But if, as our studies in this Letter indicate, microstreams might be the result of accumulated and persistent velocity enhancements resulting from a series of switchbacks, then it could be that individual switchbacks result from coronal jets, and the microstreams are a consequence of a series of such jet-driven switchbacks occurring in close succession. Thus, this would be a modification of the idea put forth by Neugebauer (2012) whereby a series of minifilament eruptions capable of producing coronal jets could accumulate and generate a microstream. In fact, homologous jets, continuing for hours at a time, have been commonly observed (e.g., Chifor et al. 2008; Cheung et al. 2015; Panesar et al. 2016a, 2016b; Sterling et al. 2017; Joshi et al. 2017; Paraschiv & Donea 2019; Moore et al. 2021). Under the minifilament-eruption scenario, the multiple minifilament/flux ropes would be ejected as long as the cancellation continues (Panesar et al. 2016a; Sterling et al. 2017). A swarm of such homologous jets, produced over a several-hour time period, conceivably could account for a microstream peak. Additionally, there is some recent evidence (Bale et al. 2021; Fargette et al. 2021) that switchbacks have an extent similar to the scale size of supergranules (∼30,000 km). Measurements of the lengths of the erupting minifilaments that produce jets range from ∼8000 km (Sterling et al. 2015) to ∼18,000 (Panesar et al. 2016a), and thus of similar order to (albeit somewhat smaller than) a typical supergranule diameter. Fargette et al. (2021) also found switchbacks to occur on another size scale, one that approximately corresponds to the size of photospheric granules, ∼1000 km. Chromospheric spicules have widths of some fraction of this size, and thus their observation could be consistent with some spicules resulting from the minifilament-eruption-jet mechanism as suggested in Sterling & Moore (2016), and then those spicules making smaller-scale switchbacks as suggested in Sterling & Moore (2020).


Figure 2 gives an overview of particle and solar wind parameters observed during a time span of 8 days before the electron event under consideration. The data seem to show no evidence for a CME and a related interplanetary shock. The solar wind speed, which had a low value of ∼300 km s−1, starts to rise gradually after October 14 and reaches a maximum of ∼650 km s−1 on October 19. At the same time the magnetic field strength and the proton density drop to low values. These variations are a typical signature of the presence of a CIR, i.e., a fast solar wind stream running into a slow solar wind stream and building up a compression region at a radial distance from the Sun of ∼2 au, or between ∼2.7 and 3 au along the field line connecting to the Sun (e.g., Gosling & Pizzo 1999, see Figure 3). The gradual increases in low-energy electron and proton fluxes (see the upper panel of Figure 2) could be caused by particle acceleration at the CIR (Giacalone et al. 2002). We found that on http://www.srl.caltech.edu/ACE/ASC/DATA/level3/ a pair of stream interaction regions (SIRs) is listed for 2002 October 14–15, and that the Harvard–Smithsonian Center for Astrophysics Interplanetary Shock Database (https://www.cfa.harvard.edu/shocks/) does not report any interplanetary shocks during 2002 October 12–20. We therefore conclude that the reflection of electrons in the 2002 October 20 event is likely due to—depending on their pitch angle—scattering or mirroring at a CIR-related compression, and not due to interaction with an interplanetary shock or propagation in a CME-related loop structure. Malandraki et al. (1997) described a technique for estimating the radial distance at which the magnetic compression arises due to stream–stream interaction by mapping the observed time variation of the solar wind speed back to the solar corona. Applying this method using the observed time profile of the solar wind speed (second panel of Figure 3), we estimate the reflectivity to be located at a radial distance of 1.9–2.1 au, corresponding to a distance along the field line connecting to the Sun of ∼2.4–2.7 au.


We repeated the plasma pressure calculation presented by Schwadron et al. (2011) and Fuselier et al. (2012) for the new ENA energy spectrum. The results for the downwind hemisphere and for the Voyager 1 region are summarized in Table 3. The measured intensity

j

ENA

 of neutralized hydrogen at a given energy translates into a pressure of the parent ion population in the heliosheath times the integration length along the line of sight, ΔP × l, in the following way:
3

Δ
P
×
l
=

4
π

3

n

H

m

H

v

j

ENA

(
E
)

σ
(
E
)

Δ
E

c

f

4

c

f

=

(
v
+

u

R

)

2

v

4

(

v

2

+
4

u

R

2

+
2

u

R

v
)
.

In Equation (3), ΔE denotes the width of the respective energy bin; for the typical radial velocity of solar wind in the flanks and the downwind hemisphere of the inner heliosheath, we assumed uR = 140 km s−1 as measured by Voyager 2, whereas uR = 40 km s−1 for the heliosheath in the Voyager 1 direction (Schwadron et al. 2011; Gloeckler & Fisk 2015). For the density of neutral hydrogen in the inner heliosheath a constant nH = 0.1 cm−3 is assumed (Schwadron et al. 2011; Gloeckler & Fisk 2015). The charge-exchange cross section between protons and neutral hydrogen decreases from (4 to 2) × 10−15 cm−2 for 0.015 to 1.821 keV (Lindsay & Stebbings 2005). The integration length l for ENA production in the plasma is approximately the thickness of the inner heliosheath. The part of Equation (3) without the velocity factor cf can be interpreted as stationary pressure. The total pressure or dynamic pressure is the stationary pressure times this factor. Integrating over all energy bins in Table 3, we obtain the total plasma pressure times heliosheath thickness as P × l = 304 pdyn cm−2 au for the downwind hemisphere and 66 pdyn cm−2 au for the Voyager 1 region (1 pdyn cm−2 au = 0.015 N m−1). If we want to put these numbers into the context of other studies, we face two problems. First, the uncertainty of the total pressure is large given the upper limits in the two lowest energy bins. Second, heliosheath plasma more energetic than 2 keV will produce ENAs that cannot be detected with IBEX-Lo. We therefore used the observed median j = 0 cm−2 sr−1 s−1 keV−1 for heliospheric ENAs in the two lowest energy bins of IBEX-Lo and relied on the study by Livadiotis et al. (2013). They compared the expected plasma pressure from a kappa distribution of protons with the plasma pressure derived from IBEX-Hi energy spectra: the energy range between 0.03 and 2 keV, roughly corresponding to the IBEX-Lo range, covered more than half of the total plasma pressure predicted from a kappa distribution. The authors found a total plasma pressure of P = 2.1 pdyn cm−2 for all sky directions except for the ENA Ribbon. Gloeckler & Fisk (2015) presented a multi-component plasma model for the heliosheath to explain Voyager and IBEX observations. At low energies they assumed the ENA energy spectra provided by Fuselier et al. (2012). They derived a total pressure of 2.5 pdyn cm−2 in all three plasma regions in the nose of the heliotail (Gloeckler & Fisk 2015). Pressure contributions from the slowed solar wind, magnetic pressure, and the pressure exerted from pickup ions and anomalous cosmic rays all had to be taken into account to obtain this total pressure.


This paper presents a new 3D RT code, RAdiation SCattering in Astrophysical Simulations (RASCAS), which was designed to construct accurate multi-wavelength mock observations (spectra, images, or datacubes) from high-resolution simulations. RASCAS deploys a general two-step methodology (e.g. Hummels et al. 2017; Barrow et al. 2017). The first step consists in extracting all relevant information from the simulation outputs: (1) the information concerning the medium through which light will propagate, and (2) the information concerning the sources of radiation. Point (1), for example, determines the number density of H I atoms, their thermal velocity dispersion and bulk velocity, and the dust density, everywhere in a chosen volume. Fully coupled radiation-hydrodynamic simulations would naturally provide the information about ionised states, but retrieving this information in pure hydrodynamic simulations may be tricky. In such case, it is necessary to process the simulation outputs with additional software and models, typically with CLOUDY (Ferland et al. 2013), as in Hummels et al. (2017) and Barrow et al. (2017), or with independent codes which solve for H and He ionisation by propagating ionising radiation in post-processing (e.g. Li et al. 2008; Yajima et al. 2012). Point (2) is also involved to a greater or lesser extent, depending on the sources. Computing the continuum emission from star particles is relatively straightforward, using spectro-photometric models of stellar populations (e.g. Bruzual & Charlot 2003; Eldridge et al. 2017). However, computing the emission lines from the gas (e.g. in the Lyman-α line or in other nebular lines) again requires a detailed knowledge of the ionisation and thermal state of the emitting species. This may be provided by the simulation code, as is the case for H and He with RAMSES-RT (Rosdahl et al. 2013), or it may be necessary to post-process the simulation to estimate the emissivities of the gas. This first step is very simulation- and model-dependent, and RASCAS chooses to encapsulate it in a simulation-plugin module and to implement two stand-alone pre-processing codes which generate an adaptive mesh with all the needed physical information about the gaseous medium, and the initial conditions for light emission in the form of lists of photon packets. These datasets, which could easily be generated from other simulations with any post-processing code, serve as inputs to RASCAS to perform the radiative transfer computation.


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


The study of the variations in chromospheric flux using Ca-K spectral line at all time-scales is important to study the solar dynamo because of relation between the Ca-K line and the magnetic fields on the Sun (Leighton 1964; Skumanich, Smythe & Frazier 1975; Sivaraman & Livingston 1982; Ortiz & Rast 2005). Short time-scale variations provide the information about the dynamics and energy transport in the chromosphere whereas the long period variations provide valuable knowledge about the dynamo process. The observed Ca-K line irradiance variation with solar cycle is due to the contribution of various features such as plages, enhanced, active and quiet network to the flux. Also, the flux modulation occurs because of varying contribution with latitude due to limb darkening. Irradiance variations in Ca-K line have been studied by many researchers using long series of spectroheliograms obtained at Kodaikanal, Mount Wilson, Sac Peak and other observatories (Ermolli et al. 2009; Foukal et al. 2009; Tlatov, Pevtsov & Singh 2009; Priyal et al. 2013, and references therein) using plage areas as a proxy to the chromospheric irradiance variation. Worden, White & Woods (1998) analysed 1400 spectroheliograms obtained at the National Solar Observatory, Sac Peak spread between the period of 1980–1996 to identify the different features such as plages, enhanced, active and quiet network using the intensity contrast technique to study the rotational modulation and solar cycle variations in the chromosphere. Walton, Preminger & Chapman (2003) concluded that faculae are responsible for 80 per cent of the solar cycle variations whereas Ermolli, Berrilli & Florio (2003) estimated that during the ascending phase of the solar cycle (1996–2002) the network contributed 40–50 per cent to the solar cycle variations. Following this work Priyal et al. (2013) digitized the spectroheliograms obtained at Kodaikanal Observatory and analysed the data for three solar cycles (1955–1985) and found good correlation with the Mount Wilson data and sunspot number.


In this paper, we report on spectroscopic CH3CN, CH3OH (methanol), and dust continuum observations with the Atacama Large Millimeter/submillimeter Array (ALMA) at 349 GHz with an angular resolution of 0′′.1. We exploit the CH3CN (19K–18K) K-ladder, with excitation energies ranging from 168 K (for K = 0) to 881 K (for K = 10), to probe, at different radii, the physical conditions in the accretion disk of an early-type young star. We targeted the star-forming region G023.01−00.41, at a trigonometric distance of 4.59

$^{+0.38}_{-0.33}$

−0.33

+0.38

 kpc from the Sun (Brunthaler et al. 2009), where we recently revealed the accretion disk around a young star of 104.6 L⊙, corresponding to a ZAMS star of 20 M⊙ (Sanna et al. 2019, their Fig. 1); the disk was imaged by means of spectroscopic ALMA observations of both CH3CN and CH3OH lines at 0′′.2 resolution inthe 230 GHz band. The disk extends up to radii of 3000 au from the central star where it warps above the midplane; here, we resolve the outer disk regions in two apparent spirals projected onto the plane of the sky. We showed that molecular gas is falling in and slowly rotating with sub-Keplerian velocities down to radii of 500 au from the central star, where we measured a mass infall rate of 6 × 10−4 M⊙ yr−1 (Sanna et al. 2019, their Fig. 5). The disk and star system drives a radio continuum jet and a molecular outflow aligned along a position angle of 57°, measured east of north (Sanna et al. 2016, their Fig. 2); their projected axis is oriented perpendicular to the disk midplane whose inclination with respect to the line-of-sight was estimated to be less than 30° (namely, the disk is seen approximately edge-on; Sanna et al. 2014, 2019). Previously, we also measured the average gas conditions over the same extent of the whole disk, by means of Submillimeter Array (SMA) observations of the CH3CN (12K–11K) emission, and we estimated a kinetic temperature of 195 K and CH3CN column density of 5.1 × 1016 cm−2 (Sanna et al. 2014, their Fig. 2 and Table 4).


In the last two decades UV, EUV, and X-ray observations from space made it possible to estimate the total mass of prominences reliably without needing to solve problems that occur when using visible light as was described in the previous paragraph. One possibility would be to estimate column mass of hydrogen and/or helium plasma in prominences using spectral observations of UV and visible lines of hydrogen and helium (Balmer and Lyman lines) and sophisticated models in which plasma is assumed not being in the state of local thermodynamic equilibrium (NLTE models; see e.g. Labrosse et al.2010, and references therein). The problem can be a rather high complexity of such NLTE models which depend on various free parameters. Another possibility is to infer column mass and subsequently the total mass from the amount of radiation absorbed by the photoionisation in the prominence plasma at resonance continua of hydrogen and helium. This estimation of the mean column mass of prominences observed near the limb was first made by Kucera et al. (1998) using extreme-ultraviolet (EUV) observations from the Coronal Diagnostic Spectrometer (CDS; Harrison et al. 1995) on board the Solar and Heliospheric Observatory (SoHO) satellite. The advantage of the observations used by Kucera et al. (1998) was that CDS as a spectrograph observed only in spectral lines of interest, but spectrographs are able to obtain spectra from only one slit position during one exposure. Larger fields of view can be scanned by the spectrograph slit, as the CDS does, for example, but in such a case, intensities in different slit positions the scan is composed of were obtained at different times. In contrast, in filtergrams, intensities in all positions of the field of view are obtained at the same time, but the filter has transmission of certain width which can be wider than the spectral line of interest. The first estimation of the prominence mass using filtergrams was made by Golub et al. (1999) using Transition Region and Coronal Explorer (TRACE1) data. Similar studies were made by Gilbert et al. (2005, 2006) using observations of EUV Imaging Telescope (EIT; Delaboudinière et al. 1995) on board SoHO in the 195 Å channel. In those two works it was shown that it is necessary to estimate an amount of coronal emission behind and in front of the prominence (hereafter referred to as background and foreground radiation, respectively) to determine correctly the amount of absorbed radiation. The foreground radiation can be measured at the darkest place at a prominence, where it is assumed that all radiation from behind the prominence was absorbed. Then, the background radiation can be derived from the total coronal emission at the prominence location. Two ways to estimate the total emission were proposed and used. The spatial interpolative approach uses interpolation from intensities measured in the corona near a prominence. The temporal interpolative approach is suitable only for erupting prominences and it uses measurements of intensity in place of prominence after its eruption. In the work of Williams et al. (2013) these two approaches are also used to estimate the column mass of material returning to limb after prominence eruption. They used observations from the Atmospheric Imaging Assembly (AIA) instrument (Lemen et al. 2012) on board the Solar Dynamics Observatory (SDO) in several EUV coronal channels of wavelengths below 228 Å (head of the resonance continuum of He ii).


where a is the area of the i, j pixel (constant for a regular grid), μ is the anglebetween the surface normal and the line of sight to the observer, ϕ is the polar angle of a system with the origin at the disk center, F is the total stellar flux, and q and u are normalized Stokes parameters. We note that the relative flux is normalized to the total flux of an unspotted photosphere in our analysis. The center-to-limb variations ofintensity I(μij) and polarization P(μij) were found through trilinear interpolation using the look-up tables from Kostogryz & Berdyugina (2015) and Kostogryz et al. (2016), according to the selected wavelength, surface gravity, and temperature of a star. Kostogryz & Berdyugina (2015) calculated the tables for continuum spectra of FGK stars (Teff = 4500 K–6900 K, log g = 2.0–5.0, and wavelength range 4000–7000 Å) for the Phoenix grid of plane-parallel models, and in Kostogryz et al. (2016) similar calculations were made for a wider range of models (Teff = 4000 K–7000 K and log g = 1.0–5.5) assuming a spherical stellar atmosphere. In addition, we used unpublished data on intensity and polarization variations for both plane-parallel and spherical cooler models with temperatures down to 3000 K, obtained with the same code by Kostogryz (2016, priv. comm.). It should be noted that these data for cooler stars do not include atomic and molecular absorption lines, which can lead to overestimated polarization values, especially for blue wavelengths and for dwarfs with higher surface gravities (depending on the selected wavelength). Evidently, a proper spectrum synthesis code is needed to calculate the intrinsic polarization for these cases. However, the depolarizing effect from absorption lines may not be very significant because when the absorption line suppresses the polarization, the intensity is also reduced. In turn, this will affect the normalized polarization parameters that we calculate less strongly. Additionally, coherent scattering processes, especially in molecular bands, as seen on the Sun (e.g., Berdyugina et al. 2002) probably increase polarization further, which counteracts the effect of the absorption lines.


White dwarfs (WDs) are the end state of stars with mass ≲8M⊙. A WD attains its stable equilibrium configuration by balancing the outward force due to the degenerate electron gas with the inward force of gravity. If the WD has a binary companion, it pulls out matter from the companion, and as a result, the mass of WD increases. Once the mass of the WD reaches the Chandrasekhar mass limit (Chandrasekhar 1931; ∼1.4M⊙ for carbon–oxygen nonrotating, nonmagnetized WDs), the pressure balance no longer sustains, and the WD bursts out to produce a Type Ia supernova (SN Ia; Choudhuri 2010). The similarity in peak luminosities of SNe Ia is used as one of the standard candles to estimate the luminosity distances for various astronomical and cosmological objects (Lieb & Yau 1987; Nomoto et al. 1997). However, recent discoveries of various under- and overluminous SNe Ia question the complete validity of considering luminosities of SNe Ia as standard candles. SNe Ia such as SN 1991bg (Filippenko et al. 1992; Mazzali et al. 1997), SN 1997cn (Turatto et al. 1998), SN 1998de (Modjaz et al. 2001), SN 1999by (Garnavich et al. 2004), and SN 2005bl (Taubenberger et al. 2008) were discovered with extremely low luminosities, which were produced from WDs with 56Ni mass content as low as ∼0.1M⊙ (Stritzinger et al. 2006). On the other hand, a different class of SNe Ia, such as SN 2003fg (Howell et al. 2006), SN 2006gz (Hicken et al. 2007), SN 2009dc (Yamanaka et al. 2009; Tanaka et al. 2010; Silverman et al. 2011; Taubenberger et al. 2011; Kamiya et al. 2012), SN 2007if (Scalzo et al. 2010; Yuan et al. 2010; Scalzo et al. 2012), SN 2013cv (Cao et al. 2016), and many more was discovered with an excess luminosity, with the observed mass of 56Ni as high as ∼1.8M⊙ (Kamiya et al. 2012), violating the Khokhlov pure detonation limit (Khokhlov et al. 1993). It was inferred that these underluminous SNe Ia were produced from WDs with a mass ∼0.6M⊙ (Mazzali et al. 1997; Turatto et al. 1998), while the same for overluminous SNe Ia could be ∼2.8M⊙ (Scalzo et al. 2010; Kamiya et al. 2012). Hence, these progenitor WDs of peculiar SNe Ia violate the Chandrasekhar mass limit: the underluminous SNe Ia were produced from sub-Chandrasekhar limiting-mass WDs (WDs burst before reaching the mass ∼1.4M⊙), and the overluminous SNe Ia were produced from super-Chandrasekhar limiting-mass WDs (WDs burst well above the mass ∼1.4M⊙). These new mass limits are important, as they may lead to modifying the standard candle.


Blaauw (1961) hypothesized that runaway stars are created when a massive component within a binary system explodes as a Type II supernova. The secondary is then ejected with a velocity comparable to the orbital velocity at the time of the supernova event. The explosion may not disrupt the system (Hills 1983), which will be observed as a OB-neutron star/black-hole system and eventually become a high-mass X-ray binary. Given that D2–EB is a double-lined O-type binary, it is unlikely that such a mechanism took place. Alternatively, D2–EB could have been part of a triple system including a very massive component (≥85 M⊙) with a lifetime of less than 4.5 Myr. However, the inferred radial velocity curve lacks evidence of a low-mass third companion, unless it orbits with a high eccentricity and/or long period. Observations of D2–EB over a longer time span than the data presented here are required to investigate the possibility of a third body in the system. Poveda et al. (1967) suggested that runaway stars are dynamically ejected due to encounters of collapsing protostars in/near the core of young clusters. Interactions in clusters that contain initial hard binaries increase the number of escapees via binary-binary interactions (Mikkola 1983). The less massive binary system reaches peculiar space velocities up to ~200 km s-1, while the more massive system travels at a speed less than ~100 km s-1 (Leonard & Duncan 1988). The binary frequency for runaways with V∞> 30 km s-1 is predicted to be 10% and it is striking that systems hosting components of M ~ 20 M⊙ as the most massive members are not predicted to escape with more than 50 km s-1 (Leonard & Duncan 1990). This does not conflict with the observed lower limit for the space velocity of D2–EB. A young, dense cluster core increases the possibility of dynamical ejection, with the consequence that the kinematic age of the runaways is similar to the age of the cluster (Gualandris et al. 2004). In this case, the unreasonably low estimated value for the tangential velocity of D2–EB makes the possibility of the dynamical ejection through binary-binary interaction unlikely.


Despite the considerable scatter in both colors and color gradients (Peletier & Balcells 1996; Taylor et al. 2005; Roediger et al. 2011a), the tight correlation between color and stellar mass of the host galaxies holds true in both the region identified as intermediate and outer in Sect. 7. ETGs form a tight red sequence (see Fig. 10) for both regions and show an average inside-out gradient of ~0.1 mag (Fig. 12, bottom). LTGs form instead two different distributions: the blue cloud of the intermediate (or bulge/bar) region becomes red (i.e., it reaches the red sequences) above 1010 M⊙ while the outer, disk-dominated region never overlaps completely the red sequence. Still, more massive disks are redder than their lower mass counterparts but the difference between the colors of the outer and the intermediate region increases with respect to the total stellar mass. This can be possibly induced by the growth of a red and dead structure in the center of massive disks, i.e. that the central part of galaxies underwent a star formation quenching process that turned them red. Our results on the average properties of color profiles broadly agree with literature data. For example MacArthur et al. (2004) have shown that the radial profile of the average ages of the stellar populations decreases from inside out and that the steepness of the decrease is a function of morphological type. Color templates shown in Fig. 9 exhibit a radial behavior fully consistent with the average age profiles shown by MacArthur et al. (2004). We find there is also a good agreement with the (g−H) color profiles published in Roediger et al. (2011a) for almost all the morphological types, although in their median profiles of early disks they find positive color gradients (and consistently positive age population gradients in their stellar population analysis, Roediger et al. 2011b) that we do not see. Roediger et al. (2011b) do not find any direct link between galaxy morphologies and the observed stellar population gradients. On the contrary, studies such as Cheung et al. (2013) and Gavazzi et al. (2015) have shown that the bar occupation fraction rises steeply above 109.5 M⊙ (as also confirmed by the works done by  Skibba et al. 2012; Masters et al. 2012) and that, above this mass,galaxies are progressively more quenched (red) in their centers, while their disks still sustain SF and hence are blue. These studies therefore highlight that the presence of structures such as bars can indeed produce the color gradients that we observe and likely also the stellar population gradients. These authors thus conclude that a secular bar drives the quenching of the star formation in the central kiloparsecs of galaxies. Moreover massive galaxies undergo bar instability earlier than their lower mass counterparts and thus have more time to grow redder than low mass systems. Moreover, Méndez-Abreu et al. (2012) on a study of the Virgo bar fraction have shown that this rises up to more than 50% above 1010 M⊙, adding a further link between color/stellar populations radial gradients that we observe and structures such as bars (Laurikainen et al. 2010). We stress, however, that disk instabilities can also rejuvinate the central stellar population by, e.g., triggering central star formation in correspondence of the ILRs of spirals or bars (an example could be the one of VCC 508 in Fig. 3a).


Among the existing IACT systems, HESS has the largest FoV and hence provides the highest sensitivity for the diffuse γ-ray flux. Its electron spectrum analysis technique could be directly used to obtain a measurement of the diffuse Galactic γ-ray flux above energies of several TeV in the Galactic Ridge (|l|  30°, |b|  2°) region; see Figs. 3 and 4. A multi-year exposure of HESS could be sufficient for detection of the diffuse emission even from regions of higher Galactic latitude. This is illustrated in Fig. 5, where thick blue and red data points show mild high-energy excesses of the electron spectra derived by Kraus (2018), Kerszberg et al. (2017), Kerszberg (2017) over broken power-law models derived from the fits to lower energy data. Comparing these excesses with the level of the IceCube astrophysical neutrino flux and with the Fermi/LAT diffuse sky flux from the region |b| > 7° (corresponding to the data selection criterium of HESS analysis Kerszberg et al. 2017; Kerszberg 2017) we find that the overall excess flux levels are comparable to expected diffuse γ-ray flux from the sky region covered by the HESS analysis (the quoted systematic error on the electron flux is Δlog(EFE) ≃ 0.4). The overall excesses within 805 and 1186 h of HESS exposures (Kraus 2018; Kerszberg 2017) are at the levels of >4σ for the analysis of Kraus (2018) and 1.7σ for the analysis of Kerszberg (2017). A factor-of-ten longer exposure (which is potentially already available with HESS) could reveal a higher significance excess at the level of up to 5σ. Such an excess is predicted in a range of theoretical models including interactions of cosmic rays injected by a nearby source (Andersen et al. 2018; Neronov et al. 2018; Bouyahiaoui et al. 2019) or decays of dark matter particles (Berezinsky et al. 1997; Feldstein et al. 2013; Esmaili & Serpico 2013; Neronov et al. 2018) or a large-scale cosmic ray halo around the Galaxy (Taylor et al. 2014; Blasi & Amato 2019).


Simon & Leighton (1964) described supergranulation as a system of atmospheric currents in the photosphere. The currents form a cellular network, which is visible in Doppler maps after the reduction of other larger scale flows (e.g. differential rotation and convective blueshift). Inside the cells, the flow is radially directed from the cell centre to its boundary. The diameters of supergranules are in the range of 10 Mm up to 45 Mm (Simon & Leighton 1964; Roudier et al. 2014; Orozco Suárez et al. 2012). Depending on the method, different values are measured (Hirzberger et al. 2008). A mean horizontal velocity of 0.4 km s−1 in supergranules was measured by Simon & Leighton (1964). Orozco Suárez et al. (2012) investigated supergranular convective flows using Fourier local correlation tracking and intergranular magnetic elements. The flow velocity in supergranules increases outwards for larger distances from the centre. After reaching a maximum of 0.35 km s−1, the velocity decreases monotonically. By averaging over 222 976 supergranular cells and applying time-distant helioseismic inversions, Švanda et al. (2014) found a symmetrical flow in supergranules, which is directed radially away from the centre of the cells to its periphery, with horizontal velocities in the range of 0.3–0.6 km s−1. Their velocity profile is found to increase with increasing distances to the supergranule centre up to a maximum value from where on a continuous decrease for larger distances starts. According to Simon & Weiss (1968), the non-stationary cells only survive their turnover time, then the flow lapses into disorder. Supergranular cells have a mean lifetime of 1.5 days, which can extend up to 4 days (Roudier et al. 2014; Hirzberger et al. 2008). De Rosa & Toomre (2004) observed the creation of supergranules due to fragmentation or merging of older cells and stated that each supergranular cell takes part in a minimum of one merging or splitting event during its lifetime. This interaction seems to be the preferred mode of evolution of the observed supergranular pattern. The mechanism of advecting magnetic field elements to the network and the similar appearance suggests a relation between the supergranular pattern and the quiet-Sun magnetic network, as was recognised by Simon & Leighton (1964). De Rosa & Toomre (2004) observed a strengthening or weakening of the network lanes due to splitting or merging of supergranules. Although there is no definite evidence of a one-to-one relation (see review by Rieutord & Rincon 2010 and references therein), in the large-scale picture, the supergranular pattern can be equated with the magnetic network. The horizontal, radially outward directed gas motion of the moat flow, which is visible in Doppler maps, resembles the characteristics of supergranular flows. In addition, magnetic lanes can form around the moat cell due to magnetic features (MMFs), which cross the moat and conglomerate, resembling the magnetic network. This relation has been described by Simon & Leighton (1964), Sheeley (1972), and Vrabec et al. (1974), for example, who proposed the sunspot to be sitting in the centre of a supergranule. Meyer et al. (1974) concluded from the observations that sunspots are related to supergranular convection, but these two flows should be distinguished because of their difference in size and occurrence by taking into account the unique relation of the moat flow to its sunspot. Švanda et al. (2014) found the moat flow to be asymmetric, while flows in supergranules are symmetric, but the investigated cells approximately show the same size. In addition, the authors described the moat cell as a downflow region, while the motion in supergranules shows an upflow−downflow behaviour. Various investigations have been carried out to study the differences and similarities between the moat flow and supergranules (see e.g. Sobotka & Roudier 2007 and the reviews by Solanki 2003 and Rieutord & Rincon 2010 and references therein). An overview of the characteristics of the moat flow and supergranules is given in Table 1.


Neutron star X-ray binaries are an important class of low-mass X-ray binaries to understand the radiative and dynamical configuration of the inner region of an accretion disc. Though from previous studies especially based on RXTE (Rossi X-ray Timing Explorer) data of Z sources, it was known that there must exist a corona/comptonization region to explain the observed hardtail in their X-ray spectra but the exact location and how it changes across the intensity variation is not yet properly understood. Among the two primary categories i.e. Z and Atoll sources, Z sources emit close to the Eddington luminosity (0.5–1.0 LEdd; Done, Gierliński & Kubota 2007a) and they exhibit ‘Z’ and ‘C’ shape intensity variation in the hardness intensity diagram (HID) or colour–colour diagrams (CCDs; Hasinger & Van der Klis 1989; Van der Klis 2006). The Z shape variation constitutes a horizontal branch (HB) at the top, a flaring branch (FB) at the bottom, and a normal branch (NB) connecting them diagonally. These are further classified into two broad groups, namely Sco and Cyg-like sources, due to their different appearance exhibited by the HB and FB i.e. less vertical orientation of HB and a weaker FB is seen among Cyg-like sources than in Sco-like (Kuulkers et al. 1994). The hybrid source XTE J1701–462 occupies a special place among NS LMXBs and is considered to be a remarkable source, as it displays all the characteristics exhibited by both Z and atoll sources (Homan et al. 2010, 2007; Lin et al. 2009). At the brightest state, the intensity variations were associated with HB, NB, and FB of Cyg-like and exhibited Sco-like variation at relatively lower brightness. During the decay phase, the variation closely resembles the soft state of an atoll source and later transits to the hard state of the atoll source just before going to the quiescent state. Many important results were noticed based on the spectral fitting of RXTE data of this source. The mass accretion rate was found to be constant along with the Z phase in Sco-like variation and different mechanisms were proposed to explain the spectral and timing variations during the Z phase variations (Lin et al. 2009). It was also found that mass accretion rate is the important driving parameter during the Z and all along with the atoll phases variation. Z sources are unique probes in the sense they provide a platform to understand the structure of accretion disc emitting close to Eddington luminosity because due to the radiation pressure the structure of the inner region of accretion is affected. The previous studies suggested that the interplay between the accretion disc and comptonization region mutually varies to produce the observed tracks in the HID. However, other physical components like a boundary layer (Popham & Sunyaev 2001) or a transition layer (TL) (Osherovich & Titarchuk 1999a, b; Titarchuk & Osherovich 1999) cannot be ruled out. The comptonization region can be in the form of a quasi-spherical cloud or it could be a base of a jet that causes the observed hard continuum in the X-ray spectrum (Migliari et al. 2007). But its association with dynamical features like various branch oscillations or band-limited noises is not known. The spectra of Z sources can also be explained by a structure known as the boundary layer over the NS surface but again, its association to the observed HBO, NBO, etc., is not properly understood (Popham & Sunyaev 2001; Gilfanov, Revnivtsev & Molkov 2003; Revnivtsev & Gilfanov 2006). Based on the detailed spectral modelling of GX 17 + 2, BL occupies a smaller area at the lower vertex (i.e. bottom of NB) in comparison to its area in other branches (Lin et al. 2012) and the comptonization dominates at the HB branch that fades away as source traverse to the FB. The inner disc radius was found to be moving towards the NS, as the Z track evolves from HB to FB. All these structural and radiative variations are found to be occurring at an almost constant mass accretion rate (Lin et al. 2009, 2012).


In this Letter, we directly test the relationship between proton kinetic instabilities and plasma turbulence in the solar wind using a hybrid expanding box model that allows us to study self-consistently physical processes at ion scales. In the hybrid expanding box model, a constant solar wind radial velocity vsw is assumed. The radial distance R is then

, where R0 is the initial position and

 is the initial value of the characteristic expansion time

 Transverse scales (with respect to the radial direction) of a small portion of plasma, comoving with the solar wind velocity, increase ∝ R. The expanding box uses these comoving coordinates, approximating the spherical coordinates by the Cartesian ones (Liewer et al. 2001; Hellinger & Trávníček 2005). The model uses the hybrid approximation where electrons are considered as a massless, charge-neutralizing fluid and ions are described by a particle-in-cell model (Matthews 1994). Here, we use the two-dimensional (2D) version of the code, fields and moments are defined on a 2D x–y grid 2048 × 2048, and periodic boundary conditions are assumed. The spatial resolution is Δx = Δy = 0.25dp0, where

 is the initial proton inertial length (vA0: the initial Alfvén velocity, Ωp0: the initial proton gyrofrequency). There are 1024 macroparticles per cell for protons that are advanced with a time step

, while the magnetic field is advanced with a smaller time step

 The initial ambient magnetic field is directed along the radial z-direction, perpendicular to the simulation plane

, and we impose a continuous expansion in the x- and y-directions. Due to the expansion, the ambient density and the magnitude of the ambient magnetic field decrease as

 (the proton inertial length dp increases ∝ R; the ratio between the transverse sizes and dp remains constant; the proton gyrofrequency Ωp decreases as ∝R−2). A small resistivity η is used to avoid accumulation of cascading energy at grid scales; initially, we set

 (μ0 being the magnetic permittivity of vacuum) and η is assumed to be

 The simulation is initialized with an isotropic 2D spectrum of modes with random phases, linear Alfvén polarization (

), and vanishing correlation between magnetic and velocity fluctuation. These modes are in the range 0.02 ≤ kdp ≤ 0.2 and have a flat one-dimensional (1D) power spectrum with rms fluctuations = 0.24 B0. For noninteracting zero-frequency Alfvén waves, the linear approximation predicts

 (Dong et al. 2014). Protons initially have the parallel proton beta

 and the parallel temperature anisotropy

 as typical proton parameters in the solar wind in the vicinity of 1 AU (Hellinger et al. 2006; Marsch et al. 2006). Electrons are assumed to be isotropic and isothermal with βe = 0.5 at t = 0.


In order to understand the accretion process and the structure of emitting regions/locations in AGNs, studies of broad-band spectral energy distributions and their temporal variations are necessary. The X-ray emission is produced in the innermost region or above the accretion disc by hot electrons, i.e. corona (Ramos Almeida & Ricci 2017), where ultraviolet (UV) photons are Compton upscattered (Haardt & Maraschi 1993), which results in a power-law continuum above 2 keV. The modified blackbody emission associated with the Keplerian portion of the accretion disc peaks around optical/UV (Sanders et al. 1989; Elvis et al. 1994). Some of the emitted UV radiation is reprocessed in a structure often known as ‘dusty torus’, located around tens of pc scale environment of AGNs, and is re-emitted in infrared/mid-infrared (MIR) (Suganuma et al. 2006; Kishimoto et al. 2007; Burtscher et al. 2013; Ramos Almeida & Ricci 2017; Leftley et al. 2018). Recent studies based on infrared observations with Very Large Telescope Interferometer suggest that the distribution of dust in the torus need not to be confined in a classical thick toroidal structure but possibly originates from two components, i.e. an equatorial thin disc and a hollow dusty cone towards the polar region (see Hönig & Kishimoto 2017; Stalevski et al. 2017, 2019). The hollow dusty cone is probably due to the puffed-up disc caused by the infrared radiation pressure, which releases the inflowing gas from the gravitational potential of the black hole (Hönig 2019). This structure is considered to be an extended polar feature probably from a dusty wind located at the edge of the NLR (López-Gonzaga et al. 2014; López-Gonzaga et al. 2016; Honig & Kishimoto 2017; Stalevski et al. 2017; Leftley et al. 2018). The MIR radiation is also considered to be emitted from this non-classical torus structure (Asmus et al. 2016) and the spectrum is often modelled by a warm component with a blackbody temperature around 300 K (e.g. Edelson & Malkan 1986). The orientation of the dusty molecular obscuring torus plays a key role in the characterization of the distinct classes of AGNs in the unification scheme (for more detail see, Antonucci 1993; Urry & Padovani 1995; Netzer 2015).


In addition to being an important participant in the evolution of galaxies, dust absorption and scattering can significantly alter the appearance of its host galaxy. Dust can absorb a large fraction of the total UV and optical energy emitted in a galaxy and re-radiate it in the IR. The absorbed energy can be re-radiated through several physical processes, each with different observational signatures. Dust emission in the far-IR (FIR) comes from equilibrium heating of dust grains and can be approximately described with a featureless modified blackbody function. However, rich spectral features that are commonly attributed to polycyclic aromatic hydrocarbons (PAHs) seen in the mid-IR emission (Leger & Puget 1984) arise predominantly in a nonequilibrium, single photon, process. Both the broad, featureless FIR and the spectral features of the mid-IR correlate with other galaxy properties, providing insight into the underlying physical processes operating within the galaxy. In local starburst galaxies Engelbracht et al. (2008) found that the equivalent width of the 8 μm aromatic emission complex negatively correlates with the radiation field hardness and positively correlates with metallicity. Gordon et al. (2008) further found that the former correlation is stronger than the latter in M101 H ii regions, suggesting that the variation in the strength of aromatic emissions is due to dust processing, rather than differences in dust formation. The ratio of the total infrared flux (TIR) to the far-UV (FUV) flux correlates with UV spectral slope, β (while the correlation holds for a general definition of TIR, FUV, and β, see e.g., Meurer et al. 1995; Kong et al. 2004 for specific definitions), both across galaxies and within galaxies (Meurer et al. 1995; Calzetti et al. 2005). While the relation is tight for starburst galaxies (Meurer et al. 1999), significant scatter exists for normal star-forming galaxies (Bell 2002). Kong et al. (2004) found that higher β values at a given IR to UV ratio in more quiescent star formation galaxies can be explained in terms of the balance between present and past averaged star formation rate (SFR). Given that β is commonly measured from the Galaxy Evolution Explorer (GALEX) FUV and near-UV (NUV) bands and that the NUV band captures the 2175 Å extinction feature, variation in the 2175 Å feature strength can have a profound impact on β, but separating such variations from the intrinsic behavior of β is challenging with empirical methods.


As the most luminous persistent sources in the Universe, quasars are bright enough to be detected up to redshifts z > 7 (Mortlock et al. 2011; Banados et al. 2018; Wang et al. 2018; Yang et al. 2020). According to the currently accepted model, quasars are extremely luminous active galactic nuclei (AGNs), where the observed intense energy release are related to the accretion of a gaseous disk onto a supermassive black hole (SMBH). Quasars have a wide spectral energy distribution, which normally contains a significant emission component in the optical-UV band LUV, the so-called big blue bump, with a softening at higher energies (Sanders et al. 1989; Elvis et al. 1994; Trammell et al. 2007; Shang et al. 2011). It has long been discussed that there is a nonlinear relationship between LUV and the quasar’s X-ray luminosity LX, parametrized as log(LX) = γlog(LUV)+β (Vignali et al. 2003; Strateva et al. 2005; Steffen et al. 2006; Just et al. 2007; Green et al. 2009; Young et al. 2010; Jin et al. 2012). From the theoretical point of view, this relation could be intrinsic since the UV emission is usually thought to originate from the optically thick disk surrounding the SMBH and the X-ray photons are thought to be generated through the inverse-Compton scattering of these disk UV photons by a plasma of hot relativistic electrons (the so-called corona) around the accretion disk. Such a relation is found to be independent of redshift (Lusso & Risaliti 2016), so that it could be used as a distance indicator to estimate cosmological parameters. The initial dispersion of the LUV − LX relation is relatively large (δ ∼ 0.35−0.4, Just et al. 2007; Young et al. 2010), but after a detailed study, Lusso & Risaliti (2016) suggest that most of the observed dispersion is not intrinsic, but it is rather due to observational effects. By gradually refining the selection technique and flux measurements, Risaliti & Lusso (2019) collected a complete sample of quasars, whose dispersion of the LUV − LX relation is smaller than 0.15 dex. The sample of main quasars is composed of 1598 data points in the range from 0.036  z  5.1. With this sample, they constructed a Hubble diagram of quasars in redshift range of 0.5  z  5.5, which is in excellent agreement with the analogous Hubble diagram for SNIa in the redshift range of 0.5  z  1.4. Moreover, this Hubble diagram of quasars has been studied in cosmological applications (Zheng et al. 2020, 2021). Considering that objects at the same redshift should have the same luminosity distance in any cosmology, here we first fit the model-independent cosmography formula that reflects the Hubble relation between the luminosity distance and redshif using the quasar sample, and then we obtained the distance moduli (also the luminosity distance) for GRBs at a given redshift with the best fit results.


Supernova explosions must be another promising source of gravitational waves. The gravitational waves from a core-collapse supernova have been mainly discussed with the numerical simulations of gravitational collapse of massive star, the bounce of central core, and subsequent accreting matter to the central compact object, i.e. protoneutron star (PNS), produced via supernova (e.g. Murphy, Ott & Burrows 2009; Cerdá-Durán et al. 2013; Müller, Janka & Marek 2013; Ott et al. 2013; Yakunin et al. 2015; Kuroda, Kotake & Takiwaki 2016; Andresen et al. 2017; O’Connor & Couch 2018). For instance, the three-dimensional (3D) numerical simulations for the core-collapse supernova tell us the existence of gravitational wave signals related to the oscillations of PNS (or core region) (Kuroda et al. 2016; Andresen et al. 2019; Radice et al. 2019; Mezzacappa et al. 2020), where the frequency increases with time from a few hertz up to kilohertz after corebounce. This signal is originally considered to be the evidence of the Brunt–Väisälä frequency at the PNS surface, i.e. the so-called surface gravity (g) mode (Cerdá-Durán et al. 2013; Müller et al. 2013), but it may be natural to consider that the signals come from the global oscillations of the PNSs because the Brunt–Väisälä frequency is a local value and depends strongly on the definition of PNS radius. In fact, the gravitational wave signals appearing in the numerical simulations can be identified with the global oscillations, such as fundamental (f-mode) oscillations of PNS (Morozova et al. 2018; Sotani et al. 2019a; Sotani & Takiwaki 2020b, c) or the g-mode-like oscillations in the region inside the shock radius (Torres-Forné et al. 2018, 2019a,b). In addition to the ramp up signals, the 3D simulations tell us the existence of another gravitational wave signal with ∼100 Hz, which seems to be associated with the standing accretion-shock instability (Kuroda et al. 2016; Andresen et al. 2017, 2019; O’Connor & Couch 2018; Radice et al. 2019; Mezzacappa et al. 2020).

O’Connor & Couch 2018
O’Connor & Couch 2018


The fate of the early PWN depends on various parameters such as the spin-down power and baryon loading. If the spin-down power is high enough, some two-dimensional simulations suggest that the equatorial wind can be redirected by the anisotropic pressure, and hoop stresses lead to bipolar outflows10

10
In this case, the (collimated) wind radius is

.
 that could explain GRBs (Bucciantini et al. 2007, 2008; Komissarov & Barkov 2007). If not, we expect a quasi-spherical expanding flow embedded in the expanding stellar material (see Figure 1). Assuming a SN explosion with

 erg, the SN ejecta expands with its velocity

 and radius

. The early PWN radius Rw also increases non-relativistically, which is given by (e.g., Metzger et al. 2014)
7

for

, otherwise

 is used. Note that we have used the ejecta density
8

where δ ∼ 0–1 is a typical value used in the literature (Kasen & Bildsten 2010; Metzger et al. 2014). The mixture of material allows us to approximate the inner density profile to be reasonably smooth and flat (Chevalier 1977; Chevalier & Fransson 1992). For demonstration, we adopt

 throughout this work (Kasen & Bildsten 2010; Metzger et al. 2014), and that the radiation pressure is given by

. Here

 is the PWN volume and

 is the PWN expansion velocity that can be different from

 In general, Rw is smaller than

, and both of

 and Rw are numerically determined in this work. Roughly speaking,

 becomes a good approximation for small values of P such that

 (implying

). The ejecta velocity

 and radius

 can be determined by
9

10

The internal energy trapped in the SN ejecta,

, is given by
11

where

 is the dynamical time. Since X-ray and gamma-ray emission is expected in month-to-year timescales, we only consider energy injection due to

. In the early phase, as in normal SNe, heating by shocks and unstable isotopes such as

Ni can be relevant. In the later phase, one may assume that late interactions with circumstellar material are negligible, and injections via the β decay of

Ni are irrelevant after their lifetime

. Visible photons leave the SN ejecta in the escape time
12

where the Thomson optical depth in the ejecta is given by

, which is estimated to be
13

where

,

 is the mean molecular weight per electron, and mu is the atomic mass unit. See also Equation (45) below. Two of the key parameters,

 and

, can be estimated from the SN peak emission and determination of the ejecta velocity

 via detailed spectroscopy. Note that the bound–free or bound–bound cross section is much higher at

 keV energies, and thermal photons are still generated at later times.


The electronic computations were performed using the molpro (Molpro 2015, http://www.molpro.net) package. In a preliminary work, we used the complete active space self-consistent field (Knowles & Werner 1985; Werner & Knowles 1985) to examine the electronic wavefunction of the HNCO–He complex. These computations showed that this wavefunction is dominantly described by a unique electron configuration (with a weight ≥0.93) over the grid used for the generation of this PES. This justifies hence the use of monoconfigurational ab initio methods. Accordingly, we applied the recently established methodology by Hochlaf and co-workers for mapping multidimensional PESs of weakly bound molecular systems with high accuracy and relatively low computational cost (Lique, Klos & Hochlaf 2010; Halvick et al. 2011; Ajili et al. 2013; Mathivon, Linguerri & Hochlaf 2013; Kalugina et al. 2014; Mogren Al Mogren et al. 2014). Briefly, these electronic computations were carried out using the explicitly correlated coupled cluster method with single, double and perturbative treatment of triple excitations (CCSD(T)-F12) (Adler, Knizia & Werner 2007; Knizia, Adler & Werner 2009) in connection with the augmented correlation-consistent aug-cc-pVTZ basis set of Dunning and co-workers (Dunning 1989; Kendall, Dunning & Harrison 1992). In addition, molpro default choices for the density fitting and resolution of identity basis sets have been applied (Yousaf & Peterson 2008). Benchmarks by Hochlaf and co-workers (Lique et al. 2010; Halvick et al. 2011; Ajili et al. 2013; Mathivon et al. 2013; Kalugina et al. 2014; Mogren Al Mogren et al. 2014) showed that results obtained from this highly correlated approach are close to those deduced using standard coupled cluster techniques extrapolated to the complete basis set (CBS) limit, whereas a strong reduction in CPU time and disc occupancy are observed. For illustration, we performed CCSD(T)/aug-cc-pVXZ calculations (X = D, T, Q, 5) on the HNCO—He cluster. Then the energies were extrapolated to the CBS limit. The comparison between CCSD(T)-F12/aug-cc-pVTZ and CBS calculations is given in Table 1. It shows that the CCSD(T)-F12/aug-cc-pVTZ results are off by 4 per cent (at the maximum) with those deduced from CBS extrapolation. We compare also our results with those done using the CCSD(T)/aug-cc-pV5Z approach. We can clearly see that the CCSD(T)-F12/aug-cc-pVTZ approach offers a good agreement with the CCSD(T)/aug-cc-pV5Z calculations with a very reduced computational cost.


The results of this first exploratory work pave the way to a series of future investigations in which we will broaden the range of initial conditions and study their impact on the empirical parameters defined here. By changing the initial structural properties of the simulated clusters, we will compare the three parameters determined in stellar systems that, after one Hubble time of evolution, have reached different dynamical states. We will also include populations of primordial binaries, which are known to halt the core contraction earlier in the cluster evolution and at lower concentrations (see, e.g., Vesperini & Chernoff 1994; Trenti et al. 2007; Chatterjee et al. 2010). The main differences between the values of A
5, P
5, and S
2.5 in simulations with and without primordial binaries are expected during the advanced phases of the evolution, toward CC and post-CC, when the milder contraction of the clusters with primordial binaries might lead to a different and/or less extreme evolution of these parameters. The study presented here will also be further extended to explore the effects of different retention fractions of dark remnants (neutron stars and black holes; see, e.g., Alessandrini et al. 2016; Giersz et al. 2019; Kremer et al. 2020, 2021; Gieles et al. 2021, for some studies on the dynamical effects of dark remnants). Finally, a forthcoming paper will be dedicated to building nCRDs and determining the three parameters here defined in a sample of observed star clusters. This requires photometric observations (i) with a high enough angular resolution to resolve individual stars even in the innermost cluster regions, (ii) sampling each system at least out to 0.5 × r

h
, and (iii) deep enough to reach a few magnitudes below the MSTO. These requirements are achieved by most HST and adaptive-optics-assisted observations currently available for many GCs, thus making the determination of the three parameters from observations relatively straightforward, although particular care is needed to deal with typical observational difficulties such as photometric incompleteness, differential reddening, and Galactic field contamination. We will discuss the relation between these parameters and other dynamical indicators (in particular, the A
+ parameter measured from BSSs; see the Introduction), thus providing quantitative assessments of the operational ability of the three nCRD diagnostics to distinguish dynamically young GCs from systems in advanced states of dynamical evolution.


NLFFF models have been widely adopted to study magnetic field structures in the solar atmosphere, for instance, magnetic flux ropes (Canou et al. 2009; Su et al. 2009; Canou & Amari 2010; Cheng et al. 2010; Guo et al. 2010a, 2010b; Jing et al. 2010), magnetic null points (Zhang et al. 2012; Sun et al. 2013, 2014), and quasi-separatrix layers (Savcheva et al. 2012, 2015; Guo et al. 2013; Zhao et al. 2014; Yang et al. 2015). Most of them are modeled in Cartesian coordinates, although some models are reconstructed in spherical geometry (Su et al. 2009; Tadesse et al. 2011; Guo et al. 2012) or with tetrahedral meshes (Amari et al. 2014b). In particular, Amari et al. (2014a) has developed another code to fulfill the need for reconstructions on the scale of local active regions within a global extrapolation, using an iterative Grad–Rubin scheme adapted to spherical coordinates. Such a state-of-the-art code resolves an active region in a global model with

 grid points. This contrasts to most earlier modeling efforts, which were limited either to a small field of view (for Cartesian coordinates) or to lower spatial resolution (for spherical coordinates) due to limited computational resources. The data volume and the computation time increase for NLFFF modeling with a large field of view and high spatial resolution simultaneously, which implies a big data problem. On the other hand, we have to use data with high spatial resolution to resolve the small-scale features of the magnetic field, such as small flux tubes and electric current channels. They are crucial for reconstructing the non-potential magnetic field. We also have to consider a field of view as large as possible to include remote magnetic field connections (DeRosa et al. 2009). Since only the bottom boundary is available at present for realistic NLFFF modeling, the magnetic field concentration should be isolated to mitigate any effects of lateral boundary conditions (Wiegelmann et al. 2006). An isolated magnetic field region has magnetic field lines originating from the bottom boundary and connecting back to the bottom. A large field of view is required to fulfill this requirement of having an isolated magnetic domain. When the field of view is large, the curvature of the Sun cannot be neglected and spherical coordinates are recommended (e.g., Guo et al. 2012; Yeates 2014).


Based on indirect evidence, there are two main candidates for the γ-ray emitting region. The first one is close to the BH and the γ-ray emission is produced inside the broad-line region (BLR; e.g., Dermer & Schlickeiser 1993; Blandford & Levinson 1995; Ghisellini & Madau 1996; Georganopoulos et al. 2001; Fan et al. 2006; Bai et al. 2009; Tavecchio & Mazin 2009; Isler et al. 2013; Hu et al. 2015). This argument is supported by constraining the size of the γ-ray emission region through the magnification factor during the γ-ray variability in some gravitationally lensed γ-ray blazars (e.g., Neronov et al. 2015; Vovk & Neronov 2016), the short variability timescales (down to several hours; e.g., Tavecchio et al. 2010), and the sharp breaks at the GeV band seen in the γ-ray spectra of some FSRQs that may caused by the opacity to pair production (e.g., Liu & Bai 2006; Bai et al. 2009; Poutanen & Stern 2010; Stern & Poutanen 2011). The second possible region for the γ-ray production is beyond the BLR (e.g., Błażejowski et al. 2000; Arbeiter et al. 2002; Sokolov & Marscher 2005; Yan et al. 2012; Meyer et al. 2015). Some multi-wavelength observations for the giant flares suggested that both the sub-millimeter and γ-rays are produced 10–20 pc from the BH (e.g., Larionov et al. 2008; Sikora et al. 2008), where it was assumed that γ-ray and radio emission is triggered by shocks propagating along a relativistic jet. The time delay between flares in radio and γ-ray bands combined with the VLBI high-resolution observation on the size of radio core also indicated that the γ-ray emitting region stays in the upstream of, but not far from the radio core (e.g., Jorstad et al. 2010; Marscher & Jorstad 2010; Pushkarev et al. 2010; Agudo et al. 2011b; Fuhrmann et al. 2014; Max-Moerbeck et al. 2014; Ramakrishnan et al. 2016). It is normally believed that γ-ray emission in blazars come from the inverse-Compton (IC) process, where external Compton (EC) plays an important role in LSP blazars, while ISP and HSP blazars (BL Lacs) generally can be explained by the synchrotron self-Compton (SSC; e.g., Krawczynski et al. 2004; Chen & Bai 2011; Kang et al. 2014; Zhang et al. 2014). In the EC process, the seed photons are determined by the location of the γ-ray emitting region, which may be dominated by an accretion disk, BLR, infrared torus, and cosmic background, respectively, if the γ-ray emitting region is located near the BH horizon, inside the BLR, inside the torus, or much beyond of the torus (e.g., Ghisellini & Tavecchio 2009). Kang et al. (2014) compared the seed photons from the BLR and dusty torus in the SED fitting of LSP blazars, and found that the seed photons from torus are preferred based on a

 method. Zheng et al. (2017) also explored this issue using a stratified jet and found that the seed photons from torus provide a better match to the observations.


MSH 11-61A (also known as G290.1-0.8) is a mixed morphology SNR detected from radio to soft X-rays (up to ~3 keV) that was formed by the core collapse of a massive progenitor star (mass ≳25 M⊙;  Filipović et al. 2005; Reynoso et al. 2006; García et al. 2012; Kamitsukasa et al. 2015; Auchettl et al. 2015a). Following these authors, the distance to the SNR is in the range 6−11 kpc; the most recently determined values converge towards 7 ± 1 kpc. We adopt a distance of 7 kpc throughout the paper1. The INTEGRAL source IGR J11014-6103 is located close to MSH 11-61A and is powered by PSR J1101-6101 (Pavan et al. 2011, hereafter Paper I; Tomsick et al. 2012; Pavan et al. 2014, hereafter Paper II; Halpern et al. 2014). The pulsar shows spin-down parameters typical for pulsars of its age: a period of P = 62.8 ms and a pulse period derivative Ṗ = (8.56 ± 0.51) × 10-15 s s-1. The estimated spin-down energy is Ė = 1.36 × 1036 erg s-1 and the surface dipolar magnetic field is 7.4 × 1011 G (Halpern et al. 2014). Previous Chandra observations aimed at the INTEGRAL source showed that PSR J1101-6101 simultaneously powers several outflows: an X-ray and radio PWN, shaped in a narrow cone elongated towards the parent SNR, and an X-ray jet and counter-jet, both oriented nearly perpendicular to the PWN axis (Tomsick et al. 2012; Paper II). The main jet extends for nearly 5′ in the sky, which corresponds to a projected length of ~11 pc, and showed a remarkable helicoidal pattern (see Paper II). Already in the data set analysed in Paper II, indications for a spatial deviation from the helical pattern of the main jet were noticed at a distance of ~50″ from the pulsar. At this position the surface brightness of the jet was low, forming what looked like a gap, but its brightness profile was compatible with expectations of Doppler-deboosting in the jet-helix model. The spatial deviation was therefore not considered significant at the time because the data were hampered by the presence of CCD chip gaps, resulting in only 50% effective exposure in that region. The counter-jet was detected at 3.7σ in the Chandra image and its flux was estimated to be ~5% that of the main jet. The conical shape of the PWN in IGR J11014-6103 was ascribed to the supersonic motion of PSR J1101-6101 in the ISM (Tomsick et al. 2012).


The study of cometary plasma composition has been subjected to a great interest after the ion mass spectrometer onboard Giotto spacecraft detected many peaks in the mass range 12 and 120 amu (Balsiger et al. 1986; Krankowsky et al. 1986; Mitchell et al. 1987; Altwegg et al. 1993). By developing photochemical models, numerous studies focused on comet 1P/Halley explained the observed ion distribution in a water-dominated coma (Allen et al. 1987; Wegmann et al. 1987; Schmidt et al. 1988; Cravens 1989; Bhardwaj, Haider & Singhal 1990, 1996; Gan & Cravens 1990; Ip et al. 1990; Haider, Bhardwaj & Singhal 1993; Häberli et al. 1995; Haider & Bhardwaj 1997, 2005; Bhardwaj 1999; Rubin et al. 2009; Cordiner & Charnley 2014). By making 2 yr of observations, the recent Rosetta space mission on comet 67P/Churyumov–Gerasimenko has revolutionized our understanding of the activity of the cometary coma. During the Rosetta observation period, continuous measurements around the nucleus were helpful to study the evolution of ion and neutral distribution and also the driving photochemical processes in the coma. Several modelling works on this comet have shown that ion composition in the coma varies based on the sublimation rate of the nucleus (Vigren & Galand 2013; Fuselier et al. 2015, 2016; Galand et al. 2016; Heritier et al. 2017, 2018; Vigren et al. 2017; Beth, Galand & Heritier 2019). All these studies show that solar photons are the primary energy source that determines the ion composition in the inner coma. Solar extreme ultraviolet photons having an energy more than 12 eV ionize H2O and produce H2O+, and the collisions among these species quickly lead to the formation of H3O+. The sublimated parent species such as CH3OH, NH3, HCN, HCOOH, and CH3CHO, have high proton affinities compared to that of H2O, causing the loss of H3O+ in the inner coma. Haider & Bhardwaj (2005) developed a comprehensive chemical network to study the ion distribution in comet 1P/Halley. Their calculations show that NH$_4^+$ is the most dominant ion in the inner coma followed by H3O+ and CH3OH$_2^+$ ions. Similarly, the model calculations of Heritier et al. (2017) on comet 67P/Churyumov–Gerasimenko showed that NH$_4^+$, CH3OH$_2^+$, H3O+, H3S+, and HCNH+ are the important ions in the inner coma. They also showed that the densities of these ions vary with the relative mixing ratios of corresponding proton affinity species coming from the nucleus. Even if the mixing ratios of parent species, which have high proton affinity, are very low (2 per cent), they can play a significant role in modifying the ionospheric composition of the inner coma. Hence, the ion distribution in the cometary coma essentially depends on the neutral composition and photochemical reactions.


The main challenge in detecting the cosmological H i signal, common to all of these experiments, is the strong contamination of systematic effects (ionospheric distortion, telescope response, calibration, etc.) and bright foregrounds (Galactic and extragalactic) (Datta, Bhatnagar & Carilli 2009). Foreground sources include diffuse Galactic synchrotron emission (DGSE) from our Galaxy (Shaver et al. 1999), free–free emission from Galactic and extragalactic sources (Cooray & Furlanetto 2004), faint radio-loud quasars (Di Matteo et al. 2002), synchrotron emission from low-redshift Galaxy clusters (Di Matteo, Ciardi & Miniati 2004), extragalactic point sources, etc. Typically, foregrounds are four to five orders of magnitude stronger than the redshifted H i signal (Zaldarriaga, Furlanetto & Hernquist 2004; Bharadwaj & Ali 2005; Jelić et al. 2008; Bernardi et al. 2009; Jelić et al. 2010; Zaroubi et al. 2012; Chapman et al. 2015). There are several different ways to deal with foregrounds, but all the methods rely on the fact that foreground sources have a smooth spectral shape. However, the redshifted H i 21 cm signal has spectral structure (Pritchard & Loeb 2012). In fact, this difference in spectral properties between the strong foreground and faint 21 cm signal can be used favourably for the detection of the cosmological signal (Datta, Bowman & Carilli 2010). Hence, accurate knowledge of the spectral ‘smoothness’ of the foreground becomes critical. Our current study makes an attempt to constrain the spectral behaviour of the foregrounds near the redshifted 21 cm signal frequencies. The three main techniques proposed to overcome foreground contamination are foreground avoidance, foreground removal and foreground suppression. Instead of an isotropic 1D power spectrum, P(k), of H i brightness temperature fluctuation, a cylindrical (2D) power spectrum, P(k⊥, k∥) is a useful diagnostic in terms of foreground avoidance. Spectral smoothness of foregrounds confines the majority of foreground power to low k∥ modes, resulting in ‘foreground wedge’. In the foreground avoidance technique, the EoR signal is searched for outside this wedge, in the so-called ‘EoR window’ (Datta et al. 2010; Parsons et al. 2012; Vedantham, Udaya Shankar & Subrahmanyan 2012; Pober et al. 2013a; Thyagarajan et al. 2013; Dillon et al. 2015). However, errors in calibration of chromatic instruments and insufficient knowledge of the wedge boundary can leak foreground power into the wedge and consequently detection of the 21 cm signal becomes challenging even inside the EoR window. Foregrounds can be modelled very precisely and subtracted from the data set. Also, without any modelling a component analysis method can be used to mitigate foregrounds (for details see Chapman et al. 2012, 2013). The foregrounds can be suppressed by weighting foreground-dominated modes appropriately (Liu & Tegmark 2011).


The oEA stars have pulsation features similar to classical δ Sct stars. However, their pulsations may be influenced by the tidal interaction and mass transfer between the components, as well as gravitational force from companions. Some pulsations in KIC 6220497 can be excited by the tidal forces of the secondary companion. Tidally excited modes occur when the orbital frequency is close to a stellar eigenfrequency in a binary star with an eccentric orbit. The signature of the pulsation modes is the frequencies at integer multiples of the orbital frequency (Welsh et al. 2011; Thompson et al. 2012; Hambleton et al. 2013). We detected four (f6, f11, f20, f24) frequencies that are the harmonics of the orbital frequency, which could be partly affected by imperfect removal of the eclipses from the light curve. Although the orbit of the binary system is circular, these frequencies could result from tidally induced pulsations (Reyniers & Smeyers 2003a,b; Southworth et al. 2011). In the upper panel of Fig. 8, we plot the dominant pulsation period versus the orbital period for 74 oEA stars, including KIC 6220497. The data are taken from the compilations of Zhang et al. (2013, 67 oEA stars) and from more recent literature (Yang, Wei & Li 2014 for FR Ori; Zhang et al. 2014 for OO Dra; Zhang, Luo & Wang 2015a for EW Boo; Zhang et al. 2015b for V392 Ori; Lee et al. 2016 for KIC 4739791; Soydugan et al. 2016 for XZ Aql). In the panel, we can see that the pulsation period of KIC 6220497 deviated from the general trend of the oEA stars and also the empirical relation between Ppul and Porb of Zhang et al. (2013). The pulsation periods in EBs increase with decreasing gravitational pull exerted by the secondary companion to the pulsating primary component (Soydugan et al. 2006). For KIC 6220497, the gravitational pull applied to per gram of the matter on the surface of the pulsating component by the lobe-filling secondary was calculated to be log F = 2.90 in cgs units, which is about 3.4 times smaller than the value of 9.89 (again, in cgs units) taken from the relation of log Ppul = −0.61log F + 5.1 calibrated by Soydugan et al. (2006). However, as shown in the lower panels of Fig. 8 from 34 oEA stars currently known, the gravitational force log F for KIC 6220497 matches well with those for the other oEA stars with similar orbital periods, while the surface gravity log g1 = 3.78 for the primary component is clearly smaller. The period–gravity relation is similar to that for radially pulsating stars suggested by Fernie (1995); as the surface gravity decreases, its pulsation period increases. Further, it is known that the more evolved the star, the slower the pulsations (cf. Liakos et al. 2012). The pulsation period and the surface gravity of KIC 6220497 indicate that the system might be a more evolved EB than the other oEA stars. We think that the pulsation periods strongly depend on the surface gravities of the pulsating components and the evolutionary status of the binary stars.


As we describe in Section 2 the case of TNDWs propagating in a plasma with equal mass fraction of 12C and 16O (CO) and density of ρ0,7 ≈ 1,1 which is typical for Type Ia supernovae, is particularly challenging for full-star simulations. In addition to the problem that the burning length-scale is much smaller than the typical cell size, near detailed balance is obtained for many isotopes while NSE is not reached. We test in Section 2 two available one-dimensional (1D) codes: a modified version of the 1D, Lagrangian version of the vulcan code (hereafter V1D; for details, see Livne 1993) and a modified version of the Eulerian, 1D hydrodynamic flash4.0 code with thermonuclear burning (Fryxell et al. 2000; Dubey et al. 2009), against the ρ0,7 = 1 case. We show that with resolutions that are typical for multidimensional full-star simulations, the V1D and the flash results are not satisfactory (up to $50{{\ \rm per\ cent}}$ error in V1D and up to $20{{\ \rm per\ cent}}$ error in flash). We demonstrate in Section 3 the operation of a new numerical scheme for thermonuclear burning that can be implemented in multidimensional full-star simulations. The new scheme allows an accurate calculation of TNDWs in a consistent way (i.e. without pre-describing the position and/or the conditions behind the TNDW) with all thermonuclear burning taking place in situ (without post-processing) for an arbitrary reaction network with hundreds of isotopes. The new scheme contains two important ingredients: (1) a burning limiter (a variant of Kushnir et al. 2013), which guarantees that the thermodynamic variables and the composition are accurate for the resolved scales, while keeping the numerical thermodynamic trajectory for unresolved scales within some controlled error from the true thermodynamic trajectory, and (2) adaptive statistical equilibrium (ASE) burning, which groups isotopes that are in detailed balance into one effective isotope, where the ratio between the isotope abundances inside the group is given from equilibrium conditions (this is an extension of the earlier attempts of Hix et al. 2007; Parete-Koon & Hix 2008; Parete-Koon, Hix & Thielemann 2008, 2010).


WASP-43b is the most heavily scrutinized phase curve, with four analyses of this data set already published (Stevenson et al. 2017; Mendonça et al. 2018; Morello et al. 2019; May & Stevenson 2020). Our phase curve semi-amplitude, eclipse depth, and radius are consistent with all of these works. The more contentious issue is that of the phase curve’s phase offset and nightside temperature. Stevenson et al. (2017) initially reported only a 2σ upper limit on the nightside temperature of 650 K, while all subsequent reanalyses (including ours) favour a significantly detectable nightside temperature of ∼800 K. As for the planet’s phase offset, Stevenson et al. (2017) and May & Stevenson (2020) favour a larger phase offset (21 ± 2 °E) than Mendonça et al. (2018) and Morello et al. (2019) (12 ± 3 °E and 11 ± 2 °E). May & Stevenson (2020) claimed that the differences between the retrieved phase offsets is the result of temporal binning which was not used by Stevenson et al. (2017) and May & Stevenson (2020) but was used by Mendonça et al. (2018), Morello et al. (2019), and this work. Fitting the temporally binned photometry for all 17 phase curves with each of our detector models already required more than 2000 CPU hours, and expanding this to unbinned photometry for all phase curve fits would require more than 125 000 CPU hours (or 434 d using our 12× multithreading computer) optimistically assuming all of detector models scaled linearly with the number of input data. However, we did try fitting just the WASP-43b unbinned phase curve with our preferred detector model (BLISS) and found that our phase offset and nightside temperature was unchanged. Including a linear slope in time also did not affect our phase offset or nightside temperature. Instead, we find that the phase offset inferred by our models depends on the choice of phase curve model, as our 4-parameter (v2) phase curve models are consistent with those of Stevenson et al. (2017) and May & Stevenson (2020), while our 2-parameter phase curve models (v1) are consistent with Mendonça et al. (2018) and Morello et al. (2019). Ultimately, we cannot decide between these two discrepant offsets as the ΔBIC between the two phase curve models for our preferred BLISS detector model is only 3.7 (insignificantly favouring the 20.4 ± 3.6 offset from the v2 model). For reference, Stevenson et al. (2014b) found phase offsets ranging from roughly −6 to 17 deg east in the Hubble/WFC3 bandpass.


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).


We obtained atmospheric parameters using the high-resolution spectra. For our candidates with early spectral types: CoRoT–34, CoRoT 310204242, and CoRoT 110660135 we derived the effective temperature Teff, surface gravity log (g)sp, and metallicity [Fe/H] using grids of synthetic spectra, based on ATLAS12 model atmospheres (Kurucz 1996). The most important elements were considered using a hybrid non-local thermal equilibrium (NLTE) approach with the DETAIL/SURFACE package (Giddings 1981). Our model spectra, as well as the fitting method are described in detail in Irrgang et al. (2014) and Heuser (2018). For all other candidates, the synthetic spectra were calculated in LTE using the ATLAS12 and SYNTHE codes (Kurucz 1993). To consider all sensitive features in the observed spectra, we performed global χ2 fits. In the cases where combined spectra were available from several instruments, we fitted them simultaneously using the same model grid taking different resolution and radial velocity into account. Regions that were not well reproduced were removed from the fit. This includes the cores of hydrogen lines, lines that are not included in our model spectra, as well as lines with uncertain atomic data. It is challenging to determine the surface gravity for F-type stars, because it is correlated with both the Teff and the abundance of calcium and magnesium. We assumed systemic uncertainties of 0.2 dex for log (g)sp, of 0.1 dex for [Fe/H], and 2  per cent in Teff, which were added in quadrature to the much smaller statistical uncertainties. The atmospheric parameters from spectroscopy are listed in Table 2. Second, we derived stellar age, mass, and radius by fitting the observed parameters to mesa evolutionary tracks (Choi et al. 2016) in the (Teff, $\log \, g$, [Fe/H]) plane as described by Irrgang et al. (2016). For CoRoT–34, 35, and 36, we used the stellar mass and radius as input for the light-curve fit, which we used to constrain log (g)lc from the light curve directly (For details, see description of the light curve fit below). We derived the final stellar age, mass, and radius as listed in Table 2 by repeating the mesa fit using log (g)lc as prior. The best-fitting evolutionary tracks are shown in Fig. 2.


At present two main processes have been put forward for triggering star formation at the peripheries of H ii regions: collect-and-collapse (CC) and radiation-driven implosion (RDI; Elmegreen & Lada 1977; Deharveng et al. 2010). In the CC process, a compressed layer of neutral material is accumulated between the ionization front and shock front, and star formation occurs when this layer becomes gravitationally unstable. Unlike the CC process, in the RDI process a pre-existing denser gas is compressed by the shocks, and then forms stars. The CC process is more attractive because it allows the formation of massive stars or clusters (Deharveng et al. 2005). To investigate the star formation triggered by the CC process, several individual H ii regions have been studied, such as Sh 104 (Deharveng et al. 2003), RCW 79 (Zavagno et al. 2006), RCW 120 (Zavagno et al. 2007), Sh2-212 (Deharveng et al. 2008), Sh2-217 (Brand et al. 2011), Sh2-90 (Samal et al. 2014), Sh2-87 (Xu & Ju 2014), N6 (Yuan et al. 2014), and Gum 31 (Duronea et al. 2015). Moreover, there are also some statistical studies of infrared bubbles (e.g., Deharveng et al. 2010; Kendrew et al. 2012; Thompson et al. 2012; Kendrew et al. 2016), which are created by the expanding H ii regions. A common feature of the above studies is that several massive fragments are found on the border of each H ii region. Some star formation activity has been detected in these fragments, such as outflow, UCH ii, and water masers. Generally, if an expanding H ii region collects its surrounding gas, the morphology of the molecular gas will show three-dimensional spherical structure. CO observations can provide velocity information to reveal the gas structure surrounding the H ii regions. Beaumont & Williams (2010) observed 43 infrared bubbles using the CO molecular line, but they did not detect the front and back faces of these shells at blueshifted and redshifted velocities. Hence, they concluded that the bubbles enclosing H ii regions are two-dimensional rings formed in parental molecular clouds with thicknesses not greater than the bubble sizes. However, molecular gas with a three-dimensional spherical structure or a two-dimensional ring around H ii region is important for understanding the triggered star formation (Deharveng et al. 2015).


One major difficulty afflicts the study of SNRs to learn about their supernovae: separating ejected material from swept-up surrounding unmodified interstellar medium (ISM) or modified CSM. Abundance clues are powerful but have limitations. Ideally, one would observe the youngest possible remnant that is large enough for adequate spatial resolution. That remnant appears to be the youngest Galactic SNR, G1.9+0.3 (Reynolds et al. 2008; see Figure 1). This object is about

100′′

 in diameter, the smallest angular size of any confirmed Galactic SNR. Unfortunately, it is very highly absorbed, with an X-ray column density of about 5 × 1022 cm−2 (Reynolds et al. 2009), implying A

V
 ∼ 23
m
, so radio and X-rays are the only useful observational channels. The angular expansion rate of 0.64 arcsec yr−1 obtained from comparing X-ray images from 2007 and 2009 (Carlton et al. 2011) gives an upper limit for the age of about 160 yr, less if (as is almost certainly the case) deceleration has occurred; spatial variations in expansion rate (Borkowski et al. 2014) are consistent with an age of about 100 yr, or a date of around 1900. The high extinction would have rendered it unobservable in optical telescopes of that era. Furthermore, its X-ray spectrum is almost entirely synchrotron emission, making it a member of the small class of X-ray synchrotron–dominated SNRs. However, long observations with Chandra have allowed the detection of thermal emission from small regions (Borkowski et al. 2011, 2013b), with spectroscopic widths of ∼14,000 km s−1 confirming the large expansion proper motion, refined with a second Chandra observation (Carlton et al. 2011). The distance is still uncertain; the high column—higher than the entire Galactic column along nearby sight lines—suggests an association with the Galactic center, and a provisional distance of order 8.5 kpc has been assumed. Nearer would be very unlikely in view of the high absorption, but too much farther would make the expansion proper motion unreasonably large. An H i observation with the Giant Metrewave Radio Telescope (Roy & Pal 2014) has been used to set a lower limit of 10 kpc, certainly consistent with the known properties of G1.9+0.3.


Many studies have been done to understand the dynamics and origin of such systems since the discovery of the first binary asteroid system, Dactyl orbiting around (243) Ida in 1993 (Chapman et al. 1995). Based on the structure of ‘rubble pile’ asteroids (a collection of gravitationally bound boulders with a distribution of size scales and very little tensile strength between them), a model for how they can disrupt due to close flybys of a planet was developed. However, close encounters with the planets proved not to be enough for creation of the current population of binary systems (Margot et al. 2002; Walsh & Richardson 2008). Another model for their formation is by increasing their spin rates due to incident and remitted solar photons, known as the Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) effect. The YORP effect on contact binary asteroids has been studied (Bottke et al. 2002; Merline et al. 2002; Scheeres 2002; Walsh & Richardson 2006). Using a model with an ellipsoid and a sphere in a planar case, Scheeres (2007) studied fission limits (spin limit to occur a fission) and the stability of that kind of system for different initial conditions. After that, the stability of a binary system was analysed using a two-ellipsoid model (Scheeres 2009). Pravec et al. (2010) made a complete study about formation of asteroid pairs through rotation fission. Jacobson & Scheeres (2011) studied the creation of binaries and other observed near-Earth asteroid (NEA) systems, including doubly synchronous binaries, high-e binaries, ternary systems and contact binaries. That study analysed the dynamics of a binary system just after rotational fission. Using a two-ellipsoid model taking into account mutual gravitational interactions and tidal dissipation, they analysed the dynamics for different mass ratios of the system under a planar assumption. The current work follows from these results, but looks at more likely, non-planar initial configurations. This extension is significant, as non-planar cases must take into account the complete rotational motion (rotation, precession and nutation) of each body. Our results are compared with the results obtained by Jacobson & Scheeres (2011).


In this paper, we use a legacy value data set covering the inner star-forming disc of NGC 300 taken with the VLT/MUSE instrument (Bacon et al. 2010), consisting of a contiguous 7 arcmin × 5 arcmin mosaic (∼4 kpc × 3 kpc) and covering the galaxy out to galactocentric radii of about 0.45R25 (with R25 ∼ 5.33 kpc being the optical radius; Paturel et al. 2003). NGC 300 is an ideal target to study stellar feedback: it is the closest (D ∼ 2 Mpc; Dalcanton et al. 2009), non-interacting, star-forming disc galaxy that can be mapped at the necessary spatial resolution [i.e. 1 arcsec, which corresponds to ∼10 pc, resolving individual star-forming regions and supernova remnants (SNRs)]. The large spatial coverage (to cover most of the star-forming disc) available not only in the optical with MUSE but throughout the electromagnetic spectrum (e.g. Helou et al. 2004; Westmeier, Braun & Koribalski 2011; Riener et al. 2018; Kruijssen et al. 2019; Schruba, Kruijssen & Leroy 2019) makes NGC 300 the ideal target for simultaneous resolved feedback, stellar population, and ISM studies. Closer galaxies like the Magellanic Clouds, M31, or M33 do not allow similar large-scale multiwavelength mapping due to their large angular sizes, while more distant galaxies (beyond a few Mpc) do not allow multiwavelength studies with similar spatial resolution across the optical, infrared, mm/sub-mm, and radio. NGC 300 perfectly bridges between ∼100 pc resolution IFU surveys of nearby galaxies like PHANGS, and upcoming (sub-) pc scale resolution IFU surveys of the Milky Way and the Magellanic Clouds like SDSS-V/LVM (Kollmeier et al. 2017). Further, NGC 300 offers a favourable inclination of ∼40° (Puche, Carignan & Bosma 1990), it is actively forming stars at a rate between ∼0.08 and ∼0.30 M⊙ yr−1 (Kang et al. 2016, and references therein), and has a well-studied population of ${\rm H\, \small {II}}$ regions (e.g. Deharveng et al. 1988; Bresolin et al. 2009; Faesi et al. 2014), planetary nebulae (PNe; e.g. Soffner et al. 1996; Peña et al. 2012; Stasińska et al. 2013), and SNRs (e.g. Blair & Long 1997; Millar, White & Filipovic 2012; Vučetić, Arbutina & Urošević 2015).


Alongside the above theoretical uncertainties in the physics of core formation in ellipticals, there have also been observational challenges. In particular, determining the size of the core has proven to be a non-trivial task. The light profiles of ellipticals are well described by the 3-parameter Sérsic profile (Sérsic 1963, 1968) over a large radial range. The most luminous ellipticals, however, show a departure from the Sérsic law in their central regions, at a radius widely known as the ‘break’ or ‘core’ radius. In these galaxies, the profiles break downward from the inward extrapolation of the outer Sérsic law. Initially the core size of a galaxy was determined by fitting the so-called ‘Nuker-profile’ (Lauer et al. 1995) to the surface brightness profile, a method that however depends sensitively on the radial fitting range and yields unreliable results when fit to surface brightness profiles with a large radial extent (e.g. Graham et al. 2003; Dullo & Graham 2012). In more recent years, it has become customary to incorporate a central flattening in the light profile by adopting a 6-parameter core-Sérsic profile (Graham et al. 2003; Trujillo et al. 2004) which provides a reliable measurement of the core size even over a large radial range (e.g. Dullo & Graham 2012, 2013, 2014). Furthermore, it has been shown that adopting a multicomponent model rather than a single core-Sérsic model over the entire radial range provides a more reliable estimate of the core size (Dullo & Graham 2014; Dullo 2019). Measured core sizes for massive ellipticals – derived in this way – are typically tens to a few hundred parsecs (e.g. Dullo & Graham 2014), while cores larger than $1{\, \mathrm{kpc}}$ are rare. A study by Lauer et al. (2007) considered a large sample of brightest cluster galaxies (BCGs) and found that fewer than 10 systems had a core size of $\sim 1\rm {kpc}$ or greater, with the largest cored system being NGC 6166 which has a core size of $\sim 1.5{\, \mathrm{kpc}}$. More recently, Dullo (2019) considered the largest sample of ‘large-core’ galaxies to date, finding that only 13(7) galaxies have core sizes larger than $0.5(1){\, \mathrm{kpc}}$.