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).


Brown dwarfs and giant exoplanets populate the same temperature range and share many physical properties, such as their molecule-dominated atmospheres and gradual cooling from ~3000 K at formation to ~100 K like the solar system gas-giant planets. Recent discoveries of very massive planets (Chauvin et al. 2005; Marois et al. 2010; Delorme et al. 2013), some possibly more massive than the 13 MJup deuterium burning mass limit, hint that planets could overlap with brown dwarfs in mass. On the other hand, the discovery of isolated L dwarfs in young clusters (Zapatero Osorio et al. 2002, 2014; Peña Ramírez et al. 2012), in young moving groups (Liu et al. 2013; Gagné et al. 2015; Gauza et al. 2015), and very cold very nearby Y dwarf objects (e.g., Kirkpatrick et al. 2012; Luhman 2014) show that very low-mass isolated brown dwarfs exist and overlap with the planetary masses. When these low-mass brown dwarfs are close enough and bright enough to be observed spectroscopically their atmospheres are much easier to study than similar exoplanets that lie near their very bright host stars. Liu et al. (2013) notably showed that the ~8 MJup brown dwarf PSO J318.5−22, a β-pictoris moving group member shares the spectral characteristics of the young directly imaged exoplanets, as well as atypically red late-L spectral type objects (e.g., Faherty et al. 2013; Gizis et al. 2015; Kellogg et al. 2016; Schneider et al. 2014, 2016; Bonnefoy et al. 2016). When CFBDSIR J214947.2−040308.9, hereafter CFBDSIR 2149, was identified (Delorme et al. 2012), it seemed to be a candidate member of the AB Doradus young moving group and, together with the low-gravity features in its spectrum, made it a unique T-type isolated planetary-mass candidate. Another earlier-type, isolated young planetary-mass T-dwarf, SDSS J111010.01+011613.1, has been identified as a bona fide member of AB Doradus moving group (\hbox{$149^{+51}_{-19}$}149-19+51 Myr; Bell et al. 2015) by Gagné et al. (2015). The late-T spectral type of CFBDSIR 2149 is typical of the coolest known directly imaged exoplanets, such as GJ 504 b or 51 Eri b (Kuzuhara et al. 2013; Macintosh et al. 2015), that the latest generation of adaptive optics systems are detecting. We therefore carried out a multi-wavelength, multi-instrument follow-up of CFBDSIR 2149 to fully characterise it and constrain its nature.


The spectra from Sloan Digital Sky Survey (SDSS) have enabled the detection of the relatively faint He ii λ4686 line in large samples of star-forming galaxies (e.g. Shirazi & Brinchmann 2012). These studies find that the observed He ii λ4686/H β intensity ratio does not drop at low metallicities. In fact, recent studies find the ratio to be increasing as the metallicity decreases (Schaerer, Fragos & Izotov 2019). Furthermore, these low-metallicity He ii λ4686-emitting galaxies often show only a weak or no evidence of the presence of WR stars (Shirazi & Brinchmann 2012). Thus, questions have been raised on the WR stars as the sole source of ionization of He+ (Plat et al. 2019). Alternative mechanisms such as hard radiation from high-mass stars in binaries (Eldridge et al. 2017), shocks from supernova remnants (Garnett et al. 1991; Dopita & Sutherland 1996), and high-mass X-ray binaries (HMXBs; Schaerer et al. 2019; Kojima et al. 2020) are often invoked. Nearby low-metallicity systems offer an opportunity to address the He+ ionization problem by enabling study of individual star-forming knots. In a detailed study of the metal-poor (Z = 3–4 per cent Z⊙) galaxy SBS 0335−052E using MUSE, Kehrig et al. (2018) discard WR stars as the source of ionization and instead propose rotating metal-free stars or a binary population with Z = 10−5 and an extremely top-heavy initial mass function (IMF) as the only plausible way of getting around the problem of the ionization budget. In a recent study, Schaerer et al. (2019) find that the observed He ii λ4686 intensity in metal-poor star-forming galaxies can be naturally reproduced if the bulk of the He+ ionizing photons is emitted by the HMXB, whose number is found to increase with decreasing metallicity. X-ray binaries in a cluster appear only after the death of the most massive stars, and hence this scenario cannot explain the He+ ionization in young systems [H β equivalent widths (EWs) ≥ 200 Å], as illustrated by Plat et al. (2019).

Alternative mechanisms such as
shocks from supernova remnants
are often invoked.


The discovery of GW170817 and its electromagnetic counterparts (GRB170817A and AT2017gfo; Abbott et al. 2017a; Coulter et al. 2017; Goldstein et al. 2017) ushered in a new era of multimessenger astrophysics, in which both gravitational waves and photons provide complementary views of the same source. While observations at optical and infrared wavelengths unveiled the onset and evolution of a radioactive-powered transient, known as kilonova, observations at X-rays and, later, radio wavelengths probed a different component of emission, likely originated by a relativistic outflow launched by the merger remnant. Troja et al. (2017) explained the observed X-ray and radio data as the onset of a standard short GRB (sGRB) afterglow viewed at an angle (off-axis). However, as already noted in Troja et al. (2017) and Kasliwal et al. (2017), a standard top-hat jet model could explain the afterglow data set collected at early times, but failed to account for the observed gamma-ray emission. Based on this evidence, Troja et al. (2017) suggested that a structured jet model (e.g. Zhang et al. 2004; Kathirgamaraju, Barniol Duran & Giannios 2018) provided a coherent description of the entire broad-band data set. Within this framework, the peculiar properties of GRB170817A/AT2017gfo could be explained, at least in part, by its viewing angle (see also Lamb & Kobayashi 2017; Lazzati et al. 2017). An alternative set of models invoked the ejection of a mildly relativistic wide-angle outflow, either a jet-less fireball (Salafia, Ghisellini & Ghirlanda 2018) or a cocoon (Nagakura et al. 2014; Hallinan et al. 2017). In the latter scenario, the jet might be chocked by the merger ejecta (Mooley et al. 2017), and the observed gamma-rays and broad-band afterglow emission are produced by the expanding cocoon. The cocoon may be energized throughout its expansion by continuous energy injection. In this paper detailed models of structured jet and cocoon, from its simplest to more elaborate version, are compared with the latest radio to X-ray data. Predictions on the late-time evolution are derived, and an unambiguous measurement capable of disentangling the outflow geometry, jet versus cocoon, is presented.


It is generally thought that the emission from radio to medium energy gamma rays is generated by the injected electrons through the synchrotron radiative mechanism. The high-energy photon emission mainly comes from inverse Compton (IC) scattering of the high-energy electrons on the background seed photons, which include the synchrotron background, the cosmic microwave background, and infrared photons in the PWNe (see, e.g., Zhang et al. 2008; Fang & Zhang 2010; Torres et al. 2013; Lu et al. 2020). On the other hand, it is also suggested that the gamma rays could be emitted by the hadronic processes. The relativistic protons accelerated in the Crab pulsar outer gap interact with the matter inside the nebula. and this process may contribute in the high-energy gamma-ray range (see, e.g., Cheng et al. 1990; Bednarek & Protheroe 1997; Khangulyan et al. 2020; Cao et al. 2021). Therefore, it has been long debated whether the high-energy emission from the PWNe is the leptonic or hadronic origin. The details of the high-energy radiation produced by leptonic process have been discussed for the Crab Nebula (see, e.g., Venter & de Jager 2007; Zhang et al. 2008; Martín et al. 2012), and that of the gamma-ray emission about the hadronic process have been also investigated (see, e.g., Cheng et al. 1990; Bednarek & Protheroe 1997; Bednarek 2003, 2007). However, with the establishment of more and more high-energy observatories, some telescopes have possessed the performance of observing photons of exceeding to the PeV from the astronomic objects. An increasing number of observational data has been reported by the different experiments. For example, the Amenomori et al. (2019) reported that the Tibet air shower array with the underground water-Cerenkov-type muon detector array observed the highest energy photons of exceeding 100 TeV with a 5.6σ statistical significance and pointed the measured spectrum with energy extended to the sub-PeV from the Crab Nebula have an absence of high-energy cutoff. Recently, more than 530 photons at energies above 100 TeV and up to 1.4 PeV from the 12 ultra-high-energy gamma-ray sources with a statistical significance greater than seven standard deviations were reported again by LHAASO (Cao et al. 2021). Together with the earlier investigations about the leptonic scenario, the radiative spectrum from the leptons has a cutoff around the sub-PeV region (see, e.g., Zhang et al. 2008; Martín et al. 2012; Zhang et al. 2020). It seems that the other components of gamma rays have a significant contribution.


X-ray reverberation in black hole X-ray binaries was first robustly detected in GX 339–4 by Uttley et al. (2011) when the source was in its hard state. Previous studies of GX 339–4 pointed to the approximate central mass being ≥6 M⊙ (e.g. Hynes et al. 2003) and a small disc inclination angle (De Marco et al. 2015). Miller et al. (2008) fitted the Suzaku spectra and found that the central black hole has a very high spin, a ∼ 0.998. The X-ray spectroscopic analysis of the hard state spectra from the RXTE archive carried out by García et al. (2015) suggested the black hole spin to be a ∼ 0.95. Spectral fitting of GX 339–4 during its very high flux state using NuSTAR and Swift also suggested a high spin of a ∼ 0.95 (Parker et al. 2016). According to the time-lag analysis, Uttley et al. (2011) found that the disc thermal emission (∼0.3–0.7 keV, soft band) leads the power-law variations (∼0.7–1.5 keV, hard band) on long timescales (> 1s). Mahmoud et al. (2019) assumed that the soft component that leads the power-law emission is a soft Comptontized component. Rapisarda et al. (2016) and Rapisarda et al. (2017) instead modelled it as a variable inner region of the thin disc. However, the disc black-body variations lag behind the power-law variations by a few milliseconds on short timescales ( 1s). This switch from low-frequency hard to high-frequency soft lags is thought to be produced by two distinct mechanisms. While the hard lags are likely due to inward propagating fluctuations (e.g. Kotov et al. 2001; Arévalo & Uttley 2006), the soft lags can be explained by thermal reverberation associated with the longer light-travel time the hard photons take from the central power-law X-ray source to the disc where they are reprocessed into relatively soft black-body emission. The thermal reverberation lags then provide clues to the geometry of the X-ray source and the inner accretion flow close to the event horizon of the central black hole.


We further constrain the stellar parameters for HD 85628 using the Virtual Observatory SED Analyzer (VOSA)5 and fitting the Hα profile of the star’s CHIRON spectrum. We fit the spectral energy distribution (SED; Fig. 8) of HD 85628 using published photometry from Tycho (BT VT; ESA 1997), APASS (BV; Henden et al. 2016), Gaia DR2 (BpRpG; Gaia Collaboration 2018), DENIS (JK; Epchtein et al. 1994), 2MASS (JHKs; Skrutskie et al. 2006), and WISE (W1W2W3W4; Wright et al. 2010), and fit Kurucz ATLAS9 stellar atmosphere models (Castelli & Kurucz 2003). Given that the star is clearly main sequence and relatively young ( 1 Gyr), we constrain the surfacegravity to be within ±0.5 dex of log g = 4.0 and metallicity within ±0.5 dex of solar, and include the extinction and 1σ uncertainty presented previously as a constraint, but allow the effective temperature to float. We find the best-fit parameters to be for a Kurucz model with Teff, = 7844

$^{57}_{-285}$−285+57
 K, log g = 4.0, and solar metallicity. We also fitted the shape of the Hα line from the average high-resolution CHIRON spectra with a grid of Kurucz spectra (as used above). While we fail to meaningfully constrain its metallicity and surface gravity in this way, the spectral line shape is consistent with a temperature of 7700 ± 300 K. Based on these independentanalyses, we adopt Teff ≃ 7800 ± 200 K. We note that this is somewhat cooler than expected given the A3V classification by Houk & Cowley (1975), since typical A3V stars have Teff ≃ 8550 K (Pecaut & Mamajek 2013), however we cannot reconcile such a hot temperature given the available data, leading us to believe that the initial classification was incorrect, and that this star is in fact an A7V star. The best-fit luminosity to SED fit using the VO Sed Analyzer (VOSA) tool, and adopting the distance based on the Gaia DR2 trigonometric parallax, is L = 12.23 ± 0.0655 L⊙ or log (L∕L⊙) ≃ 1.087 ± 0.023 dex. For the adopted effective temperature, this implies that HD 85628 has a radius of 1.92 ± 0.11 R⊙ 6.


The optical, spectrocopic and infrared remote imaging system (OSIRIS) scientific imaging cameras on the Rosetta spacecraft have been monitoring the coma activity of comet 67P Churyumov–Gerasimenko (67P hereafter) since their orbital rendezvous in 2014 August (Lara et al. 2015; Lin et al. 2015; Sierks et al. 2015; Lin et al. 2016; Shi et al. 2016; Vincent et al. 2016a,b). The solar heating of the sunlit side of the nucleus surface leads to sublimation of the volatiles and to the formation of dust jets. On 2015 March 12, a small outburst was first detected from a part of the Imhotep region on the night side (Knollenberg et al. 2016). Such mini-outbursts or night-side activities have been observed before at comet 9P/Tempel 1 by the Deep Impact mission (Farnham et al. 2007, 2013) and comet 103P/Hartley 2 by the EPOXI mission (A’Hearn et al. 2011; Bruck Syal et al. 2013). Shortly before the close approach to comet 9P/Tempel 1, the high-resolution camera on the Deep Impact spacecraft found a number of small, well-defined jets whose bases were rooted at the nucleus surface. Some of these, called limb jets, appeared to come from the darker regions and appeared to be associated with the ice patches reported by Sunshine et al. (2006). A later mission of the Stardust–New Exploration of comet Tempel 1 (NExT) imaging of 9P/Tempel 1 allowed us to connect the jets with cliffs (Farnham et al. 2013). Comet 103P/Hartley 2 also displayed several narrow jet features emitting from the un-illuminated regions beyond the terminator at the time of the flyby observations (Bruck Syal et al. 2013). Unlike the less certain identification of the source regions on Tempel 1, the source region of the night-side jets of 103P/Hartley 2 could be clearly traced to some rough surface topography. However, the mechanism for this type of activity is still unknown. Fortunately, unlike the snap shots from the previous flyby observations, the OSIRIS measurements can provide precise information on the timing and location of the outbursts via a time series of high-resolution images. After the first detection in 2015 March, the OSIRIS wide-angle camera (WAC) and narrow-angle camera (NAC) captured another outburst in mid-July of 2015. Since then, many more outbursts from the night-side and sunlit regions have been detected (Feldman et al. 2016; Grün et al. 2016), with most of their source regions located in the Southern hemisphere of comet 67P (Vincent et al. 2016a). The detected outburst events show a variety of morphological features that can be classified into three different types: broad fans, narrow jets and complex plumes. In this work, we investigate the morphology of these events and characterize their physical properties in detail, including the surface brightness profiles, ejected mass and speed if there are two or more sequential images acquired by the same filter in short duration during the time frame of the outburst.


Small grains, which contribute most to infrared emission, are removed by collisional fragmentation and blown out by radiation pressure. The removal timescale is much shorter than the ages of host stars. Disruptive collisions among underlying large bodies, which are called planetesimals, produce smaller bodies and collisional fragmentation among them results in even smaller bodies. This collisional cascade continues to supply small grains. The evolution of debris disks has been explained by the steady-state collisional cascade model (e.g., Wyatt 2008; Kobayashi & Tanaka 2010): the total mass of bodies decreases inversely proportional to time t. Therefore, the excess ratio (Fdisk/F∗) is given by (2)\begin{equation} \frac{F_{\rm disk}}{F_{*}} = \frac{t_0}{t},\label{cc} \end{equation}FdiskF∗=t0t,where t0 is the dissipation timescale that is determined by the collisional cascade. Under the assumption of the steady state of collisional cascade, the power-law size distribution of bodies is analytically obtained and the power-law index depends on the size dependence of the collisional strength of bodies (see Eq. (32) of  Kobayashi & Tanaka 2010). In the obtained size distribution, erosive collisions are more important than catastrophic collisions (see Fig. 10 of Kobayashi & Tanaka 2010). Taking into account the size distribution and erosive collisions, we derive t0 according to the collisional cascade (see Appendix E for derivation), (3)\begin{eqnarray} t_0&\sim& 1.3 \left( \frac{s_{\rm p}}{\rm 3000\,km} \right)^{0.96} \left( \frac{R}{\rm 2.5\,au} \right)^{4.18}\nonumber\\ &&\quad\times \left(\frac{\Delta R}{0.4 R}\right) \left( \frac{e}{\rm 0.1} \right)^{-1.4} {\rm Gyr},\label{eq:t0} \end{eqnarray}t0~1.3sp3000 km0.96R2.5 au4.18where sp is the size of planetesimals, R is the radius of the planetesimal belt, and e is the eccentricity of planetesimals. Interestingly, t0 is independent of the initial number density of planetesimals (Wyatt et al.  2007). Note that the perturbation from Moon-sized or larger bodies is needed to induce the collisional fragmentation of planetesimals (Kobayasi & Löhne 2014), which is implicitly assumed in this model.


It is harder to evaluate the behaviour of the young stellar population along the line of sight, since radial velocity measurements for our sample of Cepheids, needed for a thorough study, do not exist. Given this deficit, we provide only a simplified estimate using radial velocities of OBA-type stars from Evans & Howarth (2008). Since they belong to the same young population, we assume that they have a similar distance distribution and kinematics as the Cepheids. Fig. 16 shows the massive star sample in the plane of the sky. Except for the northernmost region (δ ≥ −72○), where no data exist, these stars cover a comparable area to the Cepheids (indicated as grey dots in the figure for comparison). The radial velocities show a distinct and well-known gradient across the SMC with higher velocities in the eastern part (see also fig. 5 of Evans & Howarth 2008). Such a gradient in radial velocity is also present in older (few Gyr) RGB stars (see fig. 9 of Dobbie et al. 2014). This gradient is commonly attributed to rotation of the SMC. Based on our results obtained for the Cepheids, we propose a different interpretation: this line-of-sight velocity gradient may instead be caused by the fact that the nearest parts of the galaxy, in the region of the SMC Wing, move with a higher radial velocity compared with the main body of the galaxy. Given the additional differences in tangential velocities, these outer parts might be in the process of being stripped from the SMC. Diaz & Bekki (2012) show in their simulations that tidal effects can produce a velocity gradient that is similar to that of a rotating disc. We stress again that this interpretation is based on the assumption that the Cepheid sample and the OBA-type stellar sample trace a similar three-dimensional distribution. For any conclusive answer, radial velocities of the Cepheid stars are required. Such measurements will be provided by the One Thousand and One Magellanic Fields (1001MC) survey (Cioni et al. 2019), which is a consortium survey with the forthcoming multi-object spectrograph 4MOST that will be mounted on the VISTA telescope.


First direct evidence for the geometrical distribution of the dust was found by Jaffe et al. (2004) with the help of the mid-infrared interferometric instrument (MIDI; Leinert et al. 2003) at the Very Large Telescope Interferometer (VLTI). One of the best-studied parsec-sized dust distribution is harboured by the Circinus galaxy, which is the closest (4.2 Mpc, 1 arcsec ≈20 pc; Freeman et al. 1977) and the second brightest Seyfert galaxy in the MIR. High-resolution mid-infrared (MIR) interferometric observations have revealed a two-component morphology in the brightness distribution: (i) a larger scale, elongated component in direction of the ionization cone (along PA ≈ 107°) with a full-width at half-maximum (FWHM) size of roughly 0.8 × 1.9 pc, which is responsible for 80 per cent of the total MIR flux and was interpreted either as the directly illuminated funnel walls of the dusty molecular torus or as part of the (filamentary/clumpy) outflow; (ii) a disc-like component with an FWHM size of roughly 0.2 × 1.1 pc and elongated along PA ≈ 46° (Tristram et al. 2007, 2014). Both components have a dust temperature of roughly 300 K. The disc-like component was modelled by two Gaussian emitters (a highly elongated emitter plus an unresolved source) in the simple model used by Tristram et al. (2014). This was interpreted as signs for a more complex structure as well as for asymmetry in the second component. The orientation and size of the disc-like component coincides with an edge-on warped disc seen in maser emission with the help of very long baseline interferometry traced by H2O masers (Greenhill et al. 2003). It has an outer radius of roughly 0.4 pc. A similar picture emerges for NGC 1068: A hot parsec-scale disc (FWHM ≈1.35 × 0.45 pc, T ≈ 800 K) was found with similar orientation and extent as the H2O maser disc (Greenhill et al. 1996; Greenhill & Gwinn 1997). It is surrounded by warm dust extended in polar direction with an FWHM ≈3 × 4 pc and a temperature T ≈ 300 K (Jaffe et al. 2004; Raban et al. 2009). However, in a systematic study of a larger sample of objects a large range of properties of the dust distribution has been found (Burtscher et al. 2013).


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


However, using the well-assessed new post-AGB evolutionary models, we confined the main-sequence ages of our halo sample to be mostly ∼2–5 Gyr, with the oldest being ∼6–8 Gyr, while the outer-disk sample are mostly ≲1–4 Gyr. We thus conjecture that our targets probably formed prior to the encounter with M33. Obviously, our sample represents the population that is different from the underlying, smooth, extended (and mostly metal-poor) halo component of M31 (Ibata et al. 2007, 2014), which was formed through the repeated accretion of smaller galaxies in the distant past. These bright PNe seem to resemble the younger, metal-rich population in the outer stream of M31, as revealed by HST pencil-beam pointings on the Giant Stream (Brown et al. 2006a; Bernard et al. 2015b). The metallicity of the stream fields was enriched continuously from [Fe/H] ∼ −1.5 to at least solar level about 5 Gyr ago (Bernard et al. 2015b). This timeline of metal enrichment is generally consistent with the stellar ages of our metal-rich sample. N-body simulations suggested that the Giant Stream and other stream-like features in the halo are debris of a massive (≳109–

) progenitor that was recently disrupted during the course of a merger (e.g., Ibata et al. 2004; Fardal et al. 2006, 2007, 2008, 2013; Font et al. 2006; Geehan et al. 2006; Mori & Rich 2008; Sadoun et al. 2014). The extended star formation history and the broad range of metallicity (−1.5 ≲ [Fe/H] ≲ 0.2) discovered in the stream fields can be explained by a disk galaxy progenitor (Brown et al. 2006a, 2006b; Bernard et al. 2015b). If the stellar streams in M31's halo indeed have a common origin, our sample of halo PNe then probably formed through extended star formation in this possibly massive, disk-like progenitor. Moreover, some simulations predict that the remnant of the disrupted satellite resides in the NE Shelf (e.g., Fardal et al. 2008, 2013; Sadoun et al. 2014); PN17 in our sample is located in this region and might be associated with this substructure (see Section 4.4).


RR Lyrae are old low-mass stars that, during the central helium-burning phase, show mainly radial pulsation while crossing the classical instability strip in the colour–magnitude diagram. From the observational point of view, they represent the most numerous class of pulsating stars in the Milky Way and, being associated with old stellar populations, are typically found in globular cluster and abundant in the Galactic halo and bulge. The investigation of RR Lyrae properties is motivated by their important role both as distance indicators and tracers of old stellar populations. In particular, evolving through the central helium-burning phase, they represent the low-mass, Population II counterparts of Classical Cepheids, as powerful standard candles and calibrators of secondary distance indicators. In particular, they can be safely adopted to infer distances to Galactic globular clusters (see e.g. Coppola et al. 2011; Braga et al. 2016, 2018, and references therein), the Galactic centre (see e.g. Contreras Ramos et al. 2018; Marconi & Minniti 2018; Griv, Gedalin & Jiang 2019), and Milky Way satellite galaxies (see e.g. Coppola et al. 2015; Martínez-Vázquez et al. 2019; Vivas et al. 2019, and references therein). Being associated with old stellar populations, they represent the basis of an alternative Population II distance scale (see e.g. Beaton et al. 2016, to the traditionally adopted Classical Cepheids), more suitable to calibrate secondary distance indicators that are not specifically associated with spiral galaxies (e.g. the globular cluster luminosity function, see Di Criscienzo et al. 2006, and references therein). The properties that make RR Lyrae standard candles are (i) the well-known relation connecting the absolute visual magnitude MV to the metal abundance [Fe/H] (see e.g. Sandage 1993; Caputo et al. 2000; Cacciari & Clementini 2003; Catelan, Pritzl & Smith 2004; Di Criscienzo, Marconi & Caputo 2004; Federici et al. 2012; Marconi 2012; Marconi et al. 2015, 2018; Muraveva et al. 2018, and references therein); (ii) the period–luminosity relation in the near-infrared (NIR) filters and in particular in the K 2.2 μm band (see e.g. Longmore et al. 1990; Bono et al. 2003; Dall’Ora et al. 2006; Coppola et al. 2011; Ripepi et al. 2012; Coppola et al. 2015; Marconi et al. 2015; Muraveva et al. 2015; Braga et al. 2018; Marconi et al. 2018, and references therein). In spite of the well-known advantage of using NIR filters (see e.g. Marconi 2012; Coppola et al. 2015, and references therein), in the last decades there has been a debate on the coefficient of the metallicity term of the KB and PL relation (see e.g. Bono et al. 2003; Sollima, Cacciari & Valenti 2006; Marconi et al. 2015, and references therein). On the other hand, it is interesting to note that many recent determinations (see e.g. Sesar et al. 2017; Muraveva et al. 2018) seem to converge towards the predicted coefficient by Marconi et al. (2015), with values in the range 0.16-0.18 mag dex−1. As for the optical bands, our recently developed theoretical scenario (Marconi et al. 2015) showed that, apart from the MV−[Fe/H] relation that is affected by a number of uncertainties (e.g. a possible non-linearity, the metallicity scale with the associated α elements enhancement and helium abundance variations, as well as evolutionary effects, see Caputo et al. 2000; Marconi et al. 2018, for a discussion), the metal-dependent Period–Wesenheit (PW) relations are predicted to be sound tools to infer individual distances. In particular, for the B-, V- band combination, Marconi et al. (2015) demonstrated that the inferred PW relation is independent of metallicity. In order to test this theoretical tool, we need to compare the predicted individual distances with independent reliable distance estimates, for example, the astrometric ones recently obtained by the Gaia satellite (Gaia Collaboration 2016). To this purpose, in this paper we transform the predicted light curves derived for RR Lyrae models with a wide range of chemical compositions (Marconi et al. 2015, 2018) into the Gaia bands, derive the first theoretical PW relations in these filters and apply them to Gaia Data Release 2 Data base (hereinafter Gaia DR2; Gaia Collaboration 2018; Clementini et al. 2019; Ripepi et al. 2019). The organization of the paper is detailed in the following. In Section 2, we summarize the adopted theoretical scenario, while in Section 3 we present the first theoretical light curves in the Gaia filters. From the inferred mean magnitudes and colours, the new theoretical PW relations are derived in Section 4 that also includes a discussion of the effects of variations in the input chemical abundances. In Section 5, the obtained relations are applied to Gaia Galactic RR Lyrae with available periods, parallaxes, and mean magnitudes to infer independent predictions on their individual parallaxes, to be compared with Gaia DR2 results. The conclusions close the paper.


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


Our simulation results show that the median detectable distances of targeted GW events from BH–NS mergers for a single 2nd generation GW detector and a network of such detectors are ∼300 Mpc and ∼700 Mpc, respectively (see Table 4). For comparison, Figure 12 shows that the detection rate and detectable distance for HLV (O3) are approximately the same as those for the case when only bKAGRA is running. This is basically consistent with the detection rate and the distance distribution of BH–NS merger candidates detected during LVC O3 (e.g., Anand et al. 2020; Antier et al. 2020b; Coughlin et al. 2020b; Gompertz et al. 2020; Kasliwal et al. 2020). In Section 3, we have shown that the kilonova absolute magnitude at 0.5 days after a BH–NS merger is mainly distributed in the range ∼–10 to ∼–15.5. In view of the fact that the limiting magnitude of the follow-up wide-field survey projects is almost ≲21 mag (e.g., Antier et al. 2020b; Gompertz et al. 2020; Coughlin et al. 2020b; Kasliwal et al. 2020; Wyatt et al. 2020), the maximum detectable distance for BH–NS kilonovae would be ≲200 Mpc, which can hardly cover the horizon of GW-triggered BH–NS merger events that O3 found (as shown in Figure 10). However, although BH–NS merger kilonovae can hardly be detected for the present search depths, Figures 9 and 11 reveal that there are great opportunities to discover on-axis afterglows associated with sGRBs or orphan afterglows if the BH components have a high-spin distribution. In order to cover the distance range for searching for BH–NS kilonovae for the network of 2nd generation GW detectors as completely as possible, a search limiting magnitude mlimit ≳ 23–24 is required as shown in Figure 10. Present survey projects could reach this search limiting magnitude by increasing exposure times and the number of simultaneous exposures. However, the GW candidates during O3 had very large localization areas with an average of thousands of square degrees (Antier et al. 2020b). Increasing exposure times makes it hard for the present survey projects to cover such large localization areas. Therefore, during the HLVK era, we recommend that survey projects may search for jet afterglows after GW triggers with a relatively shallow search limiting magnitude. If BH–NS mergers have a high location precision, a limiting magnitude of mlimit ≳ 23–24 can be reached, which gives a higher probability of discovering associated kilonovae.


Compact symmetric objects are very powerful (P1.4 GHz > 1025 W Hz−1), compact (linear size of 50–100 pc), and young (≲104 yr) objects with a rather symmetric radio structure and convex synchrotron radio spectra (Wilkinson et al. 1994; Murgia 2003; Polatidis & Conway 2003). The characterized convex synchrotron radio spectrum peaks at around 100 MHz in the case of compact steep spectrum (CSS) sources, at about 1 GHz in the case of GHz-peaked spectrum (GPS) objects, and up to a few GHz (e.g., 5 GHz) in the case of high-frequency peakers (HFPs; Dallacasa et al. 2000). The turnover is explained as synchrotron self-absorption (SSA) affecting in a small radio-emitting region or the free-free absorption (FFA) by the dense ambient medium. In a “young scenario”, as the source grows, the inner region (possibly a tiny radio lobe) expands, and as a result, the turnover frequency moves to lower frequencies. In this scenario, the HFPs are newborn radio sources that develop into extended radio sources (e.g., FR I, FR II) after evolving through GPS and CSS stages. It is possible that the activity is recurrent in at least some sources: there have been observations of faint extended emission around a few GPS sources (e.g., Baum et al. 1990; Stanghellini et al. 1990; Marecki et al. 2003). The extended emission could be a relic of an earlier active period, into which the reborn radio jets are expanding. Another popular explanation for the turnover and compact natures of CSS, GPS, and HFP is the “frustration” hypothesis. This theory argues that these sources are confined in small spatial scale and high-density environments, and as a consequence the radio emission is frustrated by the abundant nuclear plasma (van Breugel et al. 1984; Peck et al. 1999; Tingay & de Kool 2003; Callingham et al. 2015; Tingay et al. 2015). In addition, An & Baan (2012) also proposed that young sources with strong constant AGN power breaking through the dense inner region of the host galaxy could result in the compact morphology and the turnover properties of CSOs.


Comptonisation Monte Carlo code (MoCA; see Tamborra et al. 2018 for a detailed description of the code) is based on a single photon approach, working in a fully special relativistic scenario. MoCA allows for various and different physical and geometrical conditions of the accretion disc and of the Comptonising corona. In this paper, the corona is assumed to have either a spherical or a slab-like geometry, and to be as extended as the disc, whose radii have been set to be Rout = 500 rg and Rin = 6 rg, respectively. Even though arguments (e.g. variability, Uttley et al. 2014, and references therein, microlensing Chartas et al. 2009; Morgan et al. 2012 and timing Kara et al. 2016; De Marco et al. 2013) exist that favour a compact corona, we used extended coronae. In fact, as discussed by Marinucci et al. (2019), Comptonised spectra emerging from compact corona (Rout = 100 rg–Rin = 6) do not deviate significantly from those produced in more extended corona; see their Fig. 3. The adoption of even more compact coronae (Rout = 20 rg, Rin = 6) results only in the need for higher optical depths to recover the same spectral shape for a given temperature. However, in such cases, general relativity (GR) effects are not negligible (see Tamborra et al. 2018, for a detailed discussion on this topic), and the present version of MoCA does not include GR. For the slab-like geometry case, MoCA allows the user to set up the corona height above the accretion disc (set to 10 rg in our simulations). We use synthetic spectra computed assuming the source BH mass and accretion rate to be the same as those of Ark 120 (e.g. Marinucci et al. 2019, and references therein), namely MBH = 1.5 × 108 M⊙ and ṁ = Lbol/LEdd = 0.1. For both the slab and spherical hot electron configurations, we simulated the Comptonised spectra using a wide range of values for electron temperature and optical depth: 0.1   τ   7 and 20  kT  200 keV, and in Fig. 1 we show a sample of spectra obtained by MoCA. Moreover, spectra are computed from 0.01 keV up to 700 keV using 1000 logarithmic energy bins, and a Poissonian error accompanies each spectral point. The obtained spectra are averaged over the inclination angle and in Fig. 1 we show some exemplificative spectra normalised at 1 keV accounting for the two geometries considered in this work.


SN 2011fe, discovered a mere ≈11 h after explosion (Nugent et al. 2011) by the Palomar Transient Facility (PTF; Law et al. 2009), is the brightest SN Ia since the advent of modern astronomical detectors. Located at just $d_L \approx 6.5~\rm {Mpc}$ (e.g. Shappee & Stanek 2011; Beaton et al. 2019), SN 2011fe exploded in a region of M101 uncontaminated by intervening dust (Patat et al. 2013) providing an ideal location for testing SN Ia progenitor and explosion models. The early detection allowed extensive follow-up observations across the electromagnetic spectrum (e.g. Matheson et al. 2012; Parrent et al. 2012; Pereira et al. 2013; Hsiao et al. 2013; Johansson, Amanullah & Goobar 2013; Tsvetkov et al. 2013; Munari et al. 2013; Mazzali et al. 2014; Zhang et al. 2016) and provided direct constraints on the radius of the exploding star (Nugent et al. 2011; Bloom et al. 2012). Stringent non-detections in radio (Chomiuk et al. 2012; Horesh et al. 2012; Kundu et al. 2017) and X-ray (Horesh et al. 2012; Margutti et al. 2012) observations exclude nearby CSM at high significance. Early ultraviolet (UV) photometry did not show any evidence for the ejecta encountering a nearby companion star (Brown et al. 2012) and nebular spectra lacked the Balmer emission lines from material ablated off the donor star by the ejecta impact (Shappee et al. 2013b; Lundqvist et al. 2015; Tucker et al. 2022). Pre-explosion imaging excludes the presence of a RG or He donor star (Li et al. 2011) and disfavor an accreting WD in the ∼105 yr prior to explosion (Graur, Maoz & Shara 2014). Multi-epoch spectropolarimetry reveal consistently-low continuum polarization suggestive of a symmetric ejecta distribution with evidence for minor oblateness (Milne et al. 2017). Finally, nebular-phase observations at ≳ 1 year after maximum light allows a direct view to the inner ejecta and provides unique constraints on the explosion conditions (McClelland et al. 2013; Kerzendorf et al. 2014, 2017; Mazzali et al. 2015; Graham et al. 2015; Taubenberger et al. 2015; Dimitriadis et al. 2017; Friesen et al. 2017; Shappee et al. 2017; Tucker et al. 2022). SN 2011fe is one of the best-studied astronomical objects in the past decade and remains a key benchmark for any SN Ia theory or model.


How does the propagation of radiation and the ISM composition affect ISM observables in low-metallicity galaxies? Addressing this question is important to understand the evolution of low-metallicity galaxies, which undergo more bursty star formation than normal galaxies. Nearby star-forming dwarf galaxies present distinct observational signatures compared to well-studied disk galaxies. Dwarfs are usually metal poor, H i rich, and molecule poor as a result of large-scale photodissociation (e.g., Kunth & Östlin 2000; Hunter et al. 2012; Schruba et al. 2012). Mid-IR (MIR) and far-IR (FIR) observations have revealed bright atomic lines from H ii regions ([S iii], [Ne iii], [Ne ii], [O iii], etc.) and PDRs ([C ii], [O i]) (e.g., Hunter et al. 2001; Madden et al. 2006; Wu et al. 2008; Hunt et al. 2010; Cormier et al. 2015). Their spectral energy distributions (SEDs) are also different from spiral and elliptical galaxies and indicative of altered dust properties, with a relatively low abundance of polycyclic aromatic hydrocarbons (PAHs) and perhaps a different dust composition (e.g., Madden et al. 2006; Galliano et al. 2008; Rémy-Ruyer et al. 2013). It is still unknown, however, whether these differences between dwarf and disk galaxies are the direct result of recent star formation activity shaping the ISM or instead a consequence of the low-metallicity ISM that is independent of star formation activity. To answer this, one needs to observe tracers of the interplay between the ISM and various stages of star formation activity. While there are now a number of important studies available on PDR properties modeling FIR lines on large scales in various extragalactic environments (e.g., Kaufman et al. 2006; Vasta et al. 2010; Graciá-Carpio et al. 2011; Cormier et al. 2012; Parkin et al. 2013) or in our Galaxy under solar-metallicity conditions (e.g., Cubick et al. 2008; Bernard-Salas et al. 2012, 2015), only a few studies are published on individual extragalactic regions (Mookerjea et al. 2011; Lebouteiller et al. 2012). Of particular interest are dwarf galaxies, where the effect due to radiative feedback is expected to be most significant. The goal of this paper is to investigate how the low-metallicity ISM reacts under the effects of star formation in regions that have undergone different histories. The nearby low-metallicity galaxy NGC 4214 provides an excellent environment to perform this experiment because it has well-separated star-forming centers, one hosting a super star cluster, which allows us to study the effects of extreme star-forming conditions on the surrounding ISM.


The hot emission line of Fe xxi 1354.09 Å and the cool emission line of Si iv 1402.77 Å have been used in many spectroscopic studies to investigate chromospheric evaporation (e.g., Tian et al. 2014, 2015; Li et al. 2015b, 2017a, 2017b; Brosius et al. 2016; Zhang et al. 2016a, 2016b). It is widely accepted that the forbidden line of Fe xxi 1354.09 Å is a hot (log T ∼ 7.05) and broad emission line during solar flares (Doschek et al. 1975; Cheng et al. 1979; Mason et al. 1986; Innes et al. 2003a, 2003b). Meanwhile, IRIS spectroscopic observations show that Fe xxi 1354.09 Å is always blended with a number of cool and narrow emission lines, which are from neutral or singly ionized species. Those blended emission lines can be easily detected at the position of the flare ribbon, including known and unknown emission lines, such as the C i line at 1354.29 Å, the Fe ii lines at 1353.02 Å, 1354.01 Å, and 1354.75 Å, the Si ii lines at 1352.64 Å and 1353.72 Å, and the unidentified lines at 1353.32 Å and 1353.39 Å (e.g., Li et al. 2015a, 2016a; Polito et al. 2015, 2016; Tian et al. 2015, 2016; Young et al. 2015; Tian 2017). In order to extract the hot line of Fe xxi 1354.09 Å and the cool line of C i 1354.29 Å (log T ∼ 4.0; Huang et al. 2014), we apply a multi-Gaussian function superimposed on a linear background to fit the IRIS spectrum at the “O i” window (e.g., Li et al. 2015a, 2016a), which has been pre-processed (i.e., IRIS spectral image deformation, bad pixel despiking and wavelength calibration) with the standard routines in Solar Soft Ware (SSW; Freeland et al. 2000). In short, the line positions and widths of these blended emission lines are fixed or constrained, and their peak intensities are tied to isolated emission lines from similar species. More details can be found in our previous papers (Li et al. 2015a, 2016a). On the other hand, the cool line of Si iv 1402.77 Å (log T ∼ 4.8) at the “Si iv” window is relatively isolated, and it can be well fitted with a single-Gaussian function superimposed on a linear background (Li et al. 2014, 2017a). Using the relatively strong neutral lines (i.e., “O i” 1355.60 Å and “S i” 1401.51 Å), we also perform an absolute wavelength calibration for the spectra at the “O i” and “Si iv” windows, respectively (Tian et al. 2015; Tian 2017). Finally, the Doppler velocities of Fe xxi 1354.09 Å, C i 1354.29 Å, and Si iv 1402.77 Å are determined by fitting line centers removed from their rest wavelengths (Cheng & Ding 2016b; Guo et al. 2017; Li et al. 2017a). As the hot Fe xxi line is absent in the non-flaring spectrum, the rest wavelength for the Fe xxi line (i.e., 1354.09 Å) is determined by averaging the line centers of the Fe XXI profiles which were used in the previous IRIS observations (Brosius & Daw 2015; Polito et al. 2015, 2016; Sadykov et al. 2015; Tian et al. 2015; Young et al. 2015; Brosius et al. 2016; Lee et al. 2017), while the rest wavelengths for the C i and Si iv lines, i.e., 1354.29 Å and 1402.77 Å, respectively, are determined from their quiet-Sun spectra (Li et al. 2014, 2015a).


Interstellar turbulence is supposed to be one of the most important factors to regulate star formation activities. Shocks induced by supersonic turbulence dramatically increase the density and temperature in the post-shock layer and promote the structure formation, such as dense cores and protostars (e.g., Padoan 1995; Padoan & Nordlund 2002; Klessen et al. 2005; Matsumoto et al. 2015a; Inoue et al. 2018). Observational studies have been attempting to search for dense cores that originated from turbulent phenomena. Recent systematic surveys with ALMA found that there are no or a few starless cores with their internal substructures originating from turbulent fragmentation (cf., Padoan & Nordlund 2002; Offner et al. 2010) in each star-forming region (Dunham et al. 2016; Kirk et al. 2017). On the contrary, complex spatial/velocity gas structures in the protostellar envelopes with the spatial scale from 0.1 pc down to a few tens of astronomical units are also revealed both by the single-dish observations and the interferometric observations (e.g., Tobin et al. 2011; Tokuda et al. 2014, 2016; Maureira et al. 2017). Some multiscale polarization observations and numerical simulations suggest that turbulent motions, rather than magnetic fields, are dynamically important to form complex gas morphologies of protostellar envelopes (Hull et al. 2017a, 2017b). To understand such diversities/complexities at early stages of star formation, it is important to investigate physical properties of structures originating from the turbulent gas kinematics. In early phases of star formation, the shock waves can be formed by interactions among different density gas with the different velocities because the gas motions, such as infalling/outflowing gas, are supersonic. Detections of high-J transitions of molecular lines (e.g., CO) excited by magnetohydrodynamic (MHD) shocks have been expected by theoretical modelings (e.g., Pon et al. 2012; Lehmann & Wardle 2016). Recent submillimeter observations (e.g., Shinnaga et al. 2009; van Kempen et al. 2009a, 2009b; Kristensen et al. 2013) have detected warm envelopes seen in high-J CO lines from protostellar sources. However, the origin and heating mechanisms of warm gas in low-mass star-forming dense cores are still under debate. For example, van Kempen et al. (2009b) suggested several origins to produce the high-J CO lines; (1) inner envelope heated by protostellar luminosity, (2) shocked gas in the outflow, and (3) quiescent gas heated by UV photons. Shinnaga et al. (2009) also detected the extended CO (J = 6–5, 7–6) emission with the size scale of a few thousand astronomical units in our current target, MC27/L1521F (see also later descriptions in this section). They argued that the warm gas may be coming from shock regions created by interactions between the collapsing envelopes and the internal disk-like materials around the protostar. Although their observations were not able to resolve the internal substructures of the dense core due to the lack of the angular resolution, they pointed out the importance for investigating such warm gas formed in an early phase of star formation to understand the evolution from dense cores to protostars.


We analysed the change as a function of time, by using annual groups of line intensities for each instrumental setup as independent data points d

i
. The baseline is taken as time t
0 = 2012.45, which is the mean time point of our original data, 16.31 years after the discovery of the event (Nakano et al. 1996). The total process follows an exponential decline (see Equation (7)). As the total timescale τ
rec is so much longer than the epoch of our investigation, a free parameter, giving the curvature of the exponential, cannot be derived unambiguously and numerically stably. Thus we use the Taylor series linear approximation here. We derive independent model regression points m

i
 of the type
2

mi=c(ti−t0)+n,where∑idi−mi2σi2→Min,

with c being the average annual change. As mentioned above the errors σ

i
 vary strongly for some lines (see also Table 2). Thus Equation (2) does not resemble the χ
2 definition where

σi∝mi

 anymore. Thus standard regression algorithms used widely do not apply (York 1966; Giordano & Iavernaro 2021; Lecuna et al. 2020). The regression analysis follows Tellinghuisen (2020). The derived value of n normalizes each of the data sets with respect to the line strengths at t
0. This is slightly different from using just a weighted mean for the time t
0, but is numerically more stable against the strong year-on-year variations of the errors, which are seen especially for the helium lines. For the regression the mpfit library (Markwardt 2009) was used, with the variable errors handled according to York (1966) in the implementation of Tellinghuisen (2020). The errors given by the mpfit library for the c parameter represent the statistical error with two parameters for the calculation of the degrees of freedom. However, we are primarily interested in the significance of any slope, rather than the parameter c (respectively, its normalized counterpart C

k
 from Equation (3)) and its potential contribution to the statistical error budget. To derive the significance of the slope, a C program was written to perform a Monte Carlo (MC) simulation. The value n from Equation (2) defines the normalized values

d¯i≔di/n

 and

σ¯i≔σi/n

 given in Table 2. Each data point

d¯i

 was varied independently 10 million times in agreement with its individual Gaussian error distribution, and a new regression for the normalized change C

k
 ∀ k ∈ [1, 107] was calculated with model points M

i
 types as
3

Mi=Ck(ti−t0)+Ni,where∑id¯i−Mi2σ¯i2→Min.

Moreover, a similar set of parameters from the same MC simulated data points, assuming that there was no change in time-defining model points M, was derived
4

Mi=Ni,where∑id¯i−Mi2σ¯i2→Min.

The fractional area of overlap A between the “sloping” and “non-sloping” distribution functions yields the statistical significance (1 − A) of the slope as a single parameter. This significance is lower than what would be derived from the standard deviation of the inclination (relative change per year) given by the fit with two free parameters. Figure 7 shows an example of such a pair of histograms. A priori this solution of the MC simulation, caused by the wide spread of errors between the individual data points, does not have to be distributed as a Gaussian. Tests indeed showed that it deviates from solutions with large slopes. As the result for our cases only shows very small slopes, there is only a marginal deviation from a Gaussian. As the assumption of a regular standard deviation holds we are able to use the error function erf from the integral of the Gaussian according to Equation (5) to derive the size of the intersect
5

A=1−erf−x2,

and from this the level x × σ of significance.


A closer look at the known ejecta-dominated SNRs supports the role of surrounding winds and/or shells, and may provide additional insight into why such remnants are so rare. Several, and perhaps all of them, are ones where the ejecta are expanding into a pre-SN stellar wind from the progenitor, or into a cavity carved out by such winds. The clearest case is for Cas A, where the light-echo spectrum of the actual SN that shows it to have been a Type IIb event (Rest et al. 2008; Krause et al. 2008). These are produced from the collapse of the helium core of a red supergiant that had lost most of its hydrogen envelope before exploding, so the ejecta expand into the stellar wind from the pre-SN star (Chevalier & Oishi 2003; Orlando et al. 2016). The extreme luminosity of NGC4449-1 has been best explained by its expansion into a dense and extensive circumstellar environment produced by winds from its massive progenitor, possibly with additional contributions due to winds from other massive stars in the surrounding dense OB cluster (Milisavljevic & Fesen 2008). For G292.0+1.8 and E0102–7219, the fact that fast knots of ejecta are expanding ballistically 2000–3000 yr after the explosion requires that they must be expanding into low-density cavities—ones evacuated by pre-SN winds. In both cases, there is an outer shell of X-ray emission where the SN blast wave is interacting with the CSM. As with Cas A, this interaction also leads to the reverse shock that excites the dense fragments of ejecta, producing the optical emission. For both Puppis A and N132D, spectra of the outer radiative filaments show them to be very high in nitrogen; these too are likely overtaking winds enriched by dredged-up nitrogen. These stripped-envelope SNe—types Ib and Ic—are relatively rare compared to their cousins, types II and IIL, that explode with their envelopes more or less intact; the recent review by Smartt (2009) indicates that together SN Ib and Ic comprise only ∼20%–30% of core-collapse events.


In this work, we investigate how the climate of an Earth-like planet is affected when its orbit is perturbed by the presence of a nearby giant planet. For the first time, a GCM coupled with analytical equations that describe the orbital evolution of a terrestrial planet are used. An additional major difference between our work and previous studies is that we utilize a fully coupled ocean model and an Earth continental layout. This is in contrast to WP2002 who used a 50 m “thermodynamic slab” ocean model without horizontal ocean heat transport or Linsenmeier et al. (2015), who used an aquaplanet model and a 50 m slab ocean, but again with no horizontal ocean heat transport. We use a fully coupled ocean model because alongside atmospheric heat transport, ocean heat transport plays a vital role in the climate of Earth (Peixoto & Oort 1992). In particular, the work of Hu & Yang (2014) has shown that the effects of a fully coupled ocean versus a shallow slab ocean can be significant when looking at synchronously rotating worlds around M-dwarf stars. Godolt et al. (2015) demonstrated stark differences for planets orbiting F-type stars when changing ocean heat transport, while Rose (2015) nicely demonstrated the climatic effects of changing ocean heat transport equations for aqua-type and ridge-type worlds. The downside of a fully coupled ocean approach is that it can take hundreds of model years for a fully coupled ocean to come into equilibrium with the atmosphere. Yet, it will provide a more accurate picture of the climate of the world being modeled. In this study we focus on the effects of the terrestrial planet’s orbital eccentricity on the planet’s climate, which is an under-researched area in 3D GCM studies. At the same time, we keep θp = 235, following for modern Earth. The latter is a necessary requirement for comparing with past and future work in the literature since obliquity plays such an important role in the possible climate states of terrestrial planets.


As regards the modeling of BGK modes, there are two main theoretical approaches: the integral solution or BGK methodology and the differential (or Schamel) technique. In the former method (BGK), one assumes that the initial particle distribution function and the electrostatic potential profiles are known, so these are substituted into the Poisson equation and the integral equation is solved to obtain the trapped particle distribution function (Bernstein et al. 1957; Aravindakshan et al. 2018a, 2018b, and the references therein). In Schamel’s approach, the form of the trapped particle distribution function and of the passing (i.e., free, nontrapped) particle distribution function is assumed and substituted in Poisson’s equation, leading to a differential equation that is then solved to obtain the form of the potential (Schamel 1986; Luque & Schamel 2005, and the references therein). A distinguishing factor in the former (BGK) approach is that it involves a condition in the form of an inequality to be satisfied by the potential parameters (width and amplitude) in order for a BGK mode to be sustained. The BGK approach will be adopted in this work. The above models tacitly assume a collisionless electron-ion plasma. These assumptions are acceptable in the Earth’s magnetosphere. However, as we move farther from near-Earth plasma environments, the presence of charged dust in the plasma cannot be neglected. In the case of Saturn, there are observations of streaming ions by the Cassini spacecraft (Badman et al. 2012a, 2012b). We know that these streaming ion flows can lead to the generation of ion holes. Electrostatic solitary waves have been observed in Saturn’s magnetosphere (Williams et al. 2006) and in the dusty environment near its moon Enceladus (Pickett et al. 2015). Williams et al. (2006) reported observations of solitary structures in the vicinity of Saturn’s magnetosphere. They detected a series of bipolar pulses and speculated that these could be either electron holes or ion holes (Williams et al. 2006). Later on, Pickett et al. (2015) observed solitary wave pulses within 10 Rs (Rs is the Saturn radius) and near Enceladus. Near the Enceladus plume, they discussed how dust impacts affected the observed solitary waves. In fact, Pickett et al. (2015) pointed out that some of the bipolar electric field pulses associated with the solitary waves observed had an inverse polarity (i.e., a positive pulse first, followed by a negative pulse in a short time period) and suggested that this might be due to either an inverse direction of propagation or to a true inverse potential pulse polarity (sign). Moreover, Farrell et al. (2017) examined the conditions that allow low-energy ions, such as those produced in the Enceladus plume, to be attracted and trapped within the sheath of negatively charged dust grains. Using particle-in-cell simulations, they showed that with dust in the system, the large electric field from the grain charge disrupts pickup and leads to ion trapping. Their simulation results also reveal that the bipolar pulses reported in the Enceladus plume by Williams et al. (2006) and Pickett et al. (2015) could most probably be ion holes. In the light of the above information, we may suggest that the formation of ion holes is highly likely in the dusty plasma of environments such as the one found in Saturn. Importantly, the instrument on board Cassini, the Radio Plasma Wave Science instrument, does not have the ability to determine the polarity of the electric fields associated with the ESWs observed with 100% certainty as it lacks the ability to perform interferometry (Williams et al. 2006).


Phosphorus, which is isoelectronic with both nitrogen and the CH group, is a key element of living systems as a major component of nucleic acids and nucleotides, performing many relevant biochemical functions (Pasek & Lauretta 2005). Conversely, despite significant progress in the recent years (Jiménez-Serra et al. 2018; Rivilla et al. 2018; Fontani et al. 2019; Chantzos et al. 2020) and its importance to astrobiology, the interstellar chemistry of phosphorus is still poorly understood. The first identified phosphorus compound in the ISM was PN through observations of its rotational transitions in Orion-KL, W51M, and Sgr B2 (Turner & Bally 1987; Ziurys 1987). This observation was followed by the detection of free CP in the carbon star envelope IRC +10216 (Guelin et al. 1990). The other phosphorus-bearing molecules detected so far are HCP (Agúndez, Cernicharo & Guélin 2007), CCP (Halfen, Clouthier & Ziurys 2008), PO (Tenenbaum, Woolf & Ziurys 2007), and PH3 (Agúndez et al. 2014b), while a tentative detection of NCCP is also reported (Agúndez, Cernicharo & Guélin 2014a). Phosphorus was also detected in the coma of the comet 67P/Churyumov–Gerasimenko (Altwegg et al. 2016), with recent analysis indicating PO as its main carrier (Rivilla et al. 2020). In addition, PH3 was recently detected in the cloud decks of Venus through millimetre waveband observations (Greaves et al. 2020). Larger phosphorus-bearing molecules, such as phosphorus oxoacids (Turner et al. 2018a) and alkylphosphonic acids (Turner et al. 2018b) – the latter detected in the Murchison meteorite (Cooper, Onwo & Cronin 1992) – were identified in PH3-doped interstellar ice analogues exposed to ionizing radiation. These results, in combination with the increasing literature on phosphorus-bearing molecules in circumstellar envelopes (Ziurys, Schmidt & Bernal 2018) and solar-type star-forming regions (Lefloch et al. 2016) and protostars (Lefloch et al. 2018; Bergner et al. 2019), suggest that their role in the ISM might be greater than previously thought.


We find that it is possible to infer

 and

, at the precision of spectroscopy and relatively imprecise

 and

 for red-giant stars. We attempted to infer the [Fe/H]; this label is available from the apogee spectroscopy for our stars. However, this label failed and, on inspection, no pixels correlated with [Fe/H]. Therefore, contrary to the findings by Corsaro et al. (2017), we find that there is no information with respect to [Fe/H] in the granulation signal from the Kepler multiepoch photometry. We note that corrections to scaling relations between

 and fundamental stellar parameters include both

 and [Fe/H] (White et al. 2011; Guggenberger et al. 2016; Sharma et al. 2016). Furthermore, Viani et al. (2017) showed, in the case of

, a dependence on mean molecular weight. While we do not find the signature in the ACF amplitude, this does indicate that a [Fe/H] dependence might be expected, as was also suggested by 3D hydrodynamical simulations of convection (Collet et al. 2007; Ludwig & Steffen 2016). For our proposed methodology, the model should be applied to test data that is assumed to be derived from the underlying population as the training data. Nevertheless, to assess the impact of stellar metallicity on the inference of our labels, we performed a test where we divided stars into two groups around the mean metallicity of the sample. We created a training set of stars with [Fe/H] > 0 and a test set with [Fe/H]  0 dex. These stars broadly cover the same

,

, and

 and

 ranges, although the means of these labels are shifted. We find that the

 label is impacted at test time when training on a sample of stars with metallicities not covered in the test sample. The inferred

 is biased to be about 85 K too hot, for training on the metal-rich stars and testing on the more metal-poor stars and 85 K too cold, for the reverse (although with a similar precision as before). This indicates that the [Fe/H] of the star is constraining as to the scale of the

, even if we cannot learn this information from the data. The inference of the other three labels is not similarly affected by drawing the test and training set from different metallicity distributions. It is interesting that metallicity affects the

 and not the other labels. This means that temperature manifests itself differently in the spectra of stars with low and high metallicities. When we do not include stars with low metallicity in the training sample, we cannot accurately predict the temperatures of low metallicity stars during test, and vice versa, as temperature-induced variations in the spectrum must depend on metallicity. The fact that this is not true for other parameters implies that variations in seismic parameters produce variations in the ACF that are independent of metallicity; we therefore do not need to know the metallicity of our stars to infer these parameters to the precision captured using this technique. There is a theoretical expectation that the asteroseismic observables will vary with stellar metallicity (e.g., White et al. 2011; Guggenberger et al. 2016; Kallinger et al. 2018; Viani et al. 2017). Following on from this, there is also opportunity to investigate this in more detail with a data-driven approach.


Ouchi et al. (2008) find that there is a possible excess of the Lyα LFs at z = 3.1 and 3.7 similar to the bright-end hump, and they claim that 100% of LAEs host AGNs at the bright ends of

 and 43.4 erg s−1, respectively, based on the large-area LAE survey with the multiwavelength data set. Thus, the bright-end hump of our z = 2.2 Lyα LF may be produced by AGNs. To examine whether our LAEs at the bright end include AGNs, we use the multiwavelength data of X-ray, UV, and radio available in the SXDS, COSMOS, CDFS, HDFN, and SSA22 fields. For the X-ray data, we use the XMM-Newton source catalog in the SXDS field (Ueda et al. 2008), the Chandra1.8 Ms catalog in the COSMOS field (Elvis et al. 2009), the Chandra 4 Ms source catalog in the CDFS field (Xue et al. 2011), and the Chandra 2 Ms catalog in the HDFN field (Alexander et al. 2003). The typical sensitivity limits of these X-ray data are ∼10−16 to 10−15 erg cm −2 s−1 for the SXDS and COSMOS fields and ∼10−17 to 10−16 erg cm −2 s−1 for the CDFS and HDFN fields. We use GALEX far-UV (FUV) and near-UV (NUV) images for the UV data and obtain these images from the Multimission Archive at STScI (see also Zamojski et al. 2007 for the COSMOS field). The GALEX images reach the 3σ detection limit of ∼25–26 mag. The Very Large Array 1.4 GHz source catalogs of Simpson et al. (2006) (SXDS), Schinnerer et al. (2007) (COSMOS), and Miller et al. (2013) (CDFS) are used for the radio data. These radio data reach an rms noise level of ∼10 μJy beam−1. We find that a majority of our bright LAEs are detected in the multiwavelength data, and we summarize the numbers of these LAEs in Table 2. Under the column of “culled sample” in Table 2, we show the numbers of LAEs with no counterpart detection(s) in the X-ray, UV, and radio data. As shown in Table 2, the SXDS and COSMOS fields have the data that cover all of the X-ray, UV, and radio wavelengths. Moreover, the X-ray, UV, and radio data spatially cover the entire fields of SXDS and COSMOS with the similar sensitivities. We make a subsample that is composed of all 1576 LAEs found in the SXDS and COSMOS fields, and we refer to this subsample as SXDS+COSMOS/All. We then make another subsample consisting of 1538 LAEs with no multiwavelength counterpart detection(s) in the SXDS and COSMOS fields, which is dubbed SXDS+COSMOS/Culled.


Although, the standard form of Press–Schechter mass function with $f(\nu)=\sqrt{{2}/{\pi }} \nu \mathrm{ e}^{-\frac{\nu }{2}}$ which discussed in Press & Schechter (1974) and Bond et al. (1991) can provide a good approximation of the predicted number density of haloes, it fails by predicting approximation too many low-mass haloes and too few high-mass ones (Sheth & Tormen 1999, 2002; Lima & Marassi 2004). Thus, in this study we apply another well-known fitting formula which first proposed in Sheth & Tormen (1999):
(24)
\begin{eqnarray*}
f(\nu)=0.2709\sqrt{\dfrac{2}{\pi }}(1+1.1096\nu ^{0.6})\mathrm{ exp}(-\dfrac{0.707 \nu ^2}{2})\,\, .
\end{eqnarray*}
In a Gaussian density field, σ is given by
(25)
\begin{eqnarray*}
\sigma ^2(R)=\dfrac{1}{2 \pi ^2}{\int _0}^\infty k^2 P(k) W^2(kR) \, {\rm d}k\,\, ,
\end{eqnarray*}
where R = (3M/4πρm0)1/3 is the radius of the spherical overdense region, W(kR) is the Fourier transform of a spherical top-hat profile with radius R and P(k) is the linear power spectrum of density fluctuations (Peebles 1993). To obtain the value of σ, we follow the procedure presented in Abramo et al. (2007a). Following on Ade et al. (2016), we use the normalization of matter power spectrum σ8 = 0.815 for ΛCDM cosmology. The number density of virialized haloes above a certain value of mass M at zc, the collapse redshift obtained by
(26)
\begin{eqnarray*}
N(\: M,z)={\int _0}^\infty \dfrac{{\rm d}n(z)}{{\rm d}M^{\prime }}\, {\rm d}M^{\prime }\,\,.
\end{eqnarray*}
The above limit of integration in equation (26) is $M=10^{18}\, \mathrm{ M}_{\rm \odot}\, \mathrm{ h}^{-1}$ which such gigantic structures could not in practice be observed. Now we can calculate the number density of virialized haloes in both homogeneous and clustered DE scenarios using equations (23) and (26). In this way the total mass of a halo is equal to the mass of pressureless matter perturbations. However, the virialization of dark matter perturbations in the non-linear regime cannot be independent from the properties of DE (Lahav et al. 1991; Maor & Lahav 2005; Creminelli et al. 2010; Basse, Bjlde & Wong 2011). Thus, in clustered DE scenarios, we should consider the contribution of perturbated DE components to the total mass of the haloes (Creminelli et al. 2010; Basse et al. 2011; Batista & Pace 2013). Based on the behaviour of wde(z), DE can reduce or enhance the total mass of the virialized halo. One can obtain ϵ(z), the ratio of DE mass to be taken into account with respect to the mass of dark matter, from:
(27)
\begin{eqnarray*}
\epsilon (z)=\dfrac{m_{\rm DE}}{m_{\rm DM}}\,\, ,
\end{eqnarray*}
where the value of mDE depends on what we consider as the mass of DE component. When one only considers the contribution of the perturbations of DE, the mDE takes the form
(28)
\begin{eqnarray*}
{m_{\rm DE}}^{\mathrm{ Perturbed}}=4 \pi \bar{\rho }_{\rm DE}{\int _0}^{R_{\rm vir}} \, {\rm d}R R^2 \delta _{\rm DE}(1+3{c_{\rm eff}}^2)\,\,.
\end{eqnarray*}
In the other hand, if we assume both DE contributions of perturbation and background level, the total mass of DE in virialized haloes takes this new form
(29)
\begin{eqnarray*}
{m_{\rm DE}}^{\mathrm{ Total}}=4 \pi \bar{\rho }_{\rm DE}{\int _0}^{R_{\rm vir}} {\rm d}R R^2 [(1+3 w_{\rm DE})+ \delta _{\rm DE}(1+3{c_{\rm eff}}^2)].
\end{eqnarray*}
The quantities inside a spherical collapsing region in the framework of the top-hat profile, evolve only with cosmic time. Thus from equation (28) one can find
(30)
\begin{eqnarray*}
\epsilon (z)=\dfrac{\Omega _{\rm DE}}{\Omega _{\rm DM}}\dfrac{\delta _{\rm DE}}{1+\delta _{\rm DM}}\,\,
\end{eqnarray*}
and from equation (29) we can obtain
(31)
\begin{eqnarray*}
\epsilon (z)=\dfrac{\Omega _{\rm DE}}{\Omega _{\rm DM}}\dfrac{1+3 w_{\rm DE}+\delta _{\rm DE}}{1+\delta _{\rm DM}}\,\, .
\end{eqnarray*}
The mass of dark matter also is obtained from (see also Batista & Pace 2013):
(32)
\begin{eqnarray*}
{m_{\rm DM}}=4 \pi \bar{\rho }_{\rm DM}{\int _0}^{R_{\rm vir}} \, {\rm d}R R^2 (1+ \delta _{\rm DM})\,\,.
\end{eqnarray*}
In Fig. 5 we plot the evolution of ϵ(z) using equation (30) as the definition of DE mass. We observe that, at high redshift, where the role of DE is less important, ϵ for both of parametrizations becomes negligible. This parameter has a greater value in the case of parametrization (2).


Annealing is sometimes used to avoid effects of temperature fluctuations during the etching and/or to remove a background consisting of tracks of light ions. We did not anneal samples before etching. The reason is that nanometric structure transformations of olivine along the heavy projectile trajectory provide enhanced etching of this region. Figure 3 and simulations made in Gorbunov et al. (2015) demonstrate that the diameter of an emerging amorphized track core is up to about 10 nm in the trajectory sector where the Bragg peak of the electronic stopping of heavy ions is realized. The chemical activity of this track core may be reduced due to recrystallization during annealing. To stimulate such recrystallization within etching, the etching temperature must reach thresholds activating (a) fast diffusion of atoms/structure defects supplying structure modifications at times much shorter than the etching time, or (b) melting of the track core followed by its rapid solidification. Because of olivines’ high melting temperatures (1800°C–1850°C) the second scenario cannot be realized at the etching temperatures used (110°C) or during the hand-polishing of samples before etching. Such a temperature increase arising during treatments of samples cannot stimulate a fast diffusion of atoms, either, due to their high migration barriers (e.g., migration barriers of vacancies and interstitials in oxides with covalent binding exceeding 1–2 eV). This is well-illustrated in some experiments (Perelygin et al. 1985) when the procedure of track annealing is applied to study ancient tracks from GCR in olivine crystals from meteorites. Dissipation of “background” tracks of light iron group nuclei from GCR (initial density 1010–1011 cm−3) was detected in Perelygin & Stetsenko (1989) after annealing these crystals at higher temperatures (430 ± 1)°C for 32 hr before etching, and in a 6–8-fold decrease of track lengths for nuclei with Z ≥ 54. This correlates with the analysis (Perron et al. 1988), which demonstrated that the preliminary track annealing led to unpredictable changes in track lengths, resulting in a lower accuracy of nuclear charge determination. For example, path length variations of accelerated Kr and Xe nuclei (with energies of 12.5 and 10.0 MeV per nucleon, respectively), decelerated in olivine crystals from Marjalahti pallasite, depend on annealing time (Lal et al. 1969). The etched lengths of tracks of these nuclei are reduced by 2–3 times for the first 10–20 hr of annealing (382°C). A further increase of annealing time (up to 240 hr) is not followed by any significant decrease in track length, but these final lengths of tracks of Kr ions vary from 18 ± 3 μm to 11 ± 3 μm (40% difference), i.e., the dispersion of the measured lengths is too high. Annealing of tracks of U, Au, and Xe decelerated in olivine crystals from Marjalahti pallasite at temperatures of 430°C, 435°C, and 450°C resulted in a similar distribution of etched track lengths (Perron et al. 1988). Dispersion of L values measured in individual olivine crystals from Marjalahti pallasite sometimes reaches a 3–4-fold value. This effect has been observed, in particular, for tracks from U ions, annealed for 5 hr at a temperature of 450°C, when the L value measured in the same crystals varied within the range of Lmin = (217 ± 52) μm up to Lmax = (762 ± 77) μm. The annealing of tracks from U ions held for 5 hr at T = 435° gave the L values within the range of Lmin = (440 ± 100) μm to Lmax = (869 ± 53) μm (Perelygin & Stetsenko 1989). Similarly, almost twofold intervals of L variation were obtained for Xe and Au ion tracks. Taking into account these causes, the technique without preliminary annealing at a higher temperature is used in the presented work, i.e., we did not apply annealing of samples before their etching at a temperature of 110°C. The search for the heavy component in GCR within the framework of the OLIMPIYA project is based on the registration and measurement of the dynamic and geometric parameters of chemically etched tracks generated by nuclei with Z > 40 in combination with calibration experiments at heavy ion accelerator facilities. The detection method is an annealing-free technique based on layer-by-layer grinding and chemical etching. This technique provides for the geometrical parameters of tracks and the lengthwise track etching rate along the ion trace, as an additional parameter for identification of charges Z of the particle producing tracks.


Scaling relations for the core radii rc, core densities δc, and core masses Mc as functions of the total halo mass M200 were fitted to the simulated halo populations, which largely agree with hydrostatic considerations of the halo cores where rc is nearly constant, as well as velocity dispersion tracing in the halo envelope,

v
c
2

≈
v

200
2

$ v^2_{\rm c} \approx v^2_{200} $

. However, these trends do not agree with those obtained by fitting the Burkert profile to nearby galaxies in the SPARC dataset and the classical Milky Way dSphs. This poses an issue for SIBEC-DM with Rc ≳ 1 kpc and a largely CDM-like matter power spectrum at late times (Harko 2011; Harko & Mocanu 2012; Velten & Wamba 2012; Freitas & Gonçalves 2013; Bettoni et al. 2014; de Freitas & Velten 2015; Hartman et al. 2022), as was used in our simulations, although these scenarios are not well-motivated. For SIBEC-DM given by the field Lagrangian in Eq. (1), the self-interaction is constrained to Rc  1 kpc, otherwise an early radiation-like period and a large comoving Jeans’ length washes out too much structure to be consistent with observations (Shapiro et al. 2021; Hartman et al. 2022). In fact, Shapiro et al. (2021) found by using constraints on FDM as a proxy for SIBEC-DM, and matching their transfer function cut-offs and HMFs, that the SIBEC-DM self-interaction should be as low as Rc ∼ 10 pc to not be in conflict with observations. We were unable to probe SIBEC-DM with initial conditions and parameters consistent with the Lagrangian in Eq. (1), since the large gap between the halo cores and the cut-off scale requires both a large simulation box and very high spatial resolution. It should be noted that our SIBEC-DM-only simulations do provide a better agreement with the slopes in observed scaling relations than FDM. In particular, FDM simulations generally find

M
c

∼

M

200

γ

$ M_{\mathrm{c}}\sim M_{200}^{\gamma} $

 with 1/3  γ  0.6, while we find γ ≈ 0.75, which is closer to the observed γ ≈ 1.1. Additionally, FDM halos have core radii that generally decrease with the halo mass, while we find a slightly increasing trend due to larger halos experiencing more thermal heating, although not as steep as in the SPARC dataset and the Milky Way dSphs.


In both models, the particles interact with magnetohydrodynamic (MHD) Alfvén waves in the plasma. If the Doppler-shifted wave frequency is a constant multiple of the particle gyrofrequency in the particle guiding center frame, then a resonant interaction between the particle and the transverse component of the electric field of the MHD wave will occur (Dermer et al. 1996; Becker et al. 2006; Dermer & Menon 2009). The particle will experience either an accelerating or decelerating electric field in the transverse direction of motion over a fraction of the cyclotron period, resulting in an increase or decrease in energy. The accelerating or decelerating electric field causes the particle distributions to diffuse in energy, pushing particles to higher or lower energies in a diffusion pattern. This stochastic acceleration process typically causes the particle distributions to have a pronounced curvature in the energy spectrum (Schlickeiser 1984). The strength of the particle diffusion depends on the spectral index of the MHD turbulence, p. A Kolmogorov, p = 5/3, or a Kraichnan, p = 3/2, spectrum are most often used to model MHD turbulence. In this study, we restrict the spectral index of the turbulence to p = 2 to simulate hard sphere scattering between the MHD waves and the particle spectra. The stochastic acceleration timescale can be expressed as
3

where tdyn represents the dynamical timescale over the region in which turbulence generated (which may be smaller than the entire emission region), βA represents the Alfvén velocity of the plasma normalized to the speed of light and ξi represents the ratio of the magnetic field fluctuations relative to the background magnetic field,

. The stochastic acceleration timescale is independent of particle mass and will therefore be the same for all charged-particle species (protons, electrons/positrons, pions, and muons). The diffusion term in Equation (1) describes the stochastic acceleration of particles in the quasi-linear approximation (Dermer et al. 1996). For gyro-resonant interactions to occur in the quasi-linear regime, the magnetic field fluctuations must be much smaller than the background magnetic field,

. If the energy density in the plasma waves starts to approach the energy density of the magnetic field, then the field becomes disordered and there exists no well defined gyrofrequency. In both models, we use a ratio between the acceleration timescale and the escape timescale as an input parameter. The ratio between the acceleration and escape timescales constrain the maximum size in which turbulence is injected for stochastic acceleration to occur in the quasi-linear regime; see Section 5.


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


In order to allow us to compare the continuum shape with earlier analyses, we use phenomenological continuum models rather than more physically motivated models such as those by Becker & Wolff (2007)2 or Farinelli et al. (2016). As discussed by Müller et al. (2013), among others, phenomenological spectral models typically used to describe the continua of accreting neutron stars are the exponentially cutoff power law (cutoffpl), the power law with Fermi-Dirac cutoff (FDcut, Tanaka 1986), a negative-positive cutoff power law (NPEX, Mihara 1995), and a model consisting of a blackbody disk (diskbb, Mitsuda et al. 1984) and thermally comptonized continuum (nthcomp, Zdziarski et al. 1996; Życki et al. 1999). The residuals of the cutoffpl, FDcut, NPEX, and diskbb+nthcomp models are shown in Fig. 2, and the best-fit parameters are given in Table 1. The NPEX and FDcut residuals look very similar because they are driven to parameters that effectively mimic the cutoffpl solution. All tested continuum models describe the data similarly well. Due to its simplicity and in order to allow comparison with previous work (e.g., Younes et al. 2015), we used the cutoffpl model for all subsequent analysis. Photoelectric absorption in the interstellar medium is accounted for with the tbnew model (TBabs in XSPEC) with cross sections and abundances according to Verner et al. (1996) and Wilms et al. (2000), respectively. The iron fluorescence line complex can formally be described by a slightly broadened (

σ
=
0
.

23

−
0.04

+
0.05

$ \sigma=0.23^{+0.05}_{-0.04} $

 keV) Gaussian component at 6.59 ± 0.04 keV. This is most likely a blend of different ionization states that cannot be resolved with NuSTAR. The strongest fluorescence lines are often produced by neutral (6.4 keV), He-like (6.7 keV), and H-like iron (7.0 keV), and the structure seen in the data is also consistent with a set of narrow Kα lines from these ions, as well as neutral Kβ (7.1 keV) with a Kβ/Kα flux ratio of 13% (Palmeri et al. 2003). With fixed energies and widths, this approach is also statistically valid and has the same degrees of freedom as using one broad emission feature, but shows less interference with the continuum modeling because all line energies and widths are fixed and broadening is only due to the detector response. Using both approaches, slight residuals still remain at the iron K edge. These residuals are due to a combination of a gain-shift in NuSTAR energy calibration and the fact that the tbnew model only includes neutral iron.


Observations over the years seem to firmly support the current acceleration of the Universe and therefore the possible existence of a generic cause responsible for it which we call dark energy (DE; see e.g. Riess et al. 1998; Perlmutter et al. 1999; WMAP collaboration 2013; Planck collaboration XVI 2014; Planck collaboration XIII 2016; Planck collaboration XIV 2016, and references therein). Cosmologists have worked hard to decipher the dark energy code, but we still ignore the physical nature of the DE and hence of the ultimate cause of the observed acceleration of the Universe. Such theoretical conundrum is the so-called Cosmological Constant Problem (CCP) (Weinberg 1989; Sahni & Starobinsky 2000; Padmanabhan 2003; Peebles & Ratra 2003; Copeland, Sami & Tsujikawa 2006; Solà 2013). In fact, the cosmological constant (CC), Λ, or equivalently the vacuum energy density associated to it, $\rho _\Lambda =\Lambda /(8\pi G)$ (G being Newton’s gravitational coupling), is usually regarded as the simplest possible explanation for the DE. Historically, the CC was introduced by Einstein in the gravitational field equations 101 yr ago (Einstein 1917). A positive, constant, tiny value (in particle physics units) of order $\rho _\Lambda \sim 2.7\times 10^{-47}$ GeV4 ∼ (2.3 × 10−3 eV)4 can explain the needed speed up of our cosmos according to the observations. The standard or ‘concordance’ cosmological model embodies such an assumption as a fundamental built-in principle, together with the hypothesis of dark matter (DM), and for this reason is called the ΛCDM model. Formulated in terms of the current cosmological parameters, the ΛCDM assumes that $\rho _\Lambda =$const. throughout the history of the Universe, with $\Omega _\Lambda \simeq 0.7$ and Ωm ≃ 0.3 at present. Unfortunately, no convincing theoretical explanation is provided about the measured value of $\rho _\Lambda$. At the end of the day, no fundamental theory, not even quantum field theory (QFT), can explain this value; and, what is worse, the typical prediction is preposterously large as compared to the measured value. The difficulties inherent to this concept were recognized as of the time when Y.B. Zeldovich first observed (Zeldovich 1967) that the contribution from QFT to the vacuum energy density should be of the order of ∼m4 for any quantum field of mass m, and therefore many orders of magnitude bigger than the existing upper bound on $\rho _\Lambda$ in those days.


In Fig. 4, we plot the mass growth of each candidate DCBH halo as a function of redshift. In both the panels, we plot the mass of the halo versus the redshift. The left-hand panel contains haloes from the Normal simulation while the right-hand panel contains haloes from the Rarepeak simulation. The grey region in each panel below 106$\rm {M_{\odot }}~$ signifies the region below which the mass resolution of Renaissance becomes insufficient to confidently model haloes. Generally, we are able to track haloes below this threshold and into the grey region but below 106$\rm {M_{\odot }}~$ results should be treated with caution. The dashed blue line is the limit above which a halo must grow in order to overwhelm the impact of LW radiation, Mmin, LW (Machacek, Bryan & Abel 2001; O’Shea & Norman 2008; Crosby et al. 2013, 2016). The dashed red line is the approximate atomic cooling threshold, Matm, at which point cooling due to atomic hydrogen line emission becomes effective.5 Focusing first on the Normal region in the left-hand panel, we plot the growth rate of the three DCBH candidate haloes identified in the left-hand panel of Fig. 2. The DCBH candidate haloes are rapid growers but are not necessarily the fastest growing haloes in the Normal region. To emphasize this comparison, we also plot the growth of three rapidly growing haloes that contain stars. We select the three star-forming haloes from the final output of the Normal region but haloes at other redshifts do of course exist, which are rapidly growing and contain stars. In this case, we see that haloes with high dM/dz (i.e. the mass as a function of redshift) values can be star free or star forming and hence having a high dM/dz does not necessarily discriminate between DCBH halo candidates by itself. Rapidly growing haloes can become metal enriched through external enrichment processes. The enrichment allows the halo interior to cool and to form stars even in the presence of dynamical heating. Therefore, any semi-analytical model or subgrid prescription that uses dM/dz alone as a predictor for DCBH candidates will inevitably overestimate the number of candidates.


“Wiggling” outflows are often observed among young stellar jets and protostellar molecular outflows (Eisloffel et al. 1996; Terquem et al. 1999). Terquem et al. (1999) investigated such binary systems where the accretion disk, from which the jet originates, is inclined to the binary orbital plane. They concluded that the observed jet “wiggling” is a consequence of the jet precession caused by tidal interactions in such non-coplanar binary systems. Nichols & Slavin (2009) as well as Hollis & Michalitsianos (1993) suggested that the precession of the accretion disk around the WD may be responsible for the bending of the wide-angle outflow found in the previous studies. In analogy to these observations of young stellar jets, we suggest that the “wiggling” that we also find here for the R Aqr jet may result from disk precession as well. We estimated the precession period using the theory from Terquem et al. (1999) and the binary parameters taken from Gromadzki & Mikołajewska (2009) – Mh = 0.8M⊙ (the mass of the hot WD companion), Mp∕Mh = 1.65 (where Mp is the mass of the primary companion), D = 15.5 AU (the mean semi-major axis of the system), and e = 0.25 (eccentricity). The value of Rd is unknown in our case and we used Rd = 5 AU giving D∕Rd ≈ 3 which corresponds to the average value of 2 ≤ D∕Rd ≤ 4 (the range taken from Terquem et al. 1999). For this calculation, we assumed that the angle δ between the disk plane and that of the binary orbit is small enough (10°) and we adopted cosδ = 1. Using Eq. (1) from Gromadzki & Mikołajewska (2009), we derived the precession time of T ≈ 530 yr. This value is quite large for the wiggling waves that we see. We estimated the projected spatial wavelength λproj of the “wiggling” wave according to λ = λproj∕sin i, where i is the angle between the jet symmetry axis and the line of sight, and T = λ∕υ, where υ is the jet velocity, from Gromadzki & Mikołajewska (2009). Using i = 72° and υ ~ 100 km/s, we derive λproj ≈ 10 500 AU which is more than 20 times larger than the projected length of the observed wiggling outflow (2′′ ≈ 440 AU). However, we should note that the precessing time strongly depends on the D∕Rd; the T decreases significantly with increasing R. It may also be the case that the “wiggling” model developed for YSO jets is not fitting for R Aqr which consists of evolved objects, and both the WD and the disk where the jet probably forms are much hotter than YSO systems. Furthermore, we cannot exclude that the steady wiggling might be a sequence of dynamical interactions of the two collimated flows tilted to each other.