HD 47366 (HIP 31674, BD−12 1566, HR 2437, TYC 5373-2001-1) is listed in the Hipparcos Catalogue (ESA 1997) as a K1 III star, with a visual magnitude of V = 6.11 and a color index of B − V = 0.994. The Hipparcos parallax π = 12.5 ± 0.42 mas (van Leeuwen 2007) corresponds to a distance of 80.0 ± 2.7 pc. The reddening E(B − V) = 0.028 was obtained from the Galactic dust map of Schlegel et al. (1998), with the correction given by Bonifacio et al. (2000) and a scaling factor of

, where d is the distance, b is the Galactic latitude, and h = 125 pc is the scale height of the reddening layer. The absolute magnitude MV = 1.51 was derived from the distance and the interstellar extinction AV = 3.1E(B − V). By adopting the broadband photometric color B − V and the estimated metallicity with the empirical calibration relation of Alonso et al. (1999, 2001), we derived the bolometric correction B.C. = −0.309 and the effective temperature Teff = 4866 ± 100 K. We used a high signal-to-noise ratio (S/N ∼ 200), iodine-free spectrum taken with HRS to measure the equivalent widths (EWs) of ∼30 Fe i lines, to derive the iron abundance [Fe/H]. The line lists as well as their oscillation strengths (

) were mainly taken from Hekker & Meléndez (2007), in which iron lines were carefully selected to avoid any blend by atomic or CN lines. The model atmosphere used in this work was interpolated from the line-blanketed, local thermodynamic equilibrium (LTE) ATLAS9-ODFNEW grid (Castelli & Kurucz 2004). The microturbulent velocity vt was obtained by minimizing the trend between the abundances of different Fe i lines and their reduced equivalent widths (

). The macroturbulent velocity was estimated with the empirical relations of vmacro versus Teff given by Hekker & Meléndez (2007), and the projected rotational velocity (

) was determined with the method of Fekel (1997). The stellar mass, surface gravity (

), radius, and age were derived using a Bayesian approach with the Geneva database (Lejeune & Schaerer 2001), which includes the post-helium flash phases for stars with M ≥ 1.7 M⊙. First, we interpolated an extensive grid of evolutionary tracks, with ΔM = 0.05 within 1.2 ≤ M/M⊙ ≤ 3.6, Δ[Fe/H] = 0.02 within −0.4 ≤ [Fe/H] ≤ +0.3, and 500 points in each track. Then, for each data point, we calculated the likelihood functions of

, Teff and [Fe/H] to match the observed values by assuming Gaussian errors. We adopted uniform prior probabilities of mass and [Fe/H]. It is noted that stars evolving more slowly have a higher probability of being observed. Without correcting this evolution effect, the resulting parameters would bias toward the rapid evolution phases. We therefore weighted the probability of each point along its evolutionary track by the normalized time-step (ai+1,j − ai,j)/(an,j − aa,j), where ai,j is the age of the ith interpolated point in the jth track, and n = 500 is the number of interpolated points in each track. Eventually, the probability distribution functions (PDFs) of the parameters yield M = 1.81 ± 0.13 M⊙, R = 7.30 ± 0.33 R⊙,

, and age = 1.61 ± 0.53 Gyr. The stellar mass is particularly important to derive the minimum masses of the orbiting planets detected with the Doppler technique. However, previous spectroscopic analyses gave discrepant results (1.87 M⊙ by Liu et al. 2010; 1.2 M⊙ by Mishenina et al. 2006) for HD 47366, which may be due to the different methods on finding Teff and

. Our determinations were based on a similar method to that of Liu et al. (2010), but used the Geneva evolutionary tracks, instead of the Y2 model (Yi et al. 2003), which does not account for the evolutionary phases after the helium-core flash. We found that the probability that the star has passed through the RGB tip and in-core helium burning phase is ∼88%. The stellar parameters of HD 47366 are listed in Table 1. In Figure 2, we plotted HD 47366 on the H-R diagram, together with the evolutionary tracks for stars with different masses and metal contents.


The main assumption is that the statistical properties of the interaction of the charged particles with the fields are dominated by Gaussian distributions. This is in correspondence with the Central Limit Theorem (CLT), which requires that all stochastic systems evolve asymptotically towards Gaussian statistics provided that (i) many interactions are involved, (ii) the change in state in individual interactions is always small, and (iii) subsequent changes of state are statistically independent of each other. Besides these necessary conditions for the applicability of the FP equation, also other simplifying assumption for a better tractability of the FP equation are being made, such as (1) the magnetic fluctuations are homogeneous in space, (2) the electromagnetic fields are quasi-static, (3) the interaction has a finite decorrelation time, etc. (see more details in the books Schlickeiser 2003; Zank 2014). Unfortunately, in astrophysical and laboratory plasmas, most of the above assumptions are not valid, yet the FP equation is used extensively, without a proof of its validity. This is especially true when the plasma particles are accelerated to high energies impulsively (e.g. in solar flares, coronal mass ejections, or the Earth’s magnetotail). The acceleration volume is finite and the expected fluctuating electromagnetic fields are strong ($\vert \delta \boldsymbol{B} \vert \ge \vert \boldsymbol{B}_0 \vert$). In solar active regions, the complex magnetic topologies host many null magnetic points which are randomly distributed inside the erupting or flaring volume (Aulanier et al. 2000; Pontin 2011). In these cases, the interaction of the particles with the strong em disturbances is transient and has no time to lead to Gaussian statistics or to become homogeneous in space (Isliker, Archontis & Vlahos 2019). Before analysing the interaction of the particles with the em fluctuations, it is important to understand the evolution of the em waves. With the use of resistive MHD codes one can show that a spectrum of high amplitude electromagnetic fluctuations evolves rapidly and leads to a fragmented current system, where reconnecting current sheets and large amplitude magnetic fluctuations are present (Arzner & Vlahos 2004; Dmitruk, Matthaeus & Seenu 2004; Vlahos, Isliker & Lepreti 2004; Isliker, Vlahos & Constantinescu 2017a), and where the various statistics clearly are non-Gaussian, following largely the paradigm of the stable Levy distributions (Isliker et al. 2017a; Isliker et al. 2019). In strongly turbulent plasmas, the magnetic fluctuations are non-collective modes and cannot be described with a simple dispersion relation $\omega =\omega (\boldsymbol{k}).$ The em environment generated from the evolution of large amplitude em fluctuations is well documented in the current literature and models much better many impulsive astrophysical and laboratory plasmas (see Dmitruk et al. 2004; Zhdankin et al. 2013; Isliker et al. 2017a and the reviews by Cargill et al. 2012; Karimabadi et al. 2014; Vlahos & Isliker 2019).


In the search for new exoplanets, M dwarfs are ideal targets due to their high abundance in the Galaxy (Bochanski et al. 2010). However, M-type stars are prone to high levels of stellar activity (Walkowicz et al. 2011; Loyd et al. 2016, 2018b) that can impact the radial velocity and/or transit signal of such systems through phenomena such as flaring (Tofflemire et al. 2012), star spots, plages and faculae (Boisse et al. 2011; Llama & Shkolnik 2015; Cauley et al. 2018; Roettenbacher et al. 2022; Bruno et al. 2022), and other activity-induced variability (Dumusque 2018; Rackham et al. 2019; Bellotti et al. 2022; Collier Cameron et al. 2021). Aside from the observational implications, the planet’s physical and chemical state can be altered by stellar activity as well due to, for example, coronal mass ejections (CMEs) and stellar particle events (SPEs) (Yamashiki et al. 2019; Atri 2017, 2020; Segura et al. 2010), winds (Vidotto et al. 2015; Vidotto & Cleary 2020; Chebly et al. 2022; Colombo et al. 2022), and stellar flares (Segura et al. 2010; Venot et al. 2016; Chadney et al. 2017; Tilley et al. 2019; Chen et al. 2021; Louca et al. 2022), the latter being sudden releases of radiative energy triggered by magnetic reconnection (Benz & Güdel 2010). Stellar flares result in a temporary increase in incident flux on the planet’s atmosphere, which in turn increases the photochemical reaction rates that can change the chemical composition. Photochemistry, and photolysis in particular, is a key driver of chemical disequilibrium in the atmospheres of close-orbiting, gaseous planets. Photolysis does not only deplete the upper layers from species such as CH4 and NH3, but it can enrich the middle regions with haze precursors such as HCN and C2H2 as well, particularly on cooler planets (Moses et al. 2011; Venot et al. 2012; Zahnle & Marley 2014; Agúndez et al. 2014; Moses 2014; Miguel & Kaltenegger 2014; Rimmer & Helling 2016; Drummond et al. 2016; Hobbs et al. 2019; Shulyak et al. 2020; Barth et al. 2021; Baeyens et al. 2022). Stellar flares thus have the potential to alter the chemical composition and, subsequently, alter the atmosphere’s signature in transmission spectra.


Three semiannual galactic hydrogen spectra as a function of energy between 40 and 250 MeV have been obtained in three different consecutive time periods (from 2018 August 6 to 2020 January 5) very much inside the heliosphere (1 au); the energy profiles are shown as black circles in Figure 6. Each measured energy spectrum is compared to the theoretical prediction from the HelMod model (Boschini et al. 2019) in the same period (blue solid curve); the maximum and minimum uncertainties related to this prediction are also reported in the plots, as dashed and dotted lines, respectively. As a further comparison, data from the SOHO/EPHIN spacecraft (red square marker) between 40 MeV and 53 MeV are also presented (Müller-Mellin et al. 1995). The agreement appears to be good in all the three examined periods, considering both statistical and systematic uncertainties. Ratio between HEPD data and models (displayed in the narrower bottom panels of Figure 6) gradually worsens at lower energies, particularly below 65 MeV, where the spectrum calculated by HEPD is systematically higher. Possible explanations for this discrepancy include a contamination from high-energy protons that is not fully removed using the simulation, and a possible contamination derived from nuclei fragmentation or from very inclined sub-cutoff protons that can enter the FoV of the instrument, even after the rigidity cutoff selection. However, although systematic uncertainties are higher than 10% in the lowest portion of the energy spectra, these results could help constrain theoretical models of particle transport from the border of the heliosphere, down to 1 au. From a comparison between the first spectrum (2018 August 6–2019 January 15) and the last one (2019 June 29–2020 January 5) an overall increase of ∼9% is observed, in very good agreement with the variation observed in SOHO/EPHIN (∼8.5%). This behavior is expected, because, as the solar activity continues to wind down (from 2018 to 2020), the effect of the Sun magnetic field diminishes, resulting in higher proton fluxes. On the other hand, HEPD data do not show a clear energy dependence in the modulation over time (typically lower energies should be more modulated with respect to higher ones); unfortunately, for HEPD the overall errors (statistical and systematic) in the first and last energy bins do not allow such a precise evaluation. Table 1 contains explicit values for the galactic hydrogen spectra in the three time periods and for each of the 16 energy bins allowed by the instrument resolution; statistical and systematic uncertainties are also reported.


For JW39 and JW100 the disks’ slopes are consistent with linearity, that is the trend expected from Equation (4). This may suggests that the smoothing scale (∼10 kpc) is similar to the CRe transport scale, and, hence, the slopes resemble the standard SFR calibrators. Therefore, the spatial correlation slopes observed in the disks of JW39 and JW100 are consistent with the idea that the CRe transport scale in these galaxies is larger than observed in spiral galaxy disks (∼1–5 kpc). We investigate this result by comparing the spatial scales, L, of the two principal CRe transport processes in these systems: diffusion and advection. In the case of CRe diffusion, the spatial scale is:
5

L=4Dτ≃1.1×D1028cm2s−1τ10Myrkpc,

where τ is the timescale and D is the diffusion coefficient, which depends on the CRe energy and the local magnetic field power spectrum, and can vary between 1027 and 1029 cm2 s−1 (Strong et al. 2007). For advection, the typical spatial scale is:
6

L=V·τ≃V100kms−1τ10Myrkpc,

where V is the CRe velocity. Equation (5) shows that to reach L = 10 kpc, for a typical D = 1 × 1028 cm2 s−1, the timescale is of the order of ∼900 Myr, which is longer than the typical CRe radiative time in galactic disks. Covering these spatial scales in ≤108 yr requires a diffusion coefficient of D ≥ 9 × 1028 cm2 s−1, which is slightly higher than observed in spiral galaxies (e.g., Strong et al. 2007; Tabatabaei et al. 2013; Heesen et al. 2019). On the other hand, these scales could be consistent with the CRe advection (Equation (6)), as a typical velocity of 100 km s−1 would be able to cover 10 kpc in ∼10 Myr, which is more reasonable for low-energy electrons emitting at 144 MHz. Therefore, our results might hint that CRe transport in the disks of these jellyfish galaxies, JW39 and JW100, is either dominated by advection, due to ram pressure which is stripping the nonthermal ISM (see Section 3.1), or that the CRe diffusion might be more efficient than in normal galaxies. The diffusion coefficient D depends on the local magnetic field configuration and turbulence spectrum (Strong et al. 2007), thus it may be possible that the RPS, by affecting the ISM’s microphysics, may induce higher values of D and, hence, more efficient CRe diffusion (Equation (5)) than observed in normal spiral galaxies. However, we note that, for the rest of the sample, the spatial correlations in their stellar disks are not consistent with linearity (Figure 5). We argue that this might be due to projection effects that mix the disk and the extraplanar emissions, which, on the basis of what we observe for JW39, JO60, JW100, and JO206, follows a flat, almost uniform, distribution. Thus this blend may result in a flattening of the disks’ slopes. Another possible explanation could be a discrepancy between the sampling resolution and the transport scale that was not solved by the smoothing.


To judge the origin of a star in an SNR, its kinetics characteristics may provide very important informations. Generally, except for being stripped-off a part of its envelope, the companion may receive a velocity kick from the supernova ejecta, but the kick velocity is usually much smaller than the orbital velocity (Marietta et al. 2000; Meng et al. 2007; Pakmor et al. 2008; Liu et al. 2012; Pan et al. 2012). Then, the orbital velocity of the companion at the moment of supernova explosion may represent its final space velocity to a great extant, especially for the sdB companions here, which almost do not receive any kick velocity for their large value of $A/R_{\rm 2}^{\rm SN}$. If the spatial velocity of a star in an SNR is very different from the others in the SNR, the star is very possible to be the surviving companion in the remnant (Ruiz-Lapuente et al. 2004). In Fig. 7, we present the companion orbital velocity relative to binary centroid versus the companion radius at the moment of supernova explosion. From the figure, we can see that different companions may have very different orbital velocity. For MS companions, the orbital velocity is from 150 to 200 ${\rm km\, s^{\rm -1}}$, while the RG companions have an orbital velocity of 50–110 ${\rm km\, s^{\rm -1}}$. For the sdB companions, the orbital velocity covers a large range, from 50 to 190 ${\rm km\, s^{\rm -1}}$. Such a large range is mainly derived from the large initial orbital period range for the systems producing sdB companions, i.e. log (Pi/d) is from ∼0.4 to 1.2. In other words, although the mass transfer between a binary system must begin in HG for producing a sdB companion, it may occur at the stage very close to the MS end or at the end of the HG. The upper limit of the orbital velocity here is lower than that in Meng & Podsiadlowski (2017) by 60 ${\rm km\,s^{\rm -1}}$, which originates from the fact that after MWD = 1.378 M⊙, the binary orbital period increases with mass transfer for a reversed mass ratio (see fig. 2 in Meng & Podsiadlowski 2017). For the same reason, the lower limit of the orbital velocity is also lower than that in Meng & Podsiadlowski (2017).


Benzene (C6H6), the simplest aromatic hydrocarbon, is a molecule that has raised great interest in the astrophysical community for almost four decades. This is mainly because C6H6 is one of the main precursors of polycyclic aromatic hydrocarbons (PAHs) reported to be present in interstellar dust particles (Leger & Puget 1984; Allamandola et al. 1989; Tielens 2013 and references therein), carbonaceous chondrites (Pering & Ponnamperuma 1971; Hayatsu et al. 1977; Hahn et al. 1988), and other astrophysical environments, such as carbon-rich, high-temperature environments (circumstellar and carbon-rich protoplanetary nebulae; Buss et al. 1993; Clemett et al. 1994). Benzene rings easily produce more complex, polycyclic structures by the one-ring build-up mechanism (Simoneit & Fetzer 1996). In space, an analogous process to carbon soot formation occurring on Earth can be initiated through the completion of that first aromatic ring and may also lead to the synthesis of PAHs (Tielens & Charnley 1997). Mechanisms involving the addition of hydrocarbons, such as acetylene onto aromatic rings as well as the attachment of other aromatic rings, or hydrocarbon pyrolysis, have been proposed to characterize the growth process of PAHs (Bittner & Howard 1981; Frenklach & Feigelson 1989; Wang & Frenklach 1997; Cherchneff 2011 and references therein). PAH synthesis from shocked benzene has also been reported (Mimura 1995). PAHs are crucial materials involved in a variety of cosmochemical processes. For example, amino acids could be synthesized by aqueous alteration of precursor PAHs in carbonaceous chondrites (Shock & Schulte 1990). PAHs are also produced in laboratory-simulated planetary atmospheres of Titan and Jupiter (Sagan et al. 1993; Khare et al. 2002; Trainer et al. 2004), and results from these studies indicate that the formation of aromatic rings and polyaromatics may be, among other sources, a possible chemical pathway for the production of the atmospheric solid particles (Lebonnois et al. 2002; Wilson et al. 2003; Trainer et al. 2004). The formation and evolution of benzene in planetary environments or other solar system objects thus represents a fundamental primary stage of the PAH production and other subsequent relevant chemical and prebiotic processes (like soot formation). In this context, several works related to benzene have been devoted to better understand the physico-chemical processes of irradiated C6H6, in its gaseous and solid phases, and the derived products, by acquiring high-resolution astronomical spectra, carrying out detailed laboratory studies or developing theoretical modeling (Allamandola et al. 1989  and references therein; Callahan et al. 2013; Materese et al. 2015; Mouzay et al. 2021). Laboratory astrophysical investigations have mostly focused on performing vibrational spectroscopy of ion, electron, or UV irradiated C6H6 gas and C6H6 ice. Such investigations aim to provide data on the spectral properties of the irradiated C6H6 materials, compare them with spectra obtained from astronomical observations (e.g., observations of the interstellar medium), or to study photoprocessed benzene ices to understand the fate of benzene ices in Titan’s stratosphere and help understanding the formation of aerosol analogs observed in Saturn’s moon’s stratosphere (Mouzay et al. 2021).


Galactic winds have been ubiquitously observed in galaxies at both low and high redshifts, and they are critical to galaxy formation and evolution. Simulations calibrated to match these observations predict that a large amount of galactic material is ejected as a wind before reaccreting to either form stars or be ejected once again (Oppenheimer et al. 2010; Anglés-Alcázar et al. 2017). Current cosmological hydrodynamic simulations of galaxy formation employ a variety of subgrid models (e.g. Springel & Hernquist 2003; Oppenheimer & Davé 2006; Stinson et al. 2006; Dalla Vecchia & Schaye 2008; Agertz et al. 2013; Schaye et al. 2015; Davé, Thompson & Hopkins 2016; Tremmel et al. 2017; Pillepich et al. 2018; Davé et al. 2019; Huang et al. 2020a) that artificially launch galactic winds, but the results are sensitive to numerical resolution and the exact subgrid model employed (Huang et al. 2019, 2020a). Simulations without these subgrid wind models (e.g. Hopkins et al. 2018; Kim & Ostriker 2015; Martizzi et al. 2016) allow winds to occur ‘naturally’, but these simulations may not resolve the scales necessary to resolve the important known physical processes (Scannapieco & Brüggen 2015; Brüggen & Scannapieco 2016; Schneider & Robertson 2017; McCourt et al. 2018; Huang et al. 2020b). Hence, modelling galactic winds accurately remains a theoretical challenge for even the most refined high-resolution simulations of galaxies (see Naab & Ostriker 2017, for a review). Even if one were able to accurately model the formation of galactic winds, the subsequent propagation in galactic haloes depends on a complicated interplay of many physical processes that occur on a wide range of physical scales that cannot be simultaneously resolved in a single simulation. For example, to robustly model the propagation and disintegration of moving clouds in various situations requires cloud-crushing simulations with at least sub-parsec scale resolution (Schneider & Robertson 2017; McCourt et al. 2018), which is orders of magnitudes below the resolution limits of cosmological simulations. Furthermore, most cosmological hydrodynamic simulations concentrate their resolution in the dense, star-forming regions of galaxies and thus have lower resolution in the circumgalactic medium (CGM, but see Hummels et al. 2019; Mandelker et al. 2019; Peeples et al. 2019; Suresh et al. 2019; van de Voort et al. 2019). To date, cosmological simulations do not include physically motivated subgrid models for galactic wind evolution, which are required to capture these small-scale physical processes.


The spatial distribution of OB stars and associations, young long-period Cepheids and open clusters, star-forming regions, H ii regions, interstellar dust, and giant molecular and neutral gas clouds in the solar vicinity that have been in existence generally τ ≲ 108 yr is known to correlate with the location of the inner Sagittarius, the closest Orion, and outer Perseus spiral arm segments. (The distances for the vast majority of these spiral tracers have been determined in the literature with trigonometric or photometric methods.) The Sun is situated at the inner edge of the Orion arm (Levine et al. 2006; Hou & Han 2014; Nakanishi & Sofue 2016; Xu et al. 2018, 2021; Lallement et al. 2019; Reid et al. 2019; Skowron et al. 2019; Cantat-Gaudin et al. 2020; Fig. 2 above).3 These three spatial features nearby to the Sun appear to form part of the global spiral structure in the Galaxy. Contrary, the objects of older population with larger random velocities, for instance, main-sequence A–K stars or the oldest Cepheids and open clusters, do not currently follow the exact location of those arms (e.g. Cantat-Gaudin et al. 2020, fig. 8 therein; Griv et al. 2020, fig. 7 therein). The latter can be explained by the difference in rotation velocity between the spiral density waves and the objects. Investigating the velocity field of Xu et al.’s (2018) O and early B-type stars in the framework of the Lin–Shu density-wave proposal, we also found that the Sun lies within the Orion arm, at the inner edge of this spiral. The radial distance from the Sun to the centre of the Orion arm is ≈0.2 kpc in the direction of the Galactic anticentre, the centre of the Sagittarius arm is ≈1.8 kpc from the Sun in the direction of the GC, and the width of the arms is ≈0.5 kpc. The radial distance between the centres of the Orion and Sagittarius arms near the Sun is λrad ≈ 2 kpc (cf. Hou & Han 2014; Wu et al. 2014; Bovy et al. 2015). As for us, the nearest Orion spiral arm forms part of the dominant density-wave structure of the system.


In a quasi-isothermal jet, Uj is (17)\begin{equation} \label{eq:U_j_quasi} U_{\rm j} = \zeta n_0 m_{\rm p} c^2\left(\frac{\gamma_{\rm j}\beta_{\rm j}}{\gamma_0\beta_0}\right)^{-\Gamma}\left(\frac{z}{z_0}\right)^{-2} \cdot \end{equation}Uj=ζn0mpc2γjβjγ0β0−Γzz0-2·Substituting Eqs. (17) and (13) into Eq. (10), and assuming the jet is launched with an initial γ0β0 equal to the sound speed (Eq. (16)), the 1D Euler equation that results is \begin{eqnarray} \label{eq:AGNJET_Corrected} &&\left\{\gamma_{\rm j}\beta_{\rm j}\frac{\Gamma+\xi}{\Gamma-1}-\Gamma\gamma_{\rm j}\beta_{\rm j}-\frac{\Gamma}{\gamma_{\rm j}\beta_{\rm j}}\right\}\frac{\partial \gamma_{\rm j}\beta_{\rm j}}{\partial z} = \frac{2}{z}; \\ &&\xi = \frac{1}{\zeta}\left(\frac{\gamma_{\rm j}\beta_{\rm j}}{\gamma_0\beta_0}\right)^{\Gamma-1}; \qquad \gamma_0\beta_0=\sqrt{\frac{\zeta\Gamma(\Gamma-1)}{1+2\zeta\Gamma-\zeta\Gamma^2}} \cdot \end{eqnarray}γjβjΓ+ξΓ−1−Γγjβj−Γγjβj∂γjβj∂z=2z;ξ=1ζγjβjγ0β0Γ−1; γ0β0=ζΓ(Γ−1)1+2ζΓ−ζΓ2·The above equation should reduce to the jet Lorentz factor profile used in Falcke (1996), Markoff et al. (2005) when ζ = 1. However, it differs from Eq. (2) in Falcke (1996): (20)\begin{equation} \label{eq:Heino96} \left\{\gamma_{\rm j}\beta_{\rm j}\frac{\Gamma+\xi}{\Gamma-1}-\frac{\Gamma}{\gamma_{\rm j}\beta_{\rm j}}\right\}\frac{\partial \gamma_{\rm j}\beta_{\rm j}}{\partial z} = \frac{2}{z}; \end{equation}γjβjΓ+ξΓ−1−Γγjβj∂γjβj∂z=2z;(21)\begin{equation} \xi = \left(\gamma_{\rm j}\beta_{\rm j}\frac{\Gamma+1}{\Gamma(\Gamma-1)}\right)^{1-\Gamma} \cdot \end{equation}ξ=γjβjΓ+1Γ(Γ−1)1−Γ·The difference between our equation and the equation in Falcke (1996) can be accounted for as follows: the − Γγjβj term in Eq. (18) results from a neglected \hbox{$\frac{\partial}{\partial z}(U_{\rm j}/n)$}∂∂z(Uj/n) term, the difference in the exponent in ξ results from an arithmetic error, and finally the difference in the inside of the parenthesis of ξ terms is from setting \hbox{$\gamma_0\beta_0 = \beta_{\rm s0}^{2}$}γ0β0=βs02 instead of using the proper value given in Eq. (16). The difference between the solutions of Eqs. (18) and (20) are small and shown in Fig. 1. In Fig. 1, we also include solutions to the 1D Euler equations when the jet is isothermal (Tj = const., i.e., Eq. 20 with ξ = 1) and adiabatic (Tj ∝ (γjβj)1 − Γz2 − 2Γ, see Eq. (25)).


First, we discuss the discrepancy of the distribution scale of the radio core positions based on the discussions of the internal shock model (Koyama et al. 2015; Niinuma et al. 2015). As is discussed there, the radio cores in Mrk 501 and Mrk 421 observed at 43 or 22 GHz can usually be considered as the internal shocked regions owing to the convex shape of the radio spectrum peaking around 10 GHz (Giroletti et al. 2008; Sokolovsky et al. 2010; Lico et al. 2012; Blasi et al. 2013). The standard internal shock model of blazars considers that the discrete ejecta with higher speeds (with Lorentz factor Γf) catch up with the preceding slower ejecta (with Lorentz factor Γs), and the collision leads to the nonthermal emission (e.g., Spada et al. 2001; Tanihata et al. 2003; Guetta et al. 2004; Kino et al. 2004; Ghisellini et al. 2005). Based on the model, the distribution scale of the internal shocks (ΔDIS in Figure 7, defined as the difference between the largest distance between the internal shock and the central engine DIS,max and the closest one DIS,min) can be explained as the variation of the Lorentz factors of the ejecta (Koyama et al. 2015; Niinuma et al. 2015), by assuming the Lorentz factor ratio (Γf/Γs) and the initial separation of the ejecta (IIS). The core stable within 200 μas constrained by the VERA can be explained by Lorentz factors within a factor of two variation for the slower ejecta, i.e., 8 ≤ Γs ≤ 17, by assuming a minimum value of 8 (e.g., Kino et al. 2002), Γf/Γs ≤ 1.01 (Tanihata et al. 2003), and IIS ∼ 1 Rs (Koyama et al. 2015). This time we refined the distribution scale of the radio core within 42 μas along its main jet axis, or 4.6 × 103 Rs deprojected (see Figure 7). Based on the same assumptions as in Koyama et al. (2015), to explain the further stable distribution scale of the internal shocks, the variation of Lorentz factors of the slower ejecta is constrained to be much smaller, within 30% or 8 ≤ Γs ≤ 10. On the other hand, the radio core wandering of ΔDIS ∼ 2.6 × 105 Rs in Mrk 421 can be explained by the maximum value as Γs ∼ 60 (with different assumptions; Niinuma et al. 2015). Even by applying the same assumptions to Mrk 421 as those for Mrk 501, the maximum of the slower Lorentz factor is estimated to be Γs ∼ 50, which is still a few times as large as that of Mrk 501. Therefore, even during the X-ray and VHE γ-ray active states in 2012, the maximum Lorentz factors that explain the stability of Mrk 501's core are roughly a few times smaller than those for Mrk 421's wandering core, based on the internal shock model.


If the variation in 10Be/9Be ratios of CAIs reflects those episodic accretion events, 10Be/9Be ratios of CH–CB CAIs observed in this study would give important constraints on the evolution of the solar protoplanetary disk. Astronomical observations suggest that FUori-type outbursts are confined to the first few hundreds of thousands of years, which correspond to the class I stage of the protoplanetary disk evolution (e.g., Schulz 2012). We propose that the high and variable 10Be/9Be ratios recorded in CH–CB CAIs reflect episodic cosmic-ray fluxes caused by FUori-type outbursts. On the other hand, relatively low and less variable 10Be/9Be ratios recorded in CV CAIs may reflect less intensive episodic accretion events, possibly the EXori-type outbursts, which are confined to the evolutional stage of a few million years after the formation of the protoplanetary disk (=class II). Note that CH–CB CAIs studied here show no (or very low) signs of 26Al-derived 26Mg excesses, while most CV CAIs show clear evidence for the past presence of 26Al. If 26Al was introduced into the solar system at the earliest stage of the disk evolution (e.g., Sahijpal & Goswami 1998), differences in Be–B and Al–Mg systematics between CH–CB and CV CAIs imply that the injection of 26Al have occurred between the evolutionary stages class I and class II of the solar protoplanetary disk. This scenario is in agreement with arguments by other authors that the 26Al-free CAIs formed prior to injection and homogenization of 26Al in the early solar system (Sahijpal & Goswami 1998; Sahijpal et al. 2000; Krot et al. 2008a see more discussion in Krot et al. 2012a). Importantly, as mentioned in the introduction, CH–CB chondrites may have accreted a significant amount of outer solar system materials (Murty et al. 2007; Ivanova et al. 2008; Briani et al. 2009; Bonal et al. 2010; Olsen et al. 2016; Van Kooten et al. 2016), suggesting that CH–CB chondrites formed at outer parts of the solar protoplanetary disk relative to CV chondrites. In this case, our new Be–B and Al–Mg data set implies that the earliest formed CAIs tend to be transported into the outer part of the solar protoplanetary disk, where the parent bodies of CH–CB chondrites likely accreted. Yang & Ciesla (2012) modeled the evolution of the protoplanetary disk and material transport in the protoplanetary disk. Interestingly, Yang & Ciesla (2012) showed that outward radial transport in class I would have been greater than that of later stages of YSO evolution, suggesting that the earliest formed CAIs could be preserved in primitive bodies that accreted in the outer part of the disk. This model is consistent with our interpretation for the Be–B and Al–Mg systematics on CH–CB CAIs. It should be noted, however, that it is possible that 26Al were heterogeneously distributed in the CAI-forming regions at the earliest stage of the solar system evolution (e.g., Krot et al. 2008a; Holst et al. 2013; Park et al. 2017 and reference therein). Because no Pb–Pb ages of CH–CB CAIs are available at present, we cannot discard that possibility. Very recently, Kööp et al. (2018) found helium and neon excesses in the 26Al-free hibonite-rich CAIs, which can be attributed to in situ irradiation by energetic particles. Because 26Al-rich CAIs in CV chondrites lack comparable noble gas irradiation records (Vogel et al. 2004), Kööp et al. (2018) concluded that 26Al-free hibonite-rich CAIs experienced intense energetic particle irradiation at the earliest stage of solar protoplanetary disk evolution. This conclusion seems to be consistent with our above scenario for 26Al-free CH–CB CAIs. Note, however, that 10Be/9Be ratios of 26Al-free hibonite-rich CAIs in CM chondrites tend to be in the range of those for 26Al-rich CV CAIs (Liu et al. 2009, 2010), which is inconsistent with the above scenario. Therefore, the relationship between 10Be and 26Al in the early solar system would be more complicated than we thought.


Understanding how the diverse populations of protoplanetary discs in young stellar regions results in the range of exoplanet types and architectures found in the Galaxy is one of the major goals of planet-formation theory. This is an extremely challenging task due in part to the limited observational constraints available. The Atacama Large Millimetre/submillimetre Array (ALMA) is providing truly transformational images of protoplanetary discs with unprecedented sensitivity and resolution (Andrews 2020). However, millimetre wavelength images reveal the locations of small dust grains but provide little information on the presence of larger particles, beyond centimetre scales. Gas giant planets are mostly made of hydrogen and helium, which ALMA cannot directly observe; therefore, the information on the gas content relies on the observations of less abundant molecules, such as CO and its isotopologues, that are subjected to uncertain depletion processes in the gas-phase (e.g. Miotello et al. 2016). Planets might be detectable by ALMA, although indirectly, by the effects they have on the gas and/or dust in the disc. When planets become massive enough, they can carve gaps (e.g. Rice et al. 2006; Pinilla, Benisty & Birnstiel 2012; Zhu et al. 2012) and disturb the dynamics of the gas (Teague et al. 2018; Casassus & Pérez 2019; Pinte et al. 2019). The minimum gap-opening mass depends on the viscosity and scale-height of the disc (Crida, Morbidelli & Masset 2006; Duffell & MacFadyen 2013), but mini-Neptune-mass (Pérez et al. 2019) or even Earth-mass planets (Rosotti et al. 2016; Dong & Fung 2017) could produce detectable gaps. Gaps consistent with fully formed planets have been imaged by ALMA in discs with estimated ages ranging from  1 Myr (HL Tau and Elias 2–24; ALMA Partnership et al. 2015; Cieza et al. 2017) to ∼10 Myr (TW Hydra; Andrews et al. 2016). However, the origin of these gaps still remains to be established and several alternative explanations have been proposed, including the effect of snow-lines on the dust/gas evolution of different volatiles (Zhang, Blake & Bergin 2015), magneto-hydrodynamic effects (Flock et al. 2015), secular gravitational instability (e.g. Youdin 2011; Takahashi & Inutsuka 2014), and viscous ring-instabilities (Dullemond & Penzlin 2018). Each one of the proposed mechanisms has their merits and shortcomings, and it is possible that different mechanisms operate together or dominate in different objects or in the same object at at different times. For a recent review on disc (sub)structures, see Andrews (2020). Substructures are also expected to be ubiquitous in protoplanetary discs from a theoretical point of view. Without substructures to halt the migration of mm-size grains at large radii, dust particles should migrate towards the innermost part of the disc in time-scales shorter than 0.1 Myr (e.g. Brauer et al. 2007), which is inconsistent with the observations showing significant mm emission at large radii (≳10 au) at much older ages. Understanding the origin and evolution of substructures in protoplanetary discs and their implications for planet formation is currently one the main challenges in the field. To better understand the incidence and properties of disc substructures in any given molecular cloud, here we present 1.3 mm/230 GHz continuum ALMA long-baseline observations at 3–5 au resolution of the 10 brightest targets of the ‘Ophiuchus DIsc Survey Employing ALMA’ (ODISEA) project (Cieza et al. 2019) that were not included in ‘The disc Substructures at High Angular Resolution Project’ (DSHARP) ALMA Cycle-4 Large Program (Andrews et al. 2018). Our new observations result in the largest sample of disc images at ∼3–5 au resolution in any star-forming region observed so far at mm wavelengths (15 objects when combined with the brightest Ophiuchus objects in DSHARP). In Section 2, we discuss the sample selection, the long-baseline observations, and the data reduction. In Section 3, we characterize the observed substructures, including gaps, rings, inner discs, and cavities. In Section 4, we discuss individual objects and use the full sample of 15 bright Ophiuchus discs observed at high-resolution to construct a tentative evolutionary sequence in which the observed substructures are mostly driven by dust evolution and the formation of giant planets. We also discuss possible connections between the substructures observed in primordial discs and those seen in more evolved debris disc systems. A summary of our results and conclusions is presented in Section 5.


Among various DM candidates, the most popular candidate is the weakly interacting massive particles (WIMPs; like the neutralino), which have mass in the GeV range (Jungman et al. 1996; Bertone et al. 2005; Hooper & Profumo 2007; Feng 2010). The WIMPs are non-relativistic at the epoch of decoupling from the interacting particles and have negligible free-streaming velocities. Therefore, they are “cold,” called cold dark matter (CDM). In  the CDM scenario, “halos” formed in small clumps, and then merged together into larger and massive objects. Galaxies formed in these halos because of the cooling of atomic hydrogen (H; Tegmark et al. 1997) or molecular hydrogen (H2, Ciardi et al. 2000; Haiman et al. 2000). On large cosmological scales (from the range

 down to

), the CDM paradigm has had great success in explaining the observed universe and reproducing the luminous structures (Fixsen et al. 1996; Borgani & Guzzo 2001; Lange et al. 2001; Cole et al. 2005; Tegmark et al. 2006; Benson 2010; Hinshaw et al. 2013; Slosar et al. 2013; Wang 2013; Planck Collaboration et al. 2014; Wei et al. 2016). However, on small scales (

), there are still some discrepancies between the CDM paradigm and observations. (a) The core–cusp problem (Navarro et al. 1997; Subramanian et al. 2000). CDM simulations predict a cusp–core DM halo, whereas the observations find them cored (Salucci et al. 2012). (b) The too big to fail problem (Boylan-Kolchin et al. 2012). CDM simulations predict a central DM density significantly higher than observation allows. (c) The “missing satellite problem.” N-body simulations based on the CDM paradigm predict a number of subhalos larger than that of satellites found in our Galaxy (Klypin et al. 1999; Moore et al. 1999; Papastergis et al. 2011). Many methods have been proposed to solve these small-scale problems, such as modifying the nature of the DM from the CDM paradigm (Hu et al. 2000; Spergel & Steinhardt 2000; Su & Chen 2011; Menci et al. 2012), adding supernova feedback effect in simulation (Weinberg & Katz 2002; Mashchenko et al. 2006; Governato et al. 2010; Pontzen & Governato 2014), and considering the interplay between DM and baryons during the formation of the galaxy (El-Zant et al. 2001; Tonini et al. 2006; Pontzen & Governato 2014). However, these methods are insufficient to solve all of the above problems.


The gravitational microlensing of lensed quasars has proven to be an effective tool for measuring the properties of quasar accretion disks, and is starting to become useful for studying the X-ray corona as well. The time-dependent microlensing magnification (or demagnification) of one or more images of a lensed quasar is moderated by the finite size of the source, which smooths the complicated caustic pattern of microlensing magnifications as the quasar passes over it. This allows us to use the microlensing magnifications to estimate the source size, and such work has shown that in general the accretion disks are larger than would be expected from either thin disk modeling or total flux arguments (Pooley etÂ al. 2007; Anguita etÂ al. 2008; Morgan etÂ al. 2010; Hainline etÂ al. 2012; JimÃ©nez-Vicente etÂ al. 2012). Since the effective temperature of the disk depends on radius, its apparent size depends on wavelength, leading to a chromatic dependence of the microlensing magnification, with the same quasar image experiencing larger variability at blue wavelengths than at red wavelengths. Several studies have used this to constrain the power-law slope of the size-wavelength relation, and the results have been consistent with each other and with the thin disk prediction that the size goes like the four-thirds power of the wavelength, mostly because of their large uncertainties (Poindexter etÂ al. 2008; Bate etÂ al. 2008; Eigenbrod etÂ al. 2008; Floyd etÂ al. 2009; Blackburne etÂ al. 2011; Mosquera etÂ al. 2011). Finally, efforts to put upper limits on the size of the X-ray regions have also been successful (Pooley etÂ al. 2006, 2007; Chartas etÂ al. 2009; Dai etÂ al. 2010), and recently there have been attempts to constrain the direct and reflected components' sizes separately using color cuts or spectral decomposition (Chen etÂ al. 2011; Blackburne etÂ al. 2014; Morgan etÂ al. 2012; Chen etÂ al. 2012; Chartas etÂ al. 2012; Mosquera etÂ al. 2013).


Upper Scorpius (hereafter UpSco) is part of the nearest OB association to the Sun, Scorpius Centaurus. The region is nearby, with a distance of ∼145 pc from Hipparcos (de Bruijne et al. 1997) and a recent update from Gaia (144.2 ± 17.6 pc: Fang, Herczeg & Rizzuto 2017). UpSco is young, with different age determinations and a possible spread among its members (Preibisch & Zinnecker 1999; Preibisch, Guenther & Zinnecker 2001; Pecaut, Mamajek & Bubar 2012; Song, Zuckerman & Bessell 2012; Pecaut 2016; Rizzuto et al. 2016). The members of UpSco exhibit a significant mean proper motion (μαcos δ = −10.5 and μδ = −23.2 mas yr−1, with a standard dispersion of about 6.4 mas yr−1: de Bruijne et al. 1997; de Zeeuw et al. 1999; Fang et al. 2017). The bright end of the UpSco population has been examined in X-rays (Walter et al. 1994; Kunkel 1999; Preibisch et al. 1998), astrometrically (de Bruijne et al. 1997; de Zeeuw et al. 1999) and spectroscopically (Preibisch & Zinnecker 2002). The low-mass and substellar population has been investigated over the past decade in great detail with the advent of modern detectors, permitting wide and/or deep surveys (Ardila, Martín & Basri 2000; Martín, Delfosse & Guieu 2004; Slesnick, Carpenter & Hillenbrand 2006; Lodieu, Hambly & Jameson 2006; Lodieu et al. 2007, 2011b; Kraus et al. 2008; Béjar et al. 2008; Slesnick, Hillenbrand & Carpenter 2008; Lafrenière, Jayawardhana & van Kerkwijk 2010; Dawson, Scholz & Ray 2011; Lafrenière et al. 2011, 2014; Dawson et al. 2013, 2014; Lodieu 2013; Peña Ramírez, Béjar & Zapatero Osorio 2016; Best et al. 2017). The first transiting systems in the association have been announced in the last years, thanks to the Kepler K2 mission (Borucki et al. 2010; Lissauer, Dawson & Tremaine 2014; Batalha 2014), including a triple system composed of an F star and two solar-type stars (Alonso et al. 2015) and several M dwarf eclipsing binaries (Kraus et al. 2015; Lodieu et al. 2015; David et al. 2016). These systems are of prime importance, because they provide the first mass and radius measurements independent of models in this region. Finally, we should note the existence of a transiting Neptune-size planet candidate around an M3 member of UpSco (Mann et al. 2016; David et al. 2016).


To complement our study, we also analyzed GLOSTAR continuum images toward sites with maser emission. A full description of the GLOSTAR continuum data calibration and imaging is given in Brunthaler et al. (2021), while the full analysis of continuum images of Cygnus X will be presented in a forthcoming paper. Here, we briefly discuss the imaging strategy. The calibration and imaging of the continuum data was performed with the Obit package (Cotton 2008). The 2 GHz bandwidth was first rearranged into nine frequency subbands, which were used to image each pointing individually. Then, for each frequency subband the pointings were combined into large individual mosaics to cover the entire observed area. Finally, we combined the different frequencies to obtain the image at the reference frequency, which has circular beams of 19″ and 1.5″ in the D and Bconfiguration, respectively. Continuum and methanol line maps from Effelsberg observations have also been obtained as part of the GLOSTAR survey (Brunthaler et al. 2021, Rugel et al., in prep.) We note that continuum images were constructed for Effelsberg data, the VLA D configuration, the VLA B configuration, a combination of the VLA D and B (D+B) configurations, and a combination of the VLA D configuration and Effelsberg observations. The central frequency of these images is 5.8 GHz. Here, we only use B-configuration continuum maps to study the region of the investigated methanol maser positions and D+B maps of the region around DR21 (see Sect. 4.5). Methanol line data from Effelsberg were also inspected to look for flux variations in the VLA-detected masers (Sect. 4.4). The noise in the continuum images is not uniform, but rather varies across the mapped region, and can be high around strong sources with complex or extended emission. We locally measured the noise in regions close to the maser locations, resulting in 1σ values in the range from 0.056 to 0.43 mJy beam−1 for B-configuration images. For the D configuration, the 1σ rms noise ranges from 0.10 to 2.6 mJy beam−1. The higher values measured in D-configuration data are due to bright extended emission, which is present across the Cygnus X region, and are resolved out by the array in the B configuration. The highest local rms noise occurs around the strong radio source, DR21, a compact HII region.


It is interesting to note that for wind originating within

, their value of Be becomes almost constant when

. This corresponds to the slight decrease of the poloidal velocity beyond

 shown in the left panel of Figure 8. The reason why Be does not change beyond

 is because in this region turbulence has not well developed within our simulation time. Note that this radius is different from the inflow equilibrium radius, which is

. Within

, everything, especially the radial density profile, is fully reliable. Beyond this radius, the density profile is not reliable, but other properties, such as the level of turbulence and subsequently outflow properties, are still reliable up to a much larger “turbulence radius,” the limiting radius of turbulence steady state. This radius can be estimated as follows. Turbulence in accretion flow is because of MRI. The fastest growth rate of MRI at radius r is

. More precisely, it takes 3–4 orbits for MRI to develop and ∼10 orbits to saturate (Hawley et al. 1995). For our simulation time of

, taking a timescale of 3 orbits, we can obtain that the “turbulence radius” is

. This is close to the value of 800 rg mentioned above. Another way to understand the “turbulence radius” is as follows. For a geometrically thick disk, the largest turbulence eddies have size of order r. The corresponding eddy turnover time is

, where

 is the rms turbulent velocity. Our simulation data show

. If at a certain radius the eddy turnover time is substantially smaller than the duration of the simulation, then the local turbulence is likely to have reached quasi-steady state. Therefore, the “turbulence radius” should be some fraction of

, which gives a similar result to the above estimation. Therefore, we think that the results beyond

 are not reliable. It is very likely that Be will keep changing and the poloidal velocity still remains constant beyond

. This implies that wind can at least escape beyond the outer boundary of accretion flows. Simulations with longer run times can check this point.


Several predictions for planet(s) shaping the disk of SAO 206462 have been proposed (Muto et al. 2012; Garufi et al. 2013; Fung & Dong 2015; Bae et al. 2016; van der Marel et al. 2016a. Using linear equations from the spiral density wave theory, Muto et al. (2012) suggested two planets with separations beyond ~50 au by fitting independently the two spiral arms seen in Subaru/HiCIAO data and with masses of ~0.5 MJ by using the amplitude of the spiral wave. Garufi et al. (2013) proposed that one planet of mass 5–13 MJ located inside the cavity at a separation of 17.5–20 au could be responsible for the different cavity sizes measured for the small and large dust grains. Fung & Dong (2015) presented scaling relations between the azimuthal separation of the primary and secondary arms and the planet-to-star mass ratio for a single companion on a circular orbit with a mass between Neptune mass and 16 MJ around a 1 M⊙ star. They predicted with 30% accuracy that a single putative planet responsible for both spiral features of SAO 206462 would have a mass of ~6 MJ. Bae et al. (2016) presented dedicated hydrodynamical simulations of the SAO 206462 disk and proposed that both the bright scattered-light feature (Garufi et al. 2013) and the dust emission peak (Pérez et al. 2014) seen for the southwestern spiral arm result from the interaction of the spiral arm with a vortex, although a vortex alone can account for the S1 brightness peak. They suggested that a 10–15 MJ planet may orbit at 100–120 au from the star. However, ALMA observations at two different frequencies seem to contradict a dust particle trapping scenario by a vortex (Pinilla et al. 2015). Stolker et al. (2016) performed new fitting of the spiral arms observed in SPHERE data and found a best-fit solution with two protoplanets located exterior to the spirals: r1 ~ 168 au, θ1 ~ 52° and r2 ~ 99 au, θ2 ~ 355°. van der Marel et al. (2016a) proposed that the features seen in thermal emission in ALMA data and the scattered-light spiral arms are produced by a single massive giant planet located inside the cavity at a separation of ~30 au. Recently, Dong & Fung (2017) used the contrast of the spiral arms to predict a giant planet of ~5–10 MJ at ~100 au.


Assuming that the force-field approach to the solution of the Parker (1965) cosmic-ray transport equation is valid, the connection between historic cosmic-ray intensities and the solar properties they encountered lies in the effective diffusion coefficient that is assumed in this approximation. Establishing such a connection, however, is no simple task. Many theories have been proposed to describe the scattering of cosmic rays in the heliosphere. The most likely candidates for this task, given their reasonable agreement with observations and numerical simulations of cosmic-ray diffusion coefficients, are the quasilinear theory (QLT) of Jokipii (1966), the weakly nonlinear theory (WNLT) of Shalchi et al. (2004b), and the nonlinear guiding center theory (NLGC; or one of its variants; see, e.g., Matthaeus et al. 2003; Shalchi 2006, 2009, 2010; Ruffolo et al. 2012). Shalchi (2009) provides in depth theoretical treatments of most the abovementioned theories. These scattering theories all require as a key input an expression for the power spectrum of the turbulent fluctuations of the HMF. These spectra depend upon basic turbulence quantities, such as the magnetic variance, and various correlation scales. Turbulence power spectra are discussed in detail by, e.g., Batchelor (1970) and Matthaeus et al. (2007), whereas more background on the abovementioned turbulence quantities can be found in, e.g., Matthaeus & Goldstein (1982), Petrosyan et al. (2010), Matthaeus & Velli (2011), and Bruno & Carbone (2013). These basic turbulence quantities have been observed to show a marked dependence on the solar cycle at Earth (see, e.g., Smith et al. 2006b; Burger et al. 2014; Zhao et al. 2018). It follows then that mean free paths derived from these scattering theories would be expected to depend on the solar cycle as well, and several studies have reported such a dependence. Chen & Bieber (1993) find from an analysis of cosmic-ray anisotropies and gradients as observed by means of NMs, that larger mean free paths are associated with solar minima, and smaller mean free paths with solar maxima. The authors also report a mean free path dependence on solar magnetic polarity. Nel (2016) and Zhao et al. (2018) both extensively analyze spacecraft observations, using the turbulence quantities so calculated as inputs for expressions for diffusion coefficients derived from the QLT and NLGC theories. Both authors report that the resulting mean free paths display solar cycle dependences.


The first investigations of the rotational spectra of ethyl isocyanide were carried out in 1966 by Bolton et al. (1966). The spectra of the first vibrational and torsional excited states were measured in the centimeter wave domain (Anderson & Gwinn 1968). In this initial study, the dipole moment was determined to be μa = 3.79 D and μb = 1.31 D; this value is usually large for a molecule that includes a CN group. This causes dense and intense rotational spectra in the millimeter wave range and also in the submillimeter wave range up to 900 GHz (bQ lines). Anderson & Gwinn (1968) also observed some A–E splittings due to the internal rotation motion of the methyl group. The most recent spectroscopic study is from Krüger & Dreizler (1992) who reinvestigated the internal rotation measurements and also determined hyperfine coupling parameters due to the nitrogen quadrupole. As in our previous studies of ethyl cyanide isotopologs, it was not possible to observe internal rotation and hyperfine splittings due to our Doppler limited resolution. Our analysis was rather easy, starting from a prediction based on Krüger & Dreizler (1992) parameters. First, we analyzed and fit the most intense transitions, the aRh transitions, up to 330 GHz. These transitions were shifted only a few MHz from the initial predictions. Then bR and bQ lines were searched and included in the fit up to 330 GHz. Next, all the spectra were analyzed up to 990 GHz without difficulty. For the fitting, we employed ASFIT (Kisiel 2001) and predictions were made with SPCAT (Pickett 1991). The global fits included 6 transitions from Anderson & Gwinn (1968), 29 lines from Krüger & Dreizler (1992), and 2906 from this work. The maximal quantum numbers are J = 103 and Ka = 30. Both reductions A and S were tested. A reduction permits us to check theagreement of our new parameters set with those from Krüger & Dreizler (1992) (Table 1). Using S reduction slightly decreases root mean square from 30.3 to28.7 kHz. The condition numbers are nearly the same: 295 and 310 for the A and S reductions, respectively.The A reduction requires 23 parameters, but 5 additional parameters are required for the S reduction (Table 2). For this reason we used the A reduction even if this molecule is close to the prolate limit with kappa = −0.9521. Part of the new measurements are in Table 3. Owing to its large size, the complete version of the global fit Table S1 is supplied at the CDS. The fitting files .lin (S2), .par (S3), and the prediction .cat (S4) are also available at CDS.


We have presented the analysis of the current X-ray observations of the disc wind in MCG-03-58-007. Here, multiple and variable wind components with velocities ranging from $\sim \! -0.08\, c$ to $\sim \! - 0.2\, c$ (and potentially up to $0.35\, c$) are seen at different times. Multi-epoch observations of disc winds, like the one presented here, are crucial for revealing all the possible phases of the disc wind. For example, over a decade worth of observations of PDS 456 revealed that the wind is most likely clumpy and/or stratified with the ionization ranging from log ($\xi /\rm {erg\, cm \, s^{-1})}\sim 2$ erg cm s−1 up to log ($\xi /\rm {erg\, cm \, s^{-1})}=6$ erg cm s−1 and velocities ranging from $\sim \! -0.2\, c$ up to $\sim \! -0.46\, c$ (Reeves et al. 2016, 2018a, 2020). It is possible, as suggested in other examples of ultra fast disc winds, that we are looking at a stratified wind, where multiple components are launched at different disc radii, but not all of them are always detected. This adds MCG-03-58-007 to the small but growing list of multiphase fast X-ray winds. Other examples of AGN with at least two variable phases of the X-ray winds are PG 1211+143 (Pounds et al. 2016; Reeves et al. 2018b), IRAS 13224-3809 (Parker et al. 2017; Chartas & Canas 2018; Pinto et al. 2018), 1H 0707-495 (Kosec et al. 2018), IRAS 17020+4544 (Longinotti et al. 2015), and PG 1114+445 (Serafinelli et al. 2019). In those cases, multiple phases with a common or different outflowing velocities are detected in the X-ray band. In contrast to most of the cases reported so far, neither of the two phases seen in MCG-03-58-007 requires a different ionization (aside from slice B) suggesting that we are seeing different streamlines of the same highly ionized flow. The only exception could be the eclipsing event seen in 2015, where a solution is found with a lower ionization for the Fe K intervening absorber. However, what we most likely see during this occultation event is a higher density and lower ionization clump of the wind, which could be faster because its higher opacity makes it easier to accelerate (Waters et al. 2017). Note that this does not imply that the soft X-ray wind components, like the ones seen for example in PDS 456 or PG 1211+143, are not present; in contrast to the other examples, MCG-03-58-007 is seen through a relatively high column density (NH ∼ 2 × 1023 cm−2, see Table 2) neutral absorber, therefore these phases may be hidden behind it. MCG-03-58-007 is not the only example where multiple Fe-K zones with the same ionization and outflowing with different velocities had been detected in a single observation. For instance, two simultaneous Fe-K phases were detected at least twice in PDS456 (Reeves et al. 2018a, 2020) and possibly in PG 1211+143 (Pounds et al. 2016) and IRAS 13349+2438 (Parker et al. 2020).


In the second part of the paper, we propose the set of self-similar solutions as tests for MHD numerical codes with ambipolar diffusion capabilities. To show their usefulness and validity, a battery of tests was carried out for the Bifrost code in two spatial dimensions starting from initial conditions with cylindrical symmetry (Sect. 4). We showed that the ambipolar diffusion module in Bifrost can cope with the passage of the solutions through the current sheets, with the level of accuracy increasing the higher the spatial resolution and in spite of the intrinsic singularity in them. Vice versa, the tests show that these functions can probe the capabilities of ambipolar diffusion modules to a larger extent than the simple ZKBP solution that has been used thus far (e.g. Masson et al. 2012; Viganò et al. 2019; Nóbrega-Siverio et al. 2020b). As test functions, the various harmonics proposed in our paper have the comparative advantage that they combine the B ∝ | δ |1/3 singularity at the internal nulls (with δ the distance to the null) with the finiteness of the nonlinear diffusive flux, and this combination must be sufficiently well reproduced by the code if it is to pass the test. The ZKBP solution, instead, has a null just at the outer front, and the singularity there is of a lower order (∝|δ|1/2), with zero diffusive flux across it. On the other hand, the scarcity of tests for the ambipolar diffusion term until now is in contrast with, for instance, the case of HD shocks, for which a whole category of exact solutions is available (the solutions of the Riemann problem) that have been used to develop sophisticated numerical schemes and tests (see Laney 1998; Toro 2009). The contrast to shocks, in fact, is interesting because of the differences in their mathematical and physical nature: in shocks, it is the (magneto)hydrodynamic evolution of the hyperbolic components of the PDE that leads to the formation of the singularities, which is then smoothed through simple diffusive phenomena (typically viscosity). In the ambipolar diffusion problem, wherever there is a null, it is the diffusive phenomenon itself that creates and maintains the singularity.


Stellar properties were determined using three different techniques to model the oscillation frequencies extracted from the data. The first method relies on a dense grid of stellar models computed with the GARching STellar Evolution Code (GARSTEC; Weiss & Schlattl 2008) including the effects of microscopic diffusion, and on theoretical frequencies calculated using the Aarhus aDIabatic PuLSation code (Christensen-Dalsgaard 2008a). The results were obtained implementing a Bayesian scheme that uses the spectroscopic constraints and frequency ratios as the parameters in the fit (V. Silva Aguirre et al., submitted), the latter being almost insensitive to the surface effects in solar-like oscillators (Roxburgh & Vorontsov 2003; Silva Aguirre et al. 2011). Central values are given as the estimates of the stellar properties obtained in this manner. We also computed models using the ASTEC and YREC codes. In these cases, the fit was made to the individual frequencies after correcting for the surface effect with, respectively, an appropriately scaled version of the observed solar surface correction (Christensen-Dalsgaard 2012) and a solar-type correction as described in Carter et al. (2012). The stellar properties derived using the three techniques described above are consistent within the returned formal errors. Therefore, we added in quadrature the difference in central values of each property to the formal uncertainties determined from the GARSTEC Bayesian scheme as a measurement of the systematic spread arising from different codes and fitting techniques. In Table 2, we provide a precise estimate of the stellar age, t, from detailed frequency modeling. Values for the remaining fundamental stellar properties are consistent, within errors, with those obtained from grid-based modeling. In particular, no gain in precision was obtained for the stellar radius. On the other hand, the precision on the stellar mass is improved by nearly a factor of two, from 5.7% to 3.2%.


The initialization of solar flares remains an unsolved problem. Early ideas on how the initialization might occur were described by Norman & Smith (1978). They argued that flare process cannot start in the entire flare volume at one instant, and proposed that the flare onset was localized in a small part of an active region, from which the energy release extends as dissipation spreading process throughout the flare volume. Two types of agents that may lead to this kind of a dissipation process were addressed: electron beams and shock waves. These agents can trigger flares at large distances from their initial locations, causing sympathetic (simultaneous) flares or leading to a sequential flare energy release in one active region (Liu et al. 2009; Zuccarello et al. 2009). These triggering processes were numerically studied by Karlický & Jungwirth (1989) and Odstrčil & Karlický (1997). Karlický & Jungwirth (1989) assumed that electron beams, penetrating into the current sheet in the magnetic reconnection region, generate Langmuir waves. Then, using the particle-in-cell model, the authors studied the effects of these electrostatic waves on the plasma system. Sufficiently strong Langmuir waves were found to be able to generate ion-sound waves through the three-wave decay process (Bárta & Karlický 2000). These ion-sound waves increase electrical resistivity in the current sheet system, which results in the onset of the energy dissipation. Thus, the electron beams are able to cause magnetic reconnection. Odstrčil & Karlický (1997) studied the mechanism for the flare trigger by shock waves. They used a 2D magnetohydrodynamic model with the MHD shock wave propagating towards the current sheet. A portion of the shock wave passed through the sheet, and the rest was reflected. Nothing occurred at the very beginning of the wave-current sheet interaction. However, after some time, specific plasma flows around the current sheet were formed, which led to the start of magnetic reconnection. This shows that for reconnection to be triggered, the enhanced electrical resistivity as well as the plasma flows are important.


Active galactic nuclei (AGN) have drawn a lot of attention over the last decades because they have been beacons for the existence and demographics of super-massive black holes (BHs) throughout the history of the Universe (e.g., Soltan 1982; Kollmeier et al. 2006; Greene & Ho 2007; Schulze & Wisotzki 2010; Kelly & Shen 2013; Kormendy & Ho 2013; Schulze et al. 2015; Bañados et al. 2018). The release of gravitational binding energy via accretion of matter onto these BHs is expected to have a profound impact on the evolution of their host galaxies (e.g., Silk & Rees 1998; Granato et al. 2004; Di Matteo et al. 2005; Springel et al. 2005; Hopkins et al. 2008; Somerville et al. 2008; Fabian 2012; Harrison 2017; Harrison et al. 2018; Gaspari et al. 2019; Nelson et al. 2019). Large spectroscopic surveys such as the Sloan Digital Sky Survey (SDSS, York et al. 2000; Abazajian et al. 2009), the 2df QSO redshift survey (2QZ, Croom et al. 2004), the VIMOS VLT Deep Survey (VVDS, Le Fèvre et al. 2013) or the VIMOS Public Extragalactic Redshift Survey (VIPERS, Scodeggio et al. 2018) in combination with several deep X-ray surveys taken with ROSAT (Voges et al. 1999), Chandra (Elvis et al. 2009; Xue et al. 2011), XMM-Newton (Pierre et al. 2016), and eROSITA (Predehl et al. 2021) as well as large radio surveys (e.g., Becker et al. 1995; Condon et al. 1998; Smolčić et al. 2017; Shimwell et al. 2019; Lacy et al. 2020; Gordon et al. 2021) have provided an enormous data set to characterize the AGN population and its evolution with redshift in great detail. While the standard model for the AGN central engine has been successful in unifying the various classes of AGN appearance (Antonucci 1993; Urry & Padovani 1995; Padovani et al. 2017), some aspects such as changing-look AGN (CLAGN, e.g. MacLeod et al. 2016; Ruan et al. 2016; Graham et al. 2017; Noda & Done 2018) and tidal-disruption events (e.g., Gezari et al. 2009; Merloni et al. 2015; Auchettl et al. 2017) are just being explored more extensively in the time domain.


HD 169142 is a very young Herbig Ae-Be star with a mass of 1.65–2 M⊙ and an age of 5–11 Myr (Blondel & Djie 2006; Manoj et al. 2007) that is surrounded by a gas-rich disk (i = 13°; Raman et al. 2006; PA = 5°; Fedele et al. 2017) that is seen almost face-on. The parallax is 8.77 ± 0.06 mas (Gaia DR2 2018). Disk structures dominate the inner regions around HD 169142 (see, e.g., Ligi et al. 2018). Figure 1 shows the view obtained from polarimetric observations: the left panel shows the QΦ image in the J band obtained by Pohl et al. (2017) using SPHERE on a linear scale, and the two rings are clearly visible. The right panel shows a pseudo-ADI image of the inner regions obtained by differentiating the QΦ image (see Ligi et al. 2018, for more details). Biller et al. (2014) and Reggiani et al. (2014) discussed the possible presence of a point source candidate at small separation (0.2 arcsec from the star). However, the analysis by Ligi et al. (2018) based on SPHERE data does not support or refute these claims; in particular, they suggested that the candidate identified by Biller et al. (2014) might be a disk feature rather than a planet. Polarimetricimages with the adaptive optics system NACO at the Very Large Telescope (VLT; Quanz et al. 2013b), SPHERE (Pohl et al. 2017; Bertrang et al. 2018) and GPI (Monnier et al. 2017) show a gap at around 36 au, with an outer ring at a separation >40 au from the star. This agrees very well with the position of the rings obtained from ALMA data (Fedele et al. 2017); similar results were obtained from VLA data (Osorio et al. 2014; Macías et al. 2017). We summarize this information about the disk structure in Table 1 and call the ring at 0.17–0.28 arcsec from the star Ring 1 and the ring at 0.48–0.64 arcsec Ring 2. We remark that in addition to these two rings, both the spectral energy distribution (Wagner et al. 2015) and interferometric observations (Lazareff et al. 2017; Chen et al. 2018) show an inner disk at a separation smaller than 3 au. This inner disk isunresolved from the star in high-contrast images and consistent with ongoing accretion from it onto the young central star.While the cavities between the rings seem devoid of small dust, some gas is present there (Osorio et al. 2014; Macías et al. 2017; Fedele et al. 2017). Fedele et al. (2017) and Bertrang et al. (2018) have suggested the possibility that the gap between Rings 1 and 2 is caused by a planet with a mass slightly higher than that of Jupiter. However, this planet has not yet been observed, possibly because it is at the limit of or beyond current capabilities of high-contrast imagers. On the other hand, Bertrang et al. (2018) found a radial gap in Ring 1 at PA ~ 50° that might correspond to a similar radial gap found by Quanz et al. (2013b) at PA ~ 80°. The authors noted that if this correspondence were real, then this gap might be caused by a planet at about 0.14 arcsec from the star. So far, this planet has not been unambiguously detected either.


For our dataset of absolute magnitudes, we used data collected at the Institute of Astronomy of V. N. Karazin Kharkiv National University within the long-term observational programme to study asteroid magnitude-phase curves (Shevchenko et al. 2010, 2012, 2014a, 2016; Slyusarev et al. 2012). We also used some observational data obtained within several other programmes (Belskaya et al. 2010; Chiorny et al. 2007, 2011; Dotto et al. 2009; Hahn et al. 1989; Kaasalainen et al. 2004; Lagerkvist et al. 1998; Michalowski et al. 1995; Mohamed et al. 1994, 1995; Oszkiewicz et al. 2021; Shevchenko et al. 1992, 2003, 2009, 2014b, 2021; Velichko et al. 1995; Wilawer et al. 2022). All magnitudes were measured in the Johnson V band and extrapolated to zero phase angle using the HG1G2 system proposed by Muinonen et al. (2010), with some modifications presented by Penttilä et al. (2016). For computations, the online calculator1 for the HG1G2 photometric system was used. Since we derived absolute magnitudes in our data from the light curve maxima, and the definition of H is based on the rotationally averaged brightness, we added a half of the light curve amplitude corrected to zero phase angle to our results. We used the average correction coefficients from Zappala et al. (1990) for low- and moderate-albedo asteroids. This correction is typically very small because our light curve observations covered small phase angles. Absolute magnitudes obtained at different aspects were averaged. In such a manner, we obtained a homogeneous dataset of absolute magnitudes of about 400 asteroids up to H = 16.5 mag. Our database includes the absolute magnitude data, the G1 and G2 parameters, and the albedo and diameter values from different databases (such as Tedesco et al. 2002; Masiero et al. 2011, 2012; Nugent et al. 2015; Usui et al. 2011). The database is available at the CDS. Figure 1 shows the correlations of the absolute magnitudes from the largest datasets (MPC (HMPC), Pan-STARRS (HPS), and ATLAS (HATLAS)) with those of the Kharkiv dataset (HKH). For the ATLAS dataset, we used the absolute magnitudes in a cyan filter, since this filter overlaps the Johnson V band (Mahlke et al. 2021).


In this section, we describe a few numerical experiments carried out to analyse the importance of various hypotheses used to compute structural kernels. All models were computed using the Clés stellar evolution code (Scuflaire et al. 2008b) with the following ingredients: the CEFF equation of state (Christensen-Dalsgaard & Daeppen 1992), the OPAL opacities from Iglesias & Rogers (1996), supplemented at low temperature by the opacities of Ferguson et al. (2005) and the effects of conductivity from Potekhin et al. (1999) and Cassisi et al. (2007). The nuclear reaction rates are those from the NACRE project (Angulo et al. 1999), supplemented by the updated reaction rate from Formicola et al. (2004) and convection was implemented using the classical, local mixing-length theory (Böhm-Vitense 1958). We also used the implementation of microscopic diffusion from Thoul et al. (1994), for which three groups of elements are considered and treated separately: hydrogen, helium and the metals (all considered to have diffusion speeds of 56Fe). The oscillation frequencies and eigenfunctions were computed using the Liège adiabatic oscillation code (Scuflaire et al. 2008a). We took much care to analyse the numerical quality of the eigenfunctions and the models before computing structural kernels. Irregularities and poor quality of the computed eigenfunctions can bias the results and lead to wrong structural kernels and thus wrong inferences from inverted results. From our experience in hare-and-hounds exercises and inversions, we have determined that adding seismic constraints to the model is very efficient at bringing the reference model into the linear regime thus validating the inversion process. In other words, fitting the average large and small frequency separations is already a big improvement in terms of linearity, although individual seismic constraints, such as individual frequency ratios and individual small frequency separations are the best way to maximise the chances of being in the linear regime. Individual large frequency separations can also be used, but due to their sensitivity to surface effects, they should not be used in observed cases. As such, since in this study we did not use very elaborate seismic fitting techniques, our tests serve the only purpose of isolating various contributions to the errors and to test various hypotheses usually done when carrying out structural inversions in the context of helio- and asteroseismology.


We compare our results with a new reduction of observations from the Lowell Observatory SSS, which is running a long-term stellar activity survey complementary to the MWO HK Project. The SSS observes solar and stellar light with the same spectrograph, with the solar telescope consisting of an exposed optical fiber that observes the Sun as an unresolved source (Hall & Lockwood 1995; Hall et al. 2007). The basic measurement of SSS is the integrated flux in 1 Å bandpasses centered on the Ca ii H & K cores from continuum-normalized spectra, ϕHK, which can then be transformed to the S-index using a combination of empirical relationships derived from stellar observations:
7

where

 is the continuum flux scale for the Ca ii H & K wavelength region, which converts ϕHK to physical flux (erg cm−2 s−1).

 is a function of Strömgren

 and is taken from Hall (1996).

 (simply K in other works) is the conversion factor from the MWO HKP-2 H & K flux (numerator of Equation (1)) to physical flux (Rutten 1984). Ccf is a factor that removes the color term from S and is a function of Johnson

 (Rutten 1984). Finally, Teff is the effective temperature. See Hall et al. (2007) and Hall & Lockwood (1995) for details on the extensive work leading to this formulation. What is important to realize about this method of obtaining S is that it requires three measurements of solar properties,

,

, and

, along with the determination of one constant,

. The solar properties are taken from best estimates in the literature, which vary widely depending on the source used, and can dramatically affect the resulting SSSS for the Sun. Hall et al. (2007) used

,

, and

. The constant

 was empirically determined to be 0.97 ± 0.11 erg cm−2 s−1 in Hall et al. (2007) as the value that provides the best agreement between SSSS and

 from Baliunas et al. (1995) for an ensemble of stars and the Sun. This combination of parameters resulted in a mean SSSS of 0.170 for the Sun using observations covering cycle 23. A slightly different calibration of SSS data in Hall & Lockwood (2004) used a flux scale

 based on Johnson

, set to 0.65 for the Sun, and

 K. In Table 1 we estimated that this calibration resulted in a mean S = 0.168 for cycle 23. Hall et al. (2009), which included a revised reduction procedure and one year of data with the upgraded camera (see below), found

.


Notes. Intrinsic Lν(1400)/Lν(900) ratios obtained from different stellar population models: the BC03, assuming different initial mass functions (Salpeter, Salp, and Chabrier, Chab), star-formation histories (constant, cSFR, exponentially declining with τ = 0.1Gyr, exponentially rising with τ = −0.1Gyr), metallicties (Z⊙ and 0.02 × Z⊙), and stellar-population ages; the BPASS (Binary Population and Spectral Synthesis code Stanway et al. 2016); the Starburst99 models. We consider a range of wavelengths around 900 Å and 1400 Å, comparable to that covered by the narrow-band and the HST/ACS F606W filters in the rest frame, to estimate the average Lν. As described in Bruzual & Charlot (2003), BC03 provides the spectral energy distribution of stars obtained from a comprehensive library of theoretical model atmospheres (KBFA in the table). The library consists of Kurucz (1996) spectra for O-K stars, Bessell et al. (1991) and Fluks et al. (1994) spectra for M giants, and Allard & Hauschildt (1995) spectra for M dwarfs. In BPASS the stellar evolutionary tracks contain a contribution from isolated stars and binary systems. Also, the stellar atmosphere models are selected from the BaSeL v3.1 library (Westera et al. 2002), supplemented by Wolf-Rayet stellar atmosphere models from the Potsdam PoWR group (Hamann & Gräfener 2003). With Starburst99, it is possible to generate SEDs assuming a bunch of stellar evolutionary tracks, including stars with and without rotation (GenevaV40 and GenevaV00 respectively, Leitherer et al. 2014), and stellar atmospheres (the combination of model atmosphere from Pauldrach et al. 1998; Hillier & Miller 1998, is the recommended option). The 70%ROT+30%noROT entry indicates a model that is a combination of GenevaV40 for the 70% and GenevaV00 for the 30% (Levesque et al. 2012). The GenevaV40 and GenevaV00 tracks were released for metallicity equal to Z = 0.014 (~Z⊙, Eldridge 2012). The change in the intrinsic ratio due to the different evolutionary tracks and stellar atmospheres is shown for a Salpeter IMF, Z⊙, cSFR, and 100 Myr old stellar population. In the bottom part of the table, we report the ratios calculated from the best fit templates of AGN (Bongiorno et al. 2012), in which the SEDs are dominated by the radiation coming from an (un-)obscured AGN. (1) The intrinsic Lν(1400)/Lν(900) ratio for an unobscured TypeII AGN can be as low as 2.35 (Richards et al. 2006). In the estimation of the ratios we take into account the HI absorption occurred in star atmospheres, but we neglect that within the interstellar and circum-galactic medium.


Finally, we confirm our hypothesis on the origin of the bi-modal A(Li) distribution, and of the isthmus, by comparing results from our GCE model with data. In Fig. 8 we show the normalised A(Li) distribution of all the stars in our sample (blue histogram) compared with the result from three models of GCE: (i) imposing a gently declining SFH (SFR_0b model, dashed red lines); (ii) a gently declining SFH plus a single star formation burst at a ∼6 Gyr look-back time (SFR_1b model, dashed blue lines); and (iii) our best model (SFR_2b, black-solid lines), which contains a gently declining SFR plus two star formation bursts at ∼6 Gyr and ∼1.5 Gyr look-back times, the latter being the most impulsive. In our best model the first star formation peak is only 68% as intense as the latter and lasts 25% longer. The SFR_2b model is the one that best reproduces the observed A(Li) distribution while recovering the presently observed SFR and the thin-disk stellar and HI mass (Mor et al. 2019; Isern 2019; Ruiz-Lara et al. 2020). This result is robust as it only depends on the observed A(Li) distribution. Possible biases from the determination of the stellar ages do not have an impact on our conclusions. Figure 8 clearly shows that only a two-peaked SFH can explain the observed bi-modal A(Li) distribution when accounting for most known 7Li production and depletion mechanisms (solid black line). It is important to remark that we cannot quantify the exact intensity and length of the star formation bursts from our data and models, but we can only give a qualitative analysis. This is a consequence of: (i) the large age determination uncertainties still present in current data; (ii) the fact that the data we use is restricted to the solar neigbourhood and thus do not represent the entire Galaxy; and finally (iii) the fact that our model still misses some 7Li production and destruction processes that are currently under study (e.g. the effect of planet engulfment). In the future, new data from large surveys such as Galah (Buder et al. 2021) combined with better determinations of A(Li) in 7Li-poor low-luminosity cold dwarf stars will result in large, unbiased samples of MS stars. These new catalogues will allow us to better understand the many channels of 7Li production and destruction that occur inside dwarf stars. Also, future catalogues that include precise age determinations will allow us to better constrain the SFH of the MW, also by analysing its A(Li) distribution.


Strong outflows are commonly associated with the early stages of stellar evolution. They are likely responsible for transporting excess angular momentum away from the star–disc system and regulating the mass-accretion process and spin evolution of newly born stars (e.g. Hartmann & Stauffer 1989; Matt & Pudritz 2005; Bouvier et al. 2014). There are at least three possible types of outflows around young stellar objects: (1) a disc wind launched from the accretion disc (e.g. Blandford & Payne 1982; Ustyugova et al. 1995, 1999; Romanova et al. 1997; Ouyed & Pudritz 1997; Königl & Pudritz 2000; Pudritz et al. 2007), (2) an X-wind or a conical wind launched near the disc–magnetosphere interaction region (e.g. Shu et al. 1994, 1995; Romanova et al. 2009) and (3) a stellar wind launched from open magnetic field lines anchored to the stellar surface (e.g. Decampli 1981; Hartmann & MacGregor 1982; Kwan & Tademaru 1988; Hirose et al. 1997; Strafella et al. 1998; Matt & Pudritz 2005; Romanova et al. 2005; Cranmer 2009). However, despite recent efforts, the exact launching mechanisms of the winds and outflows as well as the mechanism behind the collimation of the ejected gas into jets are still not well understood (e.g. Edwards et al. 2006; Ferreira, Dougados & Cabrit 2006; Kwan, Edwards & Fischer 2007; Tatulli et al. 2007b; Kraus et al. 2008; Eisner, Hillenbrand & Stone 2014). Hence, high-resolution interferometric observations which can resolve the wind-launching regions are crucial for addressing this issue. If a high spectral resolution is combined with a high spatial resolution, the emission-line regions near the base of the wind (e.g. Brγ emission regions in Herbig Ae/Be stars) can be resolved in many spectral channels across the line (e.g. Weigelt et al. 2011; Kraus et al. 2012b,c; Garcia Lopez et al. 2015). This allows us to study the wavelength-dependent extent and the kinematics of the winds, which can be derived from the line visibilities and wavelength-dependent differential and closure phases. Such observations would help us to distinguish the different types of outflow scenarios.


An estimate of a sputtering cross-section can be inferred from our measurements with σs ≈ V∕d, where V is the volume occupied by

${Y}_{\textrm{s}}^{\infty}$Ys∞
 molecules and d the depth of sputtering.

$\sigma_{\textrm{s}}\approx {Y}_{\textrm{s}}^{\infty}/l_{\textrm{d}}/\textrm{ml}$σs≈Ys∞/ld/ml
, where ml is the number of CO or CO2 molecules cm−2 in a monolayer (about 6.7 × 1014 cm−2 and 5.7 × 1014 cm−2, respectively,with the adopted ice densities). As is shown in Table 1, the sputtering radius rs would therefore be about 1.26 to 2.12 times larger than the radiolysis destruction radius rd in the case of the CO2 ice, and 2.03 to 2.36 for CO in the considered energy range (~0.5-1 MeV/u). The net radiolysis is the combined effect of the direct primary excitations and ionisations, the core of the energy deposition by the ion, and the so-called delta rays (energetic secondary electrons) travelling at much larger distances from the core; that is, several hundreds of nanometres at the considered energies in this work (e.g. Mozunder et al. 1968; Magee & Chatterjee 1980; Katz et al. 1990; Moribayashi 2014; Awad & Abu-Shady 2020). The effective radiolysis track radius that we calculate is lower than the sputtering one, which points towards a large fraction of the energy deposited in the core of the track. The scatter on the ratio of these radii is due to the lack of more precise data. It nevertheless allows to put a rough constraint on the estimate of Nd in the absence of additional depth measurements, with

${N}_{\textrm{d}} \lesssim {Y}_{\textrm{s}}^{\infty}/\sigma_{\textrm{d}}$Nd≲Ys∞/σd
. If the rs∕rd ratio is high, a large amount of species come from the thermal sublimation of an ice spot less affected by radiolysis, and the fraction of ejected intact molecules is higher. The aspect ratio corresponding to these experiments evolves between about ten and twenty for CO2 and CO, whereas for water ice at a stopping power of Se ≈ 3.6 × 103eV∕1015 H2 O molecules cm−2, we show that it is closer to one (Dartois et al. 2018). The depth of sputtering is much larger for CO and CO2 than for H2O at the same energy deposition, not only because their sublimation rate is higher, but also because they do not form OH bonds. For complex organic molecules embedded in ice mantles dominated by a CO or CO2 ice matrix, with the lack of OH bonding and the sputtering for trace species being driven by that of the matrix (in the astrophysical context), the co-desorption of complex organic molecules present in low proportions with respect to CO/CO2 cannot only be more efficient, but will thus arise from deeper layers.


These properties can also be related to the fractal nature of radiative mixing layers. Recently, Fielding et al. (2020) showed that the area of the cooling surface in radiative mixing layer simulations obeys a fractal scaling, with
(31)$$\begin{eqnarray*}
\frac{A_{\rm T}}{A_{\rm L}} = \left(\frac{\lambda }{L} \right)^{2-D},
\end{eqnarray*}$$where λ is the smoothing scale and D = 2.5 was the fractal dimension argued to hold by analogy with well-known fractals, and verified in their simulations. Turbulence combustion fronts are indeed well known to be fractals, due to the dynamical self-similarity of turbulence in the inertial range. Experimental measurements by e.g. instantaneous laser tomography have given values ranging from D = 2.1−2.4 in a variety of flow geometries, with a preferred value of D = 2.35 (Hentschel & Procaccia 1984; Sreenivasan, Ramshankar & Meneveau 1989); it has been argued that this fractal dimension is universal (Catrakis, Aguirre & Ruiz-Plancarte 2002; Aguirre & Catrakis 2005). From equation (19), the fractal dimension can be used to calculate the turbulent flame speed (Gouldin et al. 1986; Peters 1988). The fractal scaling and consequent increase in area AT should extend all the way down to the Gibson scale λG, which is defined to be the scale where the turbulent velocity equals the laminar flame speed, v(λG) = SL. This is often unresolved in simulations. If we use the Kolmogorov scaling v∝λ1/3, then we obtain:
(32)$$\begin{eqnarray*}
\frac{S_{\rm T}}{S_{\rm L}} = \frac{A_{\rm T}}{A_{\rm L}} = \left(\frac{\lambda _{\rm G}}{L} \right)^{2-D} = \left(\frac{u^{\prime } }{S_{\rm L}} \right)^{3(D-2)} ,
\end{eqnarray*}$$where we have used equation (31) and v(λG) = SL. Thus, in equation (20), we have n = 3(D − 2). The experimental value of D = 2.35 gives n = 1.05, in good agreement with Damköhler’s scaling, and fair agreement with the scaling in equation (23). The Fielding et al. (2020) value of D = 2.5 gives n = 1.5, or ST = u′(u′/SL)1/2. If one uses the laminar $S_L \propto t_{\rm cool}^{-1/2}$ from our static simulations, this would imply $S_T \propto t_{\rm cool}^{1/4}$. However, in the Fielding et al. (2020) model, the speed at which a cooling layer advances is $S_L \propto t_{\rm cool}^{1/2}$, so they end up with $S_T \propto t_{\rm cool}^{-1/4}$ as well. The scalings are sensitive to the fractal dimension D and the measurement error on D obtained from the simulations is unclear at this point. In addition, the cutoff scale of turbulence may not be the Gibson scale. We caution that fractal arguments have not proven to be fully robust in the turbulent combustion context. For instance, the measured fractal parameters fluctuate depending on the extraction algorithm, and have not been able to correctly predict the turbulent burning velocity (Cintosun, Smallwood & Gülder 2007).


Type 1 AGN (NLSy1, quasars) and aligned CB-SMBH models expected signatures. Two SMBH and their BLRs induce more rich and complex differential phase patterns. There are many configurations for which the aligned CB-SMBH differs between them and single SMBH. The features of synthetic spectra given in Figs. C.2b and C.2c show a similarity with those found in 3C 390.3 (Landt et al. 2014, see their Fig. A1). This object is well-known as a double-peaked line emitter in the optical band. The double-peaked profiles can be also associated with accretion disc emission (Eracleous & Halpern 1994, 2003; Gezari et al. 2007). However, if the binary model is appropriate for this object, then associated differential phases will have a complex double S-shaped structure. This model reflect the possibility of a non-coplanar CB-SMBH, with highly inclined orbits of clouds in both BLRs. If a single SMBH model with a BLR d of 95 light days is true (see Shapovalova et al. 2010b) a differential signal would be 0.9°. Even that spectral lines of objects can share some characteristics, our model predicts that corresponding differential phases are distinct because of different SMBH and the clouds’ orbital parameters. The optically bright quasar PG 1211+143 (Landt et al. 2014) has a convex Paα shape slightly depressed of the centre, as in our synthetic case present in Fig. C.2a. The predicted differential phase would resemble an asymmetric double S shape, caused by non-coplanarity of the CB-SMBH system and high values for the clouds’ orbital elements Ωc and ωc. Moreover, the high rise spectral line in Fig. 5a is also observed in the spectrum of SDSSJ032213.90+005513.4 (Kim et al. 2010, see their Fig. 1). If the CB-SMBH model is appropriate for this object, then the expected differential phase would be similar in morphology with the previous case but distinct in their details because of different values of Ω2. In addition, asymmetric two horn feature (blue line) found in Fig. C.3b, is also highly consistent with observed line in Mrk 79 (Landt et al. 2008, see their Fig. 13). Anticipated differential phases differ from those seen in previous cases because of large values, 230°  Ω1, Ω2   330° , and decreasing ωk, k = 1, 2.


The large values of α (significantly larger than unity) observed in clouds of low column densities or masses are often interpreted in terms of the presence of a large external confining pressure (P/

 e.g., Keto & Myers 1986; Oka et al. 2001; Field et al. 2011; Leroy et al. 2015; Traficante et al. 2018a), although it is hard to imagine that such high pressures can be thermal in general, since the mean ambient thermal pressure in the interstellar medium (ISM) is rather low,

, and large deviations from it occur very infrequently (e.g., Boulares & Cox 1990; Jenkins 2004; Jenkins & Tripp 2011). Instead, it is most likely that these values correspond to ram pressure, in which case they imply mass, momentum, and energy flux across Eulerian cloud boundaries, or a displacement of Lagrangian boundaries (Ballesteros-Paredes et al. 1999; Banerjee et al. 2009). Indeed, in a previous study (Camacho et al. 2016), we find, through measurement of the mean velocity divergence within the clouds in numerical simulations of cloud formation and evolution, that roughly half the clouds with an excess of kinetic energy are undergoing compression. This can be interpreted as the clouds being subject to a ram pressure (which amounts to an inertial compression) that is making them denser and smaller, so that they eventually will become gravitationally bound. The origin of this ram pressure can be large-scale turbulence, a large-scale potential well, or other instabilities. Furthermore, one important possibility is that clouds may be falling into the potential well of a stellar spiral arm, which is the main source of large-scale compression for the gas in the Galactic disk (Roberts 1969). Thus, this is not really a “confinement,” since the clouds are not at rest. The same goes for the other half of the clouds, which are undergoing expansion. In this case, the excess of kinetic energy corresponds to the expansion motions, and again the cloud is not confined, so there is no need for a high confining pressure. In Camacho et al. (2016) and Ballesteros-Paredes et al. (2016, hereafter BP+18) it has been suggested that, for clouds formed by inertial compressions in the background medium (Ballesteros-Paredes et al. 1999), and which gradually become more strongly gravitationally bound, while the inertial compressive motions decay or dissipate, the kinetic energy transits from being dominated by the inertial motions to being dominated by the gravitationally driven motions (see also Collins et al. 2012). In that case, an initial decay of the Larson ratio and the virial parameter may be expected.


The identification and confirmation of extragalactic SNRs are mainly done using data from the radio (Lacey, Duric & Goss 1997; Hyman et al. 2001; Lacey & Duric 2001), visible (Matonick & Fesen 1997; Matonick et al. 1997; Gordon et al. 1998; Blair & Long 2004; Sonbas, Akyuz & Balman 2009; Sonbaş et al. 2010), and X-Ray (Pence et al. 2001; Ghavamian et al. 2005) wavelength ranges. Only a few extragalactic SNRs have been identified in the infrared using the [Fe ii] 1.64 $\hbox{$\mu $m}$ emission line (Greenhouse et al. 1997). The radiation of SNRs in different wavelength ranges is under the influence of biases as they cover different aspects of the ISM environment and SNR age and evolution (Pannuti et al. 2000; Leonidaki, Zezas & Boumis 2010; Sánchez-Ayaso et al. 2012; Long 2017). In the radio, only SNR candidates associated with H ii regions are identified, which means that radio SNR samples are biased towards star-forming regions. In the X-Ray, candidates are selected if they display a soft spectrum and if they are associated with an H ii region, which means that X-Ray samples have the same bias than the radio samples and are also biased against SNR candidates with hard spectra and no optical counterparts. In the optical, samples are under the influence of biases privileging the identification of SNRs located in low-density environments. A multiwavelength (X-Ray, optical, and radio) study of SNRs in NGC 300 by Pannuti et al. (2000) revealed 16 new SNRs, 2 in the radio, and 14 in the X-Ray, in addition to the 28 SNRs previously identified in the optical. The lack of new optical detection is explained by the fact that optical SNRs can only be detected when they represent relatively low confusion with other H α emission sources. The optical SNRs found here are generally located well away from star-forming regions. Consequently, SNR samples identified optically are often not complete. Another technique, based on the search for Large-Velocity-Width Sources (LVWS), is used to identify SNRs with optical spectroscopy (Chu & Kennicutt 1986; Castaneda, Vilchez & Copetti 1990). While H ii regions show low-velocity dispersion (σv ≤ 30 km s−1; Melnick 1977; Gallagher & Hunter 1983), broad emission line widths observed in the LVWS can be caused by stellar winds or SN. Using this technique, Chu & Kennicutt (1986) discovered four LVWS inside the Giant H ii regions NGC 5471 A, B, C, and NGC 5461 in the nearby galaxy M101.