquez-Semadeni 2014; Lee, Miville-Deschênes & Murray 2016). In addition, several observational studies have suggested that the star formation rate (SFR) of the clouds appears to increase over their lifetimes. For example, studies of young clusters embedded in moderate-mass MCs (∼104M⊙) (e.g. Palla & Stahler 1999, 2000; Da Rio et al. 2010) have shown that their age histograms contain a large majority of young (1–2 Myr) objects, but also a tail of older (up to several Myr) ones suggesting an accelerating star formation activity, sometimes followed by a subsequent decline (see also Povich et al. 2016; Schneider et al. 2018). In addition, Kawamura et al. (2009) reported a clear evolutionary process over the lifetime of giant molecular clouds (GMCs; of masses ∼105–106M⊙) in the Large Magellanic Cloud, evidenced by the increasing number of massive stars across the sequence of GMC ‘classes’ proposed by those authors. Finally, on the basis of the large scatter in the observed star formation efficiency (SFE) in Milky Way GMCs, Lee et al. (2016) have concluded that the SFR in those clouds must also be time variable. Numerical simulations of MC formation and evolution also exhibit time varying, increasing SFRs during their early stages (e.g. Vázquez-Semadeni et al. 2007; Hartmann, Ballesteros-Paredes & Heitsch 2012). Also, in the presence of stellar feedback, at late times the SFRs reach a maximum and begin to decrease again (e.g. Vázquez-Semadeni et al. 2010; Colín, Vázquez-Semadeni & Gómez 2013). Vázquez-Semadeni, González-Samaniego & Colín (2017) have recently shown that the simulations of Colín et al. (2013) in fact produce stellar age histograms highly resemblant of the observed ones (Palla & Stahler 1999, 2000; Da Rio et al. 2010), and reproduce observed radial age gradients in clusters (Getman et al. 2014) as well as bottom-heavy stellar initial mass functions (IMFs) in scattered regions of massive star formation (Povich et al. 2016).


It is likely that some of these products are also formed in our experiments, but except for CO2, HNCO, and NCO−, they cannot be unequivocally identified with IR spectroscopy alone. Some of them have the same functional groups as urea and their IR spectra present absorptions in the same spectral regions, albeit with different band shapes and intensities. They could contribute somehow to the changes, both in shape and intensity, observed in the absorption bands during processing and thus introduce uncertainty, but by analogy with the literature results just mentioned (Renoult et al. 1969; Navarro-González et al. 1989; Duvernay et al. 2005; Poch et al. 2014) we expect that the prevalent dissociation channels will lead to small molecules that will not interfere much with the absorptions of urea. It is worth noting that urea fits in an isoelectronic sequence with carbonic acid and acetone: O = C(OH)2, O = C(NH2)2, and O = C(CH3)2. Under energetic processing, carbonic acid ice has been shown to decompose into H2O and CO2 (Peeters et al. 2010), and acetone ice into CH4 and H2C2O (ketene) among other products (Hudson 2018). In a similar way, urea, the middle term in the sequence, should decompose into NH3 and HNCO. Acid base reactions could transform HNCO and NH3 into OCN− and NH4+. As indicated repeatedly in the text, HNCO and OCN− were found in our measurements, but we did not find NH3 (expected peak at 1070 cm−1, A = 1.4 × 10−17 cm molecule−1). The presence of NH4+, which has been reported by Poch et al (2014) in the photolysis of crystalline urea, is not evident in our measurements, but cannot be completely excluded. The ν4 bending mode of ammonium (A = 4.1 × 10−17 cm molecule−1; van Broekuizen et al. 2004) appears at 1440–1480 cm−1, but its exact location and bandwidth are strongly dependent on the ice environment (see discussion in Maté et al. 2009; Gálvez et al. 2010). In our case, the corresponding ammonium band, which would be the most obvious counterion for OCN−, could be masked by the νCN band of urea. Compounds of very high molecular weight do not seem to form in appreciable amounts in our experiments, since all products evaporate without leaving any residue upon warming of the substrate to 300 K during a few minutes.


The IRIS spectra measure the flare in a “sit-and-stare” mode with a roll angle of 45∘. The spectral scale is ∼25.6 mÅ per pixel in the far-ultraviolet (FUV) wavelengths. The IRIS slit crosses the flaring loop and one ribbon (Fig. 1). Two red bars enclose the flaring loop region used to study the quasi-periodic oscillations in this work. IRIS spectrum was pre-processed with the SSW routines of “iris_orbitval_corr_l2.pro” (Tian et al. 2014; Cheng et al. 2015) and “iris_prep_despike.pro” (De Pontieu et al. 2014). To improve the signal-to-noise ratio, we apply a running average over five pixels to the IRIS spectra along the slit (Tian et al. 2012, 2016). We also manually perform the absolute wavelength calibration using a relatively strong neutral line, O I 1355.60 Å (see De Pontieu et al. 2014; Tian et al. 2015; Tian 2017). IRIS observations show that Fe XXI 1354.08 Å is a hot (∼11 MK) and broad emission line and is always blended with many narrow chromospheric lines at the flaring ribbons (Li et al. 2015b, 2016b; Tian et al. 2015; Young et al. 2015; Brosius et al. 2016; Polito et al. 2016). However, the Fe XXI 1354.08 Å line is much stronger than those blended emission lines at the flaring loops (Tian et al. 2016). Figure 2a gives the time evolution of the line profiles of Fe XXI 1354.08 Å, averaged over the slit positions between ∼18.3″ and 21.6″. Figure 2 panels b−f show the spectral line profiles at the time indicated by the yellow lines in panel a. We can see that only the cool line of C I 1354.29 Å is blended with the hot line of Fe XXI 1354.08 Å, but its contribution is negligible. Therefore, double Gaussian functions superimposed on a linear background are used to fit the IRIS spectra at “O  I” window (Tian et al. 2016). Next, we can extract the hot line of Fe XXI 1354.08 Å, as shown by the turquoise profile. The purple profile is the cool line of C I 1354.29 Å. Two orange peaks represent the cool lines of O I 1354.60 Å and C I 1354.84 Å (Tian 2017), which are far away from the flaring line of Fe XXI 1354.08 Å. Finally, the line properties of Fe XXI 1354.08 Å are extracted from the fitting results, that is, Doppler velocity, peak intensity, and line width (Li et al. 2016b; Tian et al. 2016; Tian & Chen 2018).


We test our calibration procedure on the buzzard-v1.1 simulation, a mock DES Y1 survey created from a set of dark-matter-only simulations. The simulation and creation of the mock survey data are detailed in DeRose et al. (in preparation), Wechsler et al. (in preparation), and MacCrann et al. (2018), so we provide only a brief summary of both. buzzard-v1.1 is constructed from a set of three N-body simulations run using l-gadget2, a version of gadget2 (Springel 2005) modified for memory efficiency. The simulation boxes ranged from 1 to 4 Gpc h−1. Light cones from each box were constructed on the fly. Haloes were identified using rockstar (Behroozi, Wechsler & Wu 2013), and galaxies were added to the simulations using the Adding Density Dependent GAlaxies to Light-cone Simulations (addgals) algorithm (Wechsler et al., in preparation). addgals uses the large-scale dark matter density field to place galaxies in the simulation based on the probabilistic relation between density and galaxy magnitude. The latter is calibrated from subhalo abundance matching in high-resolution N-body simulations. SEDs are assigned to the galaxies from a training set of spectroscopic data from SDSS Data Release 7 (DR7; Cooper et al. 2011) based on local environmental density. The SEDs are integrated in the DES pass bands to generate griz magnitudes. Galaxy sizes and ellipticities are drawn from distributions fit to deep SuprimeCam $i^{{\prime }}$-band data. Galaxies are added to the simulation to the projected apparent magnitude limit of DES Year 5 (Y5) data out to redshift z = 2. The galaxy positions, shapes and magnitudes are then lensed using the multiple-plane ray-tracing code Curved-sky grAvitational Lensing for Cosmological Light conE simulatioNS (calclens; Becker 2013). Finally, the catalogue is cut to the DES Y1 footprint with RA > 0 using the footprint and bad region masking including bright stars, regions of high extinction, etc., used in the actual Y1 data, and photometric errors are added using the DES Y1 depth map (Rykoff, Rozo & Keisler 2015). This yields a total masked area of 1108.13 deg2, 12 million WL source galaxies, and 102 120 galaxies in the higher luminosity redMaGiC sample used in this paper, as will be discussed in Sections 3.2 and 3.3.


Although it is a simple concept, obtaining galaxy sizes is not an easy task and is subject to a number of assumptions. The most common way to derive galaxy sizes is by performing light-profile fitting assuming a given shape of the surface brightness profile using a χ2 minimization (e.g. Simard et al. 1999; Peng et al. 2002; Ravindranath et al. 2004; Daddi et al. 2005; Ravindranath et al. 2006; Trujillo et al. 2006; Akiyama et al. 2008; Franx et al. 2008; Tasca et al. 2009; Cassata et al. 2010, 2013; Williams et al. 2010; Mosleh et al. 2011; Huang et al. 2013; Ono et al. 2013; Stott et al. 2013; Morishita et al. 2014; van der Wel et al. 2014; Straatman et al. 2015; Shibuya et al. 2015). Another method assumes circular or elliptical apertures around a predefined galactic center and computes the size enclosing a given percentage of the total galaxy flux (e.g. Ferguson et al. 2004; Bouwens et al. 2004; Hathi et al. 2008; Oesch et al. 2010; Ichikawa et al. 2012; Curtis-Lake et al. 2016). A third approach, involving counting the number of pixels belonging to the galaxy to derive its size, was also explored in Law et al. (2007). Studies of galaxy sizes at z> 2 became possible with the deep imaging obtained with HST. The first reports on size evolution found that galaxy sizes as observed in the UV rest-frame were becoming smaller at the highest redshifts (Bouwens et al. 2003, 2004; Ferguson et al. 2004). We have now access to the size evolution up to z ~ 10 from the deepest HST imaging data (e.g., Hathi et al. 2008; Jiang et al. 2013; Ono et al. 2013; Kawamata et al. 2015; Holwerda et al. 2015; Shibuya et al. 2015). With the multiwavelength and near-infrared coverage of CANDELS (Grogin et al. 2011; Koekemoer et al. 2011) optical rest-frame measurements are reported up to z ~ 3 for a large collection of galaxies in diverse populations (e.g. Bruce et al. 2012; van der Wel et al. 2014; Morishita et al. 2014). At z ~ 2 the size of star-forming galaxies (SFGs) is, to first order, independent of the observed rest-frame bands (Shibuya et al. 2015). It is generally accepted that galaxy sizes tend to decrease with increasing redshift (e.g. Bouwens et al. 2003, 2004; Ferguson et al. 2004; Mosleh et al. 2012) and that galaxy sizes depend on stellar mass (e.g. Franx et al. 2008; van der Wel et al. 2014; Morishita et al. 2014) and luminosity (e.g. Grazian et al. 2012; Huang et al. 2013). However, some results point to a scenario consistent with no size evolution as seen in UV rest-frame from HST data (Law et al. 2007; Curtis-Lake et al. 2016) and, at a fixed stellar mass, from optical rest-frame ground-based data (Ichikawa et al. 2012; Stott et al. 2013).


We can see how this is consistent with the development of small scales via phase mixing by introducing local wavenumbers for the variation with α and β, (3)\begin{eqnarray} \xi \propto \exp {\rm i}\left[ \int \kappa_\alpha {\rm d}\alpha + \int \kappa_\beta {\rm d}\beta \right]\!. \label{number3} \end{eqnarray}ξ∝expi∫καdα+∫κβdβ.Here κα and κβ are the wavenumbers in α and β and have units that are the inverse of the units of their respective coordinates. These wavenumbers should be distinguished from the perpendicular components of the usual wave vector k, which has units of 1/length. The different wavenumbers may be related through the scale factors (h) that relate elemental coordinate increments to physical distances: dr = eαhαdα + eβhβdβ + eγhγdγ, where eα is a unit vector in the α direction, etc. In this notation ∇⊥ = (eα/hα)∂/∂α + (eβ/hβ)∂/∂β, and noting that ∇⊥ξ ≈ ik⊥ξ, Eq. (3) yields \begin{eqnarray} \bdelp\xi &=& {\rm i} \vec{k}_\perp \xi = {\rm i} \left( \frac{\vec{e}_\alpha}{h_\alpha}\frac{ \partial}{\partial\alpha} +\frac{\vec{e}_\beta}{h_ \beta}\frac{ \partial}{\partial \beta}\right)\xi \\ &\equiv& {\rm i}\left( \frac{\vec{e}_\alpha}{h_\alpha}\kappa_\alpha +\frac{\vec{e}_\beta}{h_ \beta}\kappa_\beta\right)\xi. \label{number4} \end{eqnarray}∇⊥ξ=ik⊥ξ=ieαhα∂∂α+eβhβ∂∂βξ≡Equating components of the second and fourth expressions in Eq. (5) gives the expected relations between the various wavenumbers, (6)\begin{eqnarray} k_\alpha = \kappa_\alpha /h_\alpha, \qquad k_\beta = \kappa_ \beta /h_ \beta. \label{number5} \end{eqnarray}kα=κα/hα, kβ=κβ/hβ.Equations (2) and (5) give a direct and elegant expression for the perpendicular wave vector as (7)\begin{eqnarray} \vec{k}_\perp \approx -(\bdel \omega_{\rm c}) t, \label{number6} \end{eqnarray}k⊥≈−(∇ωc)t,which is a generalisation to three dimensions of the results of Mann et al. (1995), (Wright et al. 1999) and Kaneko & Yokoyama (2015) for lower dimensional systems, which developed phase mixing in only one perpendicular coordinate. The above expression allows phase mixing in both perpendicular directions, giving physical phase mixing lengths (or wavelengths) in the α and β directions of (8)\begin{eqnarray} L_{{\rm ph}\alpha} = \frac{2\pi}{|k_\alpha |} \equiv \frac{2\pi h_\alpha}{|\partial \omega_{\rm c}/\partial\alpha |t}, \qquad L_{{\rm ph}\beta} = \frac{2\pi}{|k_ \beta |} \equiv \frac{2\pi h_\beta}{|\partial \omega_{\rm c}/\partial \beta |t}\cdot \label{number7} \end{eqnarray}Lphα=2π|kα|≡2πhα|∂ωc/∂α|t, Lphβ=2π|kβ|≡2πhβ|∂ωc/∂β|t·If the phase mixing lengths are expressed in the same units as α and β, rather than physical length as in Eq. (8), slightly simpler expressions are found, i.e. (9)\begin{eqnarray} \ell_{{\rm ph}\alpha} = \frac{2\pi}{|\kappa_\alpha |} \equiv \frac{2\pi}{|\partial \omega_{\rm c}/\partial\alpha |t}, \qquad \ell_{{\rm ph}\beta} = \frac{2\pi}{|\kappa_ \beta |} \equiv \frac{2\pi}{|\partial \omega_{\rm c}/\partial \beta |t}\cdot \label{number8} \end{eqnarray}ℓphα=2π|κα|≡2π|∂ωc/∂α|t, ℓphβ=2π|κβ|≡2π|∂ωc/∂β|t·The development of the phase mixing length can be pictured simply as the tendency for each field line to oscillate with its own natural frequency. Even if all the field lines start to oscillate with the same phase, they soon drift out of phase with one another as time passes. Not only does the phase mixing process generate perpendicular scales, but points of constant phase can be seen to move across field lines. This phase motion has been seen in magnetospheric data of Alfvén waves (see the review by Wright & Mann 2006) and the simulations of coronal oscillations by Kaneko & Yokoyama (2015). These studies note that the direction of motion is related to the spatial variation of ωc. The results of these papers for the perpendicular phase velocity in physical space generalise to Vph = ωc/k⊥, giving the components (10)\begin{eqnarray} V_{{\rm ph}\alpha} = \frac{-\omega_{\rm c} h_\alpha}{(\partial \omega_{\rm c}/\partial\alpha )t}, \qquad V_{{\rm ph}\beta} = \frac{-\omega_{\rm c} h_ \beta}{(\partial \omega_{\rm c}/\partial \beta )t}, \qquad \label{number9} \end{eqnarray}Vphα=−ωchα(∂ωc/∂α)t, Vphβ=−ωchβ(∂ωc/∂β)t, If the excitation occurred at a time ti, the subsequent properties are found by replacing t with t−ti in the above formulae.


There has additionally been the concern that the optical light curves do not look as expected if they arise from reprocessing of X-ray emission from a small central corona, e.g. of size similar to that which we measure from microlensing observations, i.e. $\rm{\, \stackrel{\lt }{_\sim }\,}10 R_{G}$ (Dai et al. 2010; Mosquera et al. 2013), or from X-ray low/high energy reverberation, i.e. ∼4Rg (Cackett et al. 2014; Emmanoulopoulos et al. 2014). The observed optical light curves are smoother than expected and an insufficient fraction of the X-ray emission hits the disc to power the optical variability (e.g. Berkley, Kazanas & Ozik 2000; Arévalo et al. 2008). Larger coronal sizes are required. Gaskell (2008) also notes the energetics problem and proposes variations originating independently in different parts of the disc. However, although such a model is useful for explaining the uncorrelated variations between bands which are sometimes seen, it cannot explain the well correlated multiwavelength variations seen in the Swift observations. Gardner & Done (2017) proposed an alternative model in which the X-ray emission does not directly impact on the outer disc but mainly heats up the very inner edge of the disc, which then inflates and re-radiates at hard UV wavelengths on to the outer disc. In this model there should be an additional lag between the X-ray and UVW2 emission, over and above that expected from an extrapolation of the longer wavelength lags down to the X-ray waveband. This additional lag would correspond to the thermal time-scale for the incident X-ray heating to pass through the inner disc to the re-radiation surface. Gardner & Done (2017) note the existence of such a lag when the unfiltered X-ray and UVW2 observations of NGC 5548 are compared. However, McHardy et al. (2014) do not see any additional lag in NGC 5548 if those light curves are filtered to remove variations on time-scales longer than 20 d. In NGC 4151, Edelson et al. (2017) see a very large excess lag between the X-ray and UVW2 bands. Unlike in NGC 5548, the excess lag in NGC 4151 is strongly energy dependent, with the highest energy X-rays having the largest lag. NGC 4151 is the most absorbed of the few AGN whose lags have been well studied so far and so the energy dependence may be a function of scattering in the absorbing medium.