The broad blue WR bump feature around 4686 Å was searched in all the star-forming regions in the galaxies. A clear detection of the broad blue WR bump was made only in two star-forming regions hosted by SBS 1222+614 as shown in Fig. 8. This detection is in good agreement with Shirazi & Brinchmann (2012), who have also reported the WR features in SBS 1222+614. The broad blue bump consists of a blend of C iii/C iv λ4650, 4658, N iii λ4634, 4640, [Ar iv] λ4711, 4740, and He ii λ4686 emission lines. This detection generally indicates a good number (102–105) of young WR stars in the galaxy (e.g. Kunth & Sargent 1981; Kunth & Schild 1986). The blue bump appears mainly due to the presence of late-type WN (WNL) and early-type WC (WCE) stars (Schaerer & Vacca 1998). The red WR bump around 5808 Å is also expected in the WR galaxies. We also possibly identified the red bump feature in the SBS 1222+614 (# a + b) region as shown in Fig. 9. The red WR bump appears mainly due to the presence of emission lines [N ii] λ5795 and He i λ5875 from the WCE stars. The red bump is rarely detected in WR galaxies as it contains very weak emission line and is expected in high-mettalicity region (Guseva, Izotov & Thuan 2000). Although we could not detect the WR features in the star-forming regions of other galaxies in our sample, the optical SDSS spectrum for the brightest regions of knot #b and #a in IC 3521 and CGCG 0410-023, respectively, shows a detection of WR features (Brinchmann et al. 2008). The SDSS spectrum also shows the detection of the broad WR blue bump having a relatively lower strength in the knot #b of CGCG 038-051. These detections are missed out in this study most likely due to the low SNR in the blue part of the spectra. The starburst ages estimated to be very young (≤6 Myr; see Table 3) for these star-forming regions including those present in SBS 1222+614 are consistent with the detection of the WR features, which appears only during the very early periods of star formation. Although a few other star-forming regions such as the knot #a in IC 3521 and CGCG 038-051 and knot #c in CGCG 041-023 showing a very young starburst of ≤6 Myr are expected to have the WR features, it is not clear from the present data if these regions also host WR stars or not. Some star-forming regions such as knot #c and b in CGCG 038-051 and CGCG 041-023, respectively, show the starburst of ages of ∼10 Myr, indicating that they have probably completed their WR phases. Overall, the detections of the WR features from our own observations and those from the SDSS data from at least one star-forming region in each galaxy in the sample suggest that the sample galaxies are undergoing young massive star formation phase having a significant population of WR stars.


The full sample for which the circumstellar CO line emission will be modeled consists of the ∼180 C-, M-, and S-type AGB stars analyzed in Schöier & Olofsson (2001), González Delgado et al. (2003), and Ramstedt et al. (2006) together with additional sources presented in Danilovich et al. (2015). In this initial paper, the new interferometric data for the southern M- and C-type stars are presented. Some of the available sample statistics for the full ∼180 star DEATHSTAR sample are shown in Fig. 1. The distance distribution (Fig. 1, middle) is compared with the estimated distribution in the solar neighborhood (Jura 1990; Jura & Kleinmann 1992; Jura et al. 1993). The estimated distribution is derived from 2MASS and ground-based observations (Jura & Kleinmann 1990) and assumes a smooth distribution of 40 C-type stars kpc−2, a scale height of 200 pc, and that there are a third as many S-type as C-type stars. For the full ∼180 star DEATHSTAR sample, the C-type stars from Schöier & Olofsson (2001) are all brighter than K = 2 mag. The M-type sample consists of the non-Mira stars from the General Catalog of Variable Stars (GCVS; Samus’ et al. 2017) with quality flag 3 in the IRAS 12, 25, and 60 μm bands and 60 μm flux ≳3 Jy with the addition of the Mira stars in González Delgado et al. (2003). The S-type sample also consists of stars that have good quality flux measurements in the IRAS 12, 25, and 60 μm bands, that are found in the General Catalog of Galactic S stars, and that are detected in Tc and are hence intrinsic. The completeness of the S-type sample is discussed in Ramstedt et al. (2009) and it is thought to be complete out to 600 pc. Furthermore, stars of all three spectral types are only included in the sample if they are detected in CO radio line emission, which could be reproduced under the assumption of spherical symmetry. Sources that show strongly asymmetric line profiles when observed with single-dish telescopes, or with known CO-detached shells, are hence not included (e.g., R Scl, U Ant, EP Aqr, and π1 Gru). In this paper, we also exclude stars that have previously been observed with ALMA; however, they will be included in the future analysis. The lower panel of Fig. 1 shows that the stellar and wind parameters of the full ∼180 star sample cover the ranges expected for AGB stars. As expected, fewer stars are found at the high end. The sample is biased to mass-losing stars since only stars that are previously detected in CO radio line emission are included. It is also likely that the full range of AGB masses is not covered simply because higher mass stars are rare. It is our assessment that the full ∼180 star DEATHSTAR sample is representative of Galactic mass-losing AGB stars and covers the relevant ranges of wind and stellar parameters to provide the necessary constraints for theoretical models.


Finally, we attempt to characterize the reflection component using the full 2–35 keV spectra with a sophisticated model [M4: ${\tt{\rm constant}}$*${\tt{\rm TBabs}}$*(${\tt{\rm simplr}}$*${\tt {\rm kerrbb2}}$+${\tt{\rm kerrconv}}$*(${\tt{\rm ireflect}}$*${\tt{\rm simplc}}$)), to evaluate the impact on the spin measurement and understand the changes of the accretion flow and the interaction between the disc and the corona. This model features a self-consistent treatment of the thermal, Compton scattering and the reflection component: ${\tt {\rm kerrbb2}}$ describes the thermal component and supplies the seed photons for ${\tt{\rm simplr}}$ (a modified version of ${\tt{\rm simpl}}$, Steiner et al. 2011) to generate the Compton component; while a portion of the Compton component will escape to reach an observer, the remains (refer as ${\tt{\rm simplc}}$, Steiner et al. 2011) will strike back to the disc to generate the reflected component. The reflection fraction Rref in ${\tt{\rm ireflect}}$ (Magdziarz & Zdziarski 1995), defined as the ratio of the Compton photons striking back to the disc to that escaping to infinity, is restricted to negative value thereby only the reflected component is returned by ${\tt{\rm ireflect}}$. It is linked to the reflection constant parameter x in ${\tt{\rm simplr}}$ via the relation x = 1 + |Rref| (Gou et al. 2011). We set the elemental abundance to unity and the iron abundance AFe to five times the solar abundance (Bharali et al. 2019; Buisson et al. 2019; Xu et al. 2020). The disc temperature Tin is fixed at the value returned by ${\tt{\rm diskbb}}$ (M1, refer to Gou et al. 2011). The ionization parameter ξ is fixed at 1000 (i.e. log(ξ) = 3, Xu et al. 2020; Buisson et al. 2019), as it is difficult to be constrained. Finally we use ${\tt{\rm kerrconv}}$ (Brenneman & Reynolds 2006) to apply relativistic effects assuming an unbroken emissivity profile with index q = 3. The key parameters in ${\tt {\rm kerrbb2}}$ and ${\tt{\rm kerrconv}}$ are linked together.


The stream velocity is proportional to the halo virial velocity, which can be related to the sound speed of gas at the virial temperature, yielding Mb ∼ 1. The density contrast is obtained by assuming pressure equilibrium between hot gas at Tb ∼ Tv, the virial temperature of an NFW halo, and cold gas at Ts ∼ 104K, set by the steep drop in the cooling rate below that temperature (Sutherland & Dopita 1993). If both the halo and the stream are roughly isothermal, then this ratio is constant throughout the halo. In practice, the stream temperature can be as high as ∼3 × 104 K due to photoheating from the UV background (e.g. Goerdt et al. 2010), while the post-shock temperature in the hot halo near Rv may only be ∼0.5Tv (Dekel & Birnboim 2006, P18). Finally, the stream radius is related to its velocity and density through the mass accretion rate along the stream, ${\dot{M}}_{\rm s}\simeq \pi R_{\rm s}^2 \rho _{\rm s}V_{\rm s}$. Cosmological simulations suggest that this is typically a fixed fraction of the total accretion rate on to the halo virial radius (Danovich et al. 2012), which is constrained by cosmology (e.g. Dekel et al. 2013). The final expressions, including uncertainties in model parameters, are
(42)
\begin{eqnarray*}
M_{\rm b}\simeq 0.75-2.25,
\end{eqnarray*}
(43)
\begin{eqnarray*}
\delta \simeq (10-100)\times M_{12}^{2/3} (1+z)_3^{-1},
\end{eqnarray*}
(44)
\begin{eqnarray*}
\frac{R_{\rm s}}{R_{\rm v}} \simeq (0.01-0.1)\times \left(\delta _{75} M_{\rm b,1.5}\right)^{-1/2},
\end{eqnarray*}
where $M_{12}=M_{\rm v}/10^{12}\, \mathrm{M}_\odot$, (1 + $z$)3 = (1 + $z$)/3, δ75 = δ/75, and Mb,1.5 = Mb/1.5. We note that δ ∼ 10 implies that the background gas has a temperature of ${\sim } 3\times 10^5\, {\rm K}$, which would make it thermally unstable unless it is illuminated by a very hard ionizing background (e.g. Efstathiou 1992, though see also Binney, Nipoti & Fraternali 2009, who argue that buoyancy effects may stabilize the halo against thermal instability even without a photoionizing source). This implies that δ ≳ 30 is likely the most physically plausible regime.


The SFG sample was constructed using the Great Observatories All-Sky LIRG Survey (GOALS sample, Armus et al. 2009), from which we extracted 158 galaxies, with data from Inami et al. (2013), who report the fine-structure lines at high resolution in the 10 − 36 μm interval, and Stierwalt et al. (2014), who include the detections of the H2 molecular lines and the PAH features at low spectral resolution. For those galaxies in the GOALS sample that have a single IRAS counterpart, but more than one source detected in the emission lines, we have added together the line or feature fluxes of all components, to consistently associate the correct line or feature emission to the total IR luminosity computed from the IRAS fluxes. To also cover lower luminosity galaxies, as the GOALS sample only includes luminous IR galaxies (LIRGs) and ultra-luminous IR galaxies (ULIRGs), we included 38 galaxies from Bernard-Salas et al. (2009) and Goulding & Alexander (2009), to reach the total sample of 196 galaxies with IR line fluxes in the 5.5 − 35 μm interval in which an AGN component is not detected. For the Bernard-Salas et al. (2009), Goulding & Alexander (2009), and the GOALS samples, we excluded all the composite starburst-AGN objects identified as those with a detection of [NeV] either at 14.3 or 24.3 μm. It is worth noting that the original samples from Goulding & Alexander (2009) and Bernard-Salas et al. (2009) have spectra solely covering the central region of the galaxies. To estimate the global SFR, we corrected the published line fluxes of the Spitzer spectra by multiplying them by the ratio of the continuum reported in the IRAS point source catalogue to the continuum measured on the Spitzer spectra extracted from the CASSIS database (Lebouteiller et al. 2015). We assumed here that the line emission scales (at first order) with the IR brightness distribution. In particular, we considered the continuum at 12 μm for the [NeII]12.8 μm and [NeIII]15.6 μm lines, and the continuum at 25 μm for the [OIV]25.9 μm, [FeII]26 μm, [SIII]33.5 μm, and [SiII]34.8 μm lines. This correction was not needed for the AGN sample and the GOALS sample because of the greater average redshift of the galaxies in the 12MGS and GOALS samples. In particular, the 12MGS active galaxy sample has a mean redshift of 0.028 (Rush et al. 1993), while the GOALS sample has a mean redshift of 0.026. The galaxies presented by Bernard-Salas et al. (2009) have instead an average redshift of 0.0074, while the sample by Goulding & Alexander (2009) has an average redshift of 0.0044. For the other lines in the 10 − 36 μm interval, Goulding & Alexander (2009) did not report a detection, and we used the data presented in Bernard-Salas et al. (2009) for a total of 15 objects. Both Bernard-Salas et al. (2009) and Goulding & Alexander (2009) reported data from the high-resolution Spitzer-IRS spectra. Data in the 50 − 205 μm interval were taken from Díaz-Santos et al. (2017). For the GOALS sample, 20 starburst galaxies were taken from Fernández-Ontiveros et al. (2016), and 23 objects were taken from the ISO-LWS observations of Negishi et al. (2001). As a result, we obtained a total sample of 193 objects. Lastly, the PAH features’ fluxes were measured from the low-resolution Spitzer-IRS spectra by Brandl et al. (2006), including 12 objects from the sample of Bernard-Salas et al. (2009) and 179 objects from Stierwalt et al. (2014).


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.


There are many methods, beyond those already employed here, that can be used to identify, and probe the masses of, black holes. This includes reverberation mappings of AGNs (e.g. Bahcall, Kozlovsky & Salpeter 1972; Blandford & McKee 1982; Netzer & Peterson 1997), the ‘fundamental plane of black hole activity’ (Merloni et al. 2003; Falcke, Körding & Markoff 2004), spectral modelling of the high-energy X-ray photon coming from the hot accretion discs around IMBHs (Pringle & Rees 1972; Narayan & Yi 1995), high-ionization optical emission lines (Baldwin et al. 1981; Kewley et al. 2001), and high-spatial-resolution observations of maser emission using radio and millimetre/submillimetre interferometry (e.g. Miyoshi et al. 1995; Greenhill et al. 2003; Humphreys et al. 2016; Asada et al. 2017). In addition, the merging of black holes is now quite famously known to produce gravitational radiation during their orbital decay (Abbott et al. 2016). The merging of galaxies containing their own central IMBH is similarly expected to result in the eventual merging of these black holes. The Kamioka Gravitational Wave Detector (KAGRA; Aso et al. 2013) will be a 3-km-long underground interferometer in Japan capable of detecting the gravitational radiation emanating from collisions involving black holes with masses up to 200 M⊙ (Tápai, Zoltán & László 2015). The planned Deci-Hertz Interferometer Gravitational wave Observatory (DECIGO; Kawamura et al. 2011) and the European, Laser Interferometer Space Antenna (LISA) Pathfinder mission15 (Anza et al. 2005; McNamara 2013), with their greater separation of mirrors, will be able to detect longer wavelength gravitational waves and thus better reach into the domain of intermediate-mass and supermassive black hole mergers, the latter of which are currently being searched for via ‘pulsar timing arrays’ (PTAs) (e.g. Hobbs et al. 2010; Kramer & Champion 2013; Shannon et al. 2015). A key constraint to the expected detection threshold of such signals from PTAs – in particular the background of cosmic ripples from the merger of massive black holes (themselves arising from the merger of galaxies) – is the (black hole)-to-(host galaxy/bulge) mass ratio (see equation 4 for spiral galaxies). An additional source of long-wavelength gravitational radiation will arise from the inspiral of compact stellar-mass objects, such as neutron stars and black holes, around these IMBHs (Mapelli et al. 2012). It is reasonable to expect that the densely packed nuclear star clusters, which coexist with low-mass SMBHs (e.g. González Delgado et al. 2008; Seth et al. 2008; Graham & Spitler 2009), will similarly surround many IMBHs. Gravitational radiation and the gravitational tidal disruption of ill-fated stars that venture too close to these black holes (Komossa et al. 2009, Komossa 2013, and references therein; Zhong, Berczik & Spurzem 2015; Stone & Metzger 2016; Lin et al. 2018) are therefore expected from these astrophysical entities. There is, therefore, an array of future observations that could yield further confidence and insight into the realm of IMBHs.


The secondary eclipses of the binary are 0.03–0.04 mag deep, and so relatively small data reduction issues can have large effects on the fidelity of the light curve. Our brightness measurements were derived from aperture photometry using DAOPHOT (Stetson 1987), although we took several additional steps to increase the precision of the results. We conducted a curve-of-growth analysis of 12 apertures photometered per star using DAOGROW (Stetson 1990) in order to correct all measured stars to a uniform large aperture. We then attempted to unify the data for each filter to a consistent zero point by using ensemble photometry (Sandquist et al. 2003; Honeycutt 1992). This essentially uses all measured stars on the frame to determine magnitude offsets resulting from differences in exposure time, airmass, atmospheric transparency, and the like. Our implementation iteratively fits for position-dependent corrections that result from variations from point-spread function across the frame. These steps each brought noticeable reductions in the amount of scatter in the light curves. However, we still found that the shape of the ground-based light curves of the secondary eclipse did not match what was expected from the Kepler observations. After some investigation, we found that features in the light curve were correlated with those for the brightest star near KIC 9777062 in our images. (The star was about 70 pixels or 28″ distant on the sky, so there was no significant overlap of the point-spread function when the seeing was generally 4–8 pixels FWHM.) We found that after subtracting the light curve of this star the out-of-eclipse light levels and the shapes of the primary and secondary eclipse light curves were much more consistent from night to night. When more distant stars on the images were tested, we found a much poorer degree of correlation. We conclude that short length-scale variations were not being corrected for (and could not be corrected for, due to lack of star sampling on the image) with whole-image zero-point corrections or image-scale position-dependent corrections. The variations were of around 0.01 mag size, but could significantly affect the secondary eclipse light curves. We could not identify any features on our flat-field images that could explain the light-curve variations, and they occurred whether dome flats, twilight flats, or hybrid flats (combining the smoothed large-scale variations from the twilight flats and small-scale variations from dome flats) were used. The ground-based eclipse observations are shown in the bottom rows of Figure 1.


δ Ori Aa+Ab = Mintaka Aa+Ab = 34 Ori Aa+Ab = HD 36486 A+B = BD −00 983 A+B = ALS 14 779 A+B. δ Ori is Orion’s Belt westernmost star and a multiple system at the center of the Mintaka cluster (Caballero & Solano 2008). It has two close bright visual components (Aa and Ab) and two distant dim ones (B and C) that will not be considered here. Aa is itself composed of two spectroscopic components (Aa1+Aa2) in an eclipsing orbit with a5.7325 d period, while Ab is two magnitudes fainter than the two Aa components and located 0.′′ 267 away in 1993 and moving away from the primary (Hartmann 1904; Harvin et al. 2002). We observed the system on two consecutive nights and in both cases we were able to spatially resolve Ab from Aa, this being one of the two systems in this paper (σ Ori is the other one) where the power of Lucky Spectroscopy becomes more apparent. The two spectra for Aa yield the same spectral type as for the combined Aa+Ab value from GOSSS I, O9.5 IINwk, but the lines are slightly narrower. When analyzing the data for GOSSS I, the combined spectrum was close to being (n), something that does not happen for the spatially resolved spectra (this has the additional advantage of giving us a more purespectrum for a classical O9.5 II classification standard). There are very small variations between the two epochs for Aa, likely due to the motion of Aa1 and Aa2 but the signature of the latter in the combined spectrum is very weak (Shenar et al. 2015). The two epochs for Ab yield the same spectral type, O9.7 III:(n), and in both cases there are indications of only a slight residual contamination from Aa, with the second epoch being noisier. The (n) qualifier indicates that Ab is a fast rotator, as previously noted by Harvin et al. (2002) and Shenar et al. (2015). The differences between the spectral types of Aa (Aa1+Aa2) and Ab are consistent with the Teff and log g differences measured by Shenar et al. (2015) using spectral disentangling (as opposed to the spatial deconvolution used here). Richardson et al. (2015) also spatially resolved Aa and Ab in the UV using HST/STIS and obtained very similar values of Teff around 31 kK for Aa1 and Ab, with error bars close to 2000 K, which is also consistent with our spectral classifications. That paper using UV data is the only one we have found where δ Ori Aa+Ab was spatially deconvolved, making our result the first time it has been done in the optical.


In Fig. 7 we compare UGC 1378’s SFR density versus gas surface density (the Schmidt–Kennicutt relation) to data in the literature. The gas surface density corresponds to H i calculated from the 0th moment map from Mishra et al. (2017) in the same areas as SFR density. Points for the HSB and LSB discs are plotted as black and grey circles, respectively. We plot the mean SFR and H i surface density for the entire galaxy with a large open circle. The black line corresponds to the relation with an exponent of 1.4 found by Kennicutt (1998). Triangles give results for LSB galaxies published by Wyder et al. (2009), and bright and faint crosses show normal spiral galaxies from Kennicutt (1998) – total and H isurface densities. A blue line shows the best-fitting relation for the H isurface density of Bluedisk galaxies from Roychowdhury et al. (2015). We also plot the SFR in the outer regions of spiral galaxies (Bigiel et al. 2010, square symbols). In Fig. 7 the UGC 1378 measurements lie between normal spirals and LSB galaxies. The HSB disc data lie above the relation plotted for normal spirals, possibly indicating that the SFR is boosted by the bar driving gas to the star-forming rings. We cannot account for molecular gas since there are no available measurements for UGC 1378. The contribution of molecular gas would likely move the HSB disc of UGC 1378 towards the locus of normal galaxies. Because the HSB SFR of UGC 1378 is close to the predicted SFR from the Kennicutt (1998) relation obtained from H i densities (faint crosses in Fig. 7). The LSB disc of UGC 1378 lies below the correlation and accounting for molecular gas would only increase the deviation from the normal Schmidt–Kennicutt relation. Similar deviations are observed in ‘classical’ LSB galaxies, Bluedisk galaxies (Roychowdhury et al. 2015), outer parts of HSB spiral galaxies (Bigiel et al. 2010), and H idiscs in early-type galaxies (Yıldız et al. 2017). These deviations for LSB galaxies are at least partially explained by their lower gas densities leading to lower SFRs (Abramova & Zasov 2011). A recent episode of gas accretion on to the disc of UGC 1378 may also contribute to a lower SFR if the gas is not yet fully participating in the star formation. Lutz et al. (2017) studied a sample of very H i rich galaxies and proposed that very high specific angular momentum in H irich galaxies prevents the accreted gas from being transported to the mid-plane of the disc and being converted into stars. This mechanism may act to preserve giant gaseous discs.


Assuming that non-jetted H ii galaxies are powered by SF, the relation between radio luminosities in such galaxies and MBH can be deciphered as a link between thermal/non-thermal SF luminosity and BH mass, in the form $L_{\rm SF} \propto M_{\rm BH}^{0.61}$, which has the largest scatter of the observed linear regressions, due to the large uncertainties of MBH estimates at low values and numerous radio non-detections. This unprecedented relation is likely the result of the observed link found between SF indicators such as radio, far-infrared, optical or line luminosities, and galaxy mass (e.g. Mauch & Sadler 2007; Gürkan et al. 2018). Moreover, the SF contribution in the radio band with respect to the AGN activity is expected to increase with galaxy mass (Aird, Coil & Georgakakis 2019). In fact, the observed correlation suggests that the radio production due to SF broadly increases with BH mass, as the latter quantity is approximately a constant proportion of the galaxy mass (from a third down to a fifth in the lowest MBH ∼ 105 M⊙, Häring & Rix 2004; Reines & Volonteri 2015; Martín-Navarro & Mezcua 2018), i.e. the stellar content: more stars likely produce more radio emission. This is consistent with the idea that SF, although mostly included in the disc (Bluck et al. 2020) and known to scale with galaxy mass (Speagle et al. 2014), would possibly also scale with MBH. More precisely, the nuclear starburst is plausibly set by the available gas mass present in the NSC (MNSC, Fernández-Ontiveros, Prieto & Acosta-Pulido 2009; Neumayer, Seth & Böker 2020), which scales with the galaxy dynamical mass ($M_{\rm NSC} \propto M _{\mathrm{ dyn}}^{0.55}$, Scott & Graham 2013), which in turn respond to the SMBH gravitational well (Cen 2015; Pitchford et al. 2016). Such a sequence of links eventually enacts the radio-MBH and radio-optical relations observed for star-forming galaxies, e.g setting the fraction of radio emission with respect to the photoionizing energy from young stellar populations and SN products.


Pre-main-sequence stars are typically surrounded by protoplanetary disks, and since such disks are generally highly optically thick at optical/near-infrared (NIR) wavelengths, they may cast shadows on their surroundings. Such disk shadows have been observed on a wide range of angular scales; recently, high-contrast imaging has revealed shadows cast on outer disks by misaligned inner disks on subarcsecond scales (e.g., Marino et al. 2015; Benisty et al. 2018; Casassus et al. 2018). Such shadows reveal that angular distortions are common in inner disks. This is consistent with the existence of a class of self-shadowed disks in which the inner disk scale height is higher than that of the outer disk, leading to a general shadowing and related cooling of the outer disk (Dullemond & Dominik 2004; Dong 2015). A related type of disk shadow, but on a vastly larger angular scale of arcminutes, are shadows cast on large-scale reflection nebulosity. These great disk shadows can occur if a young, usually spatially unresolved, star-disk system is illuminating a reflection nebula, and are especially apparent for systems viewed close to edge-on (Hodapp et al. 2004; Pontoppidan & Dullemond 2005). Neither of these two types of disk shadow should be confused with silhouette disks that obscure background nebulosity, such as the Orion proplyds (O’dell 1998), or dark dust lanes in isolated edge-on disks (Burrows et al. 1996; Stapelfeldt et al. 1998; Duchêne et al. 2010). The projection of the disk onto a large reflection nebula can greatly magnify a small structure in the obscuring disk. Indeed, the apparent angular size of great disk shadows is only limited by the size of the reflection nebula illuminated by the central star, and may be orders of magnitude larger than the protoplanetary disk itself. Great disk shadows therefore present a unique opportunity to explore the geometry of disks on scales otherwise not resolved by direct imaging, primarily the disk scale height, inclination, and position angle.


While spatially extended optical jets and bipolar CO molecular outflows have been observed in numerous Class 0/I protostars (e.g. Reipurth & Bally 2001; Bally 2016, and references therein), near-infrared high-resolution spectroscopy and spectroimaging observations in the past two decades have made it possible to study the kinematics of the outflowing gas and physical properties at the base of the jet within a few hundred au of the driving source in Class 0/I protostars (e.g. Davis et al. 2001, 2003, 2011; Nisini et al. 2005, 2016; Caratti o Garatti et al. 2006; Takami et al. 2006; Antoniucci et al. 2008, 2011, 2017; Garcia Lopez et al. 2008, 2013). These microjets are bright in [Fe ii] forbidden and H2 rovibrational emission lines, hence showing the presence of forbidden emission-line (FEL) regions and molecular hydrogen emission-line (MHEL) regions in low-mass Class 0/I protostars. While multiple low- and high-velocity components are observed in both MHELs and FELs, the higher velocity gas is slightly further offset from the driving source than the slower gas, and the kinematics of the H2 emission differs from [Fe ii] emission, revealing complicated kinematic structures. Evidence of H2 emission from cavity walls is also seen in some protostars, suggesting the presence of a wide-angled wind. Strong emission in the well-known accretion diagnostics of Paschen and Brackett hydrogen recombination lines is observed in protostars, with the ratio of the accretion luminosity to bolometric luminosity spanning from ∼0.1 to ∼1. The mass accretion and loss rates for Class 0/I low-mass protostars span the range of 10−6–10−8 M⊙ yr−1, and the derived jet efficiencies (ratio between mass ejection and accretion rates) range between ∼1 per cent and 10 per cent (e.g. Davis et al. 2001, 2003, 2011; Nisini et al. 2005, 2016; Caratti o Garatti et al. 2006; Takami et al. 2006; Antoniucci et al. 2008, 2011, 2017; Garcia Lopez et al. 2008, 2013). These measurements are within the range predicted by the magnetohydrodynamic jet launching models (e.g. Frank et al. 2014).


Collisionless shocks are one of the most ubiquitous phenomena in space plasmas. The directed flow energy is converted into other forms at the shock front: ion and electron heating, particle acceleration, and magnetic field enhancement. One of the most important problems of the collisionless shock physics is prediction of the post-shock (downstream) state of the plasma and fields given the corresponding plasma and magnetic field state before the shock (upstream). In the absence of dissipative processes the relations between the upstream and downstream parameters (Rankine–Hugoniot relations, boundary conditions, and jump conditions) are just conservation laws of particle number, momentum, and energy. There is a complete hierarchy of scales in collisionless shocks and, accordingly, the boundary conditions depend on the scale at which the boundaries are placed. The standard Rankine–Hugoniot relations (RH) are formulated on the largest, magnetohydrodynamic (MHD) scale, at which the distributions thermalize (Kennel 1994). In many space plasma environments the ambient conditions change on spatial or temporal scales, which are too short to achieve such thermalization. Observational comparison of the upstream and downstream plasma is often done in various regions that do not satisfy the conditions for establishing the MHD RH. In the close vicinity of the shock front, ion distributions are significantly gyrophase dependent, and the jump conditions at the very transition should take this into account (Gedalin & Balikhin 2008; Gedalin 2016a). On larger scales or for measurements invoking substantial temporal and/or spatial averaging, the distributions become gyrotropic but can still remain anisotropic, since isotropization may be slow. The corresponding RH should take into account this anisotropy (Lyu & Kan 1986; Gedalin 2017; Gedalin et al. 2020). Additional complications arise when there are different populations of ions that undergo gyrotropization and isotropization on different scales. Eventual equilibration of temperatures may never happen. Even for different populations of ions of the same kind eventual merging into one thermal population may never be observed. The latter situation is expected to be typical when pickup ions (PUIs) are important constituents, as at the termination shock (Zank et al. 1996; Li et al. 2008; Richardson et al. 2008; Burrows et al. 2010; Matsukiyo & Scholer 2011, 2014; Ariad & Gedalin 2013; Jokipii 2013; Mostafavi et al. 2017, 2018; Kumar et al. 2018). In this case, MHD has to be replaced with a multispecies model, where each population obeys the corresponding conservation laws separately, while the magnetic field jump is obtained by combining all species together. In this approach one has to know the equations of state for each species. Typically, some form of thermodynamics motivated state equations are assumed (Florinski et al. 2009; Borovikov et al. 2011; Pogorelov et al. 2013; Zank et al. 2014; Mostafavi et al. 2018). This approach implicitly assumes that the population is in a kind of local thermodynamic equilibrium. However, observations show that this is not the case. In fact, the downstream ion distribution is determined primarily by ion dynamics in the macroscopic fields of the shock front. Interaction with the electromagnetic fluctuations plays a secondary role causing slow relaxation toward equilibrium, while binary collisions are negligible. The resolution of particle observations in the vicinity of the heliospheric termination shock corresponds to the scale on which the solar wind protons are possibly (but not certainly) isotropic but PUI are still anisotropic. Yet most studies of RH at the termination shock aim at the determination of jump conditions on the MHD scale, assuming isotropy of the distributions. Some previous analyses within a two-fluid model (solar wind and PUI) introduced heat flux and collisionless viscosity of PUI (Zank et al. 2014; Mostafavi et al. 2016, 2017, 2018; Zank 2016). This approach explicitly assumes that ion scattering within the shock transition is substantial so that the focused transport equation is valid throughout the shock (Zank et al. 2014). However, the shock transition is scatter-free (Toptyghin 1980; Drury 1983), so that the approach loses the physics of relation between the kinetic and MHD scales. Accordingly, the obtained magnetic profiles are monotonic and cannot explain observed overshoots (Mostafavi et al. 2018). Previous attempts to take into account the ion kinetics at a shock front assumed magnetic moment conservation (Fahr & Chalov 2008; Fahr et al. 2012; Fahr & Siewert 2013, 2015). However, it has been shown that magnetic moment is, in general, not conserved (Terasawa 1979; Gedalin 2020), and such approximation may be satisfactory only in the perpendicular regime. Proper establishment of the boundary conditions on MHD scales requires establishing a relation of the ultimately isotropic distributions to the collisionless ion dynamics within a shock front. This objective requires proper determination of downstream gyrophase averaged distributions, which are gyrotropic but anisotropic, with further relating these to the isotropic pressure (Gedalin et al. 2020). In the present paper, we numerically determine the parameters of these distributions, which will be used for modifying the Rankine–Hugoniot relation.


It is also very encouraging to note that recent analyses of heavy-ion reaction experiments in terrestrial laboratories and properties of NSs from multiple messengers have led to some new progress in constraining the Esym(ρ) up to about twice the saturation density. For example, shown in Figure 1 are the values of symmetry energy at 2ρ0, that is, Esym(2ρ0), from (1) the FOPI-LAND (Russotto et al. 2011) and (2) the ASY-EOS (Russotto et al. 2016) Collaborations by analyzing the relative flows and yields of light mirror nuclei as well as neutrons and protons in heavy-ion collisions at beam energies of 400 MeV/nucleon, (3) (Chen) an extrapolation of the systematics of low-density symmetry energy (Chen 2015), (4) (Zhang & Li) direct inversions of observed NS radii, tidal deformability, and maximum mass in the high-density EOS space (Zhang et al. 2018; Zhang & Li 2019a, 2020a), (5) (Xie & Li) a Bayesian inference from the radii of canonical NSs observed by using X-rays and gravitational waves from GW170817 (Xie & Li 2019), (6) (Zhou et al.) analyses of NS radii, tidal deformability, and maximum mass within an extended Skyrme Hartree–Fock approach (eSHF) (Zhou & Chen 2019; Zhou et al. 2019), (7) (Nakazato & Suzuki) analyzing cooling timescales of protoneutron stars as well as the radius and tidal deformability of GW170817 (Nakazato & Suzuki 2019), and (8) a Bayesian inference directly from the X-ray data of seven quiescent low-mass X-ray binaries in globular clusters (Baillot d’Etivaux et al. 2019). Despite the rather different assumptions and methods used in analyzing the different types of laboratory and observational data, it is very interesting to see that they all together are consistent with a fiducial value of Esym(2ρ0) = 47 MeV within the still relatively large error bars of the individual analyses. Moreover, several recent theoretical studies also predicted values of Esym(2ρ0) consistent with its fiducial value of 47 MeV. For example, an upper bound of Esym(2ρ0) ≤ 53.2 MeV was derived recently by Tong et al. (2020) by studying the radii of neutron drops using the state-of-the-art nuclear energy density functional theories. Quantum Monte Carlo calculations using local interactions derived from chiral EFT up to next-to-next-to-leading order predicted a value of Esym(2ρ0) ≈ 46 ± 4 MeV (Lonardoni et al. 2020), while the latest many-body perturbation theory calculations with consistent nucleon-nucleon and three-nucleon interactions up to fourth order in the EFT expansion predicted a value of Esym(2ρ0) ≈ 45 ± 3 MeV (Drischler et al. 2020). They are both consistent with the fiducial value of

 and have much smaller error bars. It is worth noting that the chiral EFT is currently applicable to a maximum density of about 2ρ0.


To explain the morphological transformation, two main evolutionary paths have been proposed in the literature. A slow cosmological path naturally follows from the strong redshift evolution of galaxy sizes,

 (Mosleh et al. 2012; Newman et al. 2012; van der Wel et al. 2014b; Shibuya et al. 2015). Star-forming galaxies quench star formation and add to the passive population with approximately the same size in a later epoch (van Dokkum et al. 2015; Lilly & Carollo 2016). A second, fast path involves a downward transition in the mass–size plane, at approximately constant redshift (Barro et al. 2013, 2014; Dekel & Burkert 2014; Zolotov et al. 2015). This process requires a substantial “compaction” of the formally extended star-forming galaxies. One possible mechanism would be a major merger, which is known from observations and simulations to lead to substantial angular momentum redistribution, orbit reconfiguration, and mixing (Mihos & Hernquist 1996; Wuyts et al. 2010). Another possibility is an internal angular momentum redistribution within the star-forming disk. This process has been considered to be effective at high redshift (Noguchi 1999; Immeli et al. 2004a, 2004b; Elmegreen et al. 2008; Genzel et al. 2008; Bournaud et al. 2011), when galaxies are gas rich (Tacconi et al. 2013) and effective viscous dissipation leads to radial inward transport of gas and stars with a timescale of a few hundred megayears (Dekel et al. 2009) and buildup of a central dense core (bulge component) through circumnuclear concentration of gas. Nelson et al. (2016b) find in massive galaxies at z ∼ 1.4 that central 1 kpc regions are highly attenuated by dust and are responsible for half of the total star formation rate (SFR). In conjunction with morphological quenching (Martig et al. 2009; Genzel et al. 2014a), and powerful AGN outflows (Bower et al. 2006; Croton et al. 2006; Förster Schreiber et al. 2014; Genzel et al. 2014b), the compaction process may then lead to an inside-out quenching near the Schechter mass (Tacchella et al. 2015, 2016).


The strong linearity between the two indices shown in Figure 5 must be ascribed to their strong temperature dependence and to the proximity of the Mg ii core and FUV formation heights on one side, and Mg ii continuum and MUV on the other. Most of the radiation contributing to the FUV and MUV originates in the higher photosphere and chromosphere (Thuillier et al. 2012), where atmosphere models of quiet and magnetic structures present similar (and rather small) temperature and density gradients (c.f.r. Figure 1 in Fontenla et al. 2011). This means that, at least at first order, an increase of the activity corresponds to an increase of equal amount of the temperature and density from which both MUV and FUV, as well as Mg ii wings and core, originate. Under the assumption that the lambda-integrated fluxes can be described by a Plank function, it is easy to show that the color index must scale linearly with the temperature, at least for small temperature variations. Therefore, since the spectral brightness variations over a magnetic cycle do not exceed a few tens of K (Fontenla et al. 2011), the [FUV–MUV] color index must also scale linearly with the activity. In LTE, a linear dependence of the core/wing ratio is expected (e.g., Criscuoli et al. 2013), but such dependence is probably less obvious for the Mg ii h and k line, whose cores form in NLTE conditions. Nevertheless, collisions play an important role in the formation of the line (Linsky & Avrett 1970), making the core of this doublet strongly sensitive to temperature (e.g., Carlsson et al. 2015). Indeed, numerical magnetohydrodynamic simulations indicate that the brightness temperature derived from the Mg ii h and k cores is a good approximation for the plasma temperature at the corresponding formation heights (Leenaarts et al. 2013b). Moreover, the Bremen Mg ii index is derived from data of relatively modest spectral resolution, so that the cores are not well resolved. This means that the core intensities used to construct the Mg ii index must have a non-negligible contribution from several layers of the atmosphere, from the lower photosphere, where the response function of the spectral region between the two h and k peaks reaches its maximum (Uitenbroek 1997), to the base of the transition region (Thuillier et al. 2012; Leenaarts et al. 2013b; Carlsson et al. 2015), where the cores form. Employing again a Plank function to describe both the core and the wing intensities of the Mg ii doublet it is easy to show that the Mg ii index must scale linearly with temperature, at least for small temperature perturbations.


For the purpose of this study, we adopt the general concept that the global solar wind is generally composed of relatively steady high-speed solar winds from long-lived high latitude open coronal field regions. The high-speed solar winds from the northern and southern hemispheres are separated by a layer of—on average—slower, denser, more complicated, and variable outflows and structures (Gosling 1996; McComas et al. 2008). This boundary layer between the polar outflows has a latitudinal extent that is roughly defined by the heliospheric current sheet (HCS) maximum excursion. In the solar wind, there also exist various anomalous episodes, as consequences of transient and/or energetic activities that may be remote (in the corona) or heliospheric in origin. The following phenomena or transients relating to anomalous solar wind parameters have been studied and have inspired our study. (1) False magnetic field polarity reversals—evoking images of switchbacks—that have been argued as being interchange reconnection debris (Owens et al. 2013, 2017, 2020), and recently also observed much closer to the Sun by the Parker Solar Probe mission (Laker et al. 2021), and the origin is being debated. (2) Heliospheric magnetic field (HMF) departures from the Parker spiral to nearly radial field at 1 au (Murphy et al. 2002; Watari et al. 2005). The great majority of the initial mass function orientation statistics fall in the vicinity of Parker spiral fields for typical solar wind speeds. However, blocks of time occasionally stand out when the HMF is nearly radial. (3) Interplanetary coronal mass ejections (ICMEs), magnetic clouds (MCs), and other flux ropes, whose structures are foreign to the ambient solar wind and whose plasma differs from the background plasma, often bring anomalously low temperatures and plasma beta (Burlaga et al. 1981; Klein & Burlaga 1982; Burlaga 1988; Richardson & Cane 1995; Kilpua et al. 2009). (4) The intervals of counterstreaming suprathermal electrons (CSEs), which are often interpreted as closed loops of magnetic fields with both ends being connected to a hot electron source within the corona (Bame et al. 1981; Gosling et al. 1987, 1992). (5) Heat flux dropouts, suggesting complete disconnection from hot electron sources (McComas et al. 1989). Many studies have been devoted to these phenomena, including their relationship to the location of the HCS/coronal streamer belt and their solar cycle variations (McComas et al. 1989; Fitzenreiter & Ogilvie 1992; Gosling et al. 1992, 1993; Shodhan et al. 2000; Murphy et al. 2002; Watari et al. 2005; Lavraud et al. 2010; Yu et al. 2014, 2016; Owens et al. 2017, 2020). Weaker solar cycles and advanced imaging and modeling capabilities have raised the profile of pseudostreamers and their boundaries as contributors to the outflows within this slow wind layer (Wang et al. 2012; Owens et al. 2013, 2014). Similarly, the density blobs that are released from the ends of the coronal streamers are another source of slow solar wind (Sheeley & Wang 2007; Rouillard et al. 2010a, 2010b) that belong to this collection of features. These have been associated with in situ observations of small flux rope-like structures in the solar wind at 1 au (Kilpua et al. 2009; Rouillard et al. 2010a, 2010b; Viall & Vourlidas 2015; Sanchez-Diaz et al. 2017; Lavraud et al. 2020). Clearly, there are many reasons and sources of evidence for the occurrence of anomalous characteristics that differ from the typical ambient solar wind. The question is whether they occur in organized ways that provide insights into their origins.


We use data from instruments on board STEREO-A, STEREO-B, ACE, SOHO, Wind, the Geostationary Operational Environmental Satellites (GOES), MESSENGER and the Solar Dynamics Observatory (SDO). Remote-sensing observations of the CME and the activity phenomena over the solar surface were provided by the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) instrument suite on board STEREO (Howard et al. 2008), the Large Angle and Spectrometric Coronagraph experiment (LASCO) on board SOHO (Brueckner et al. 1995), the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board SDO, and the X-ray telescopes on board GOES. Synoptic maps including PFSS model results provided by the Global Oscillation Network Group (GONG, http://gong.nso.edu/) and by Solarsoft PFSS package were also examined. Radio observations were provided by the S/WAVES (Bougeret et al. 2008) investigation on board STEREO and by the WAVES (Bougeret et al. 1995) experiment on board Wind. In situ energetic particle observations were provided by the Solar Electron and Proton Telescope (SEPT; MÃ¼ller-Mellin et al. 2008), the Low Energy Telescope (LET; Mewaldt et al. 2008), and the High Energy Telescope (HET; von Rosenvinge et al. 2008) on board STEREO (all of them part of the IMPACT instrument suite; Luhmann et al. 2008), the Comprehensive Suprathermal and Energetic Particle Analyzer (COSTEP; MÃ¼ller-Mellin et al. 1995), and the Energetic and Relativistic Nuclei and Electron (ERNE; Torsti et al. 1995) instrument on board SOHO, the Electron, Proton, and Alpha Monitor (EPAM; Gold et al. 1998) on board ACE, the 3D Plasma and Energetic Particle Investigation (3DP) on board Wind, and the Energetic Particle and Plasma Spectrometer (EPPS; Andrews et al. 2007) on board MESSENGER. Additionally, Fe/O ratios at ACE were obtained using data from the Solar Isotope Spectrometer (SIS; Stone et al. 1998). Finally, solar wind plasma and magnetic field data were obtained from the Plasma and Suprathermal Ion Composition (PLASTIC; Galvin et al. 2008) investigation on board STEREO, the STEREO Magnetic Field Experiment (AcuÃ±a et al. 2008), the ACE Magnetic Field Experiment (Smith et al. 1998), and the ACE/Solar Wind Electron Proton Alpha Monitor (SWEPAM; McComas et al. 1998). Due to gaps in ACE/SWEPAM data, plasma data from the Charge, Element, and Isotope Analysis System (CELIAS; Hovestadt et al. 1995) instrument on board SOHO were also used. Magnetic field data from MESSENGER were obtained from the Magnetometer Instrument on board this s/c (Anderson et al. 2007). Interplanetary disturbance identifications were cross-checked using the STEREO and ACE level 3 event list maintained by L. Jian (http://www-ssc.igpp.ucla.edu/forms/stereo/stereo_level_3.html, http://www.srl.caltech.edu/ACE/ASC/DATA/level3/) and the near-Earth ICME list maintained by I. Richardson and H. Cane (http://www.srl.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm; see also Cane & Richardson 2003).

Radio observations were provided by
and the High Energy Telescope


To describe the H i bispectrum in redshift space, we apply the standard redshift space kernels (see Heavens et al. 1998; Scoccimarro et al. 1999 for derivations) such that
(10)$$\begin{eqnarray*}
B_\rm {H\,\small {I}}(\boldsymbol{k}_{1},\boldsymbol{k}_{2},\boldsymbol{k}_{3}) &=& 2\, \overline{T}_\rm {H\,\small {I}}^2\left[Z_1(\boldsymbol{k}_{1}) Z_1(\boldsymbol{k}_{2}) Z_2(\boldsymbol{k}_{1}, \boldsymbol{k}_{2}) P_\text{lin}(k_{1}) P_\text{lin}(k_{2})\right.\nonumber\\
&&\left. +\, \text{cycl.}\right] D_\text{FoG}(\boldsymbol{k}_{1},\boldsymbol{k}_{2},\boldsymbol{k}_{3},\sigma _\text{B}),
\end{eqnarray*}$$where cycl. represents cyclic permutations which run over all possible pairs of $\boldsymbol{k}_{1},\boldsymbol{k}_{2}$ and $\boldsymbol{k}_{3}$. Plin represents the real-space, linear matter power spectrum for which we use the CLASS Boltzmann solver (Blas, Lesgourgues & Tram 2011; Lesgourgues 2011). Z1 is given in equation (7) and Z2 denotes the second-order kernel and is given by
(11)$$\begin{eqnarray*}
Z_2(\boldsymbol{k}_{i}, \boldsymbol{k}_{j}) &=& b_1 F_2(\boldsymbol{k}_{i}, \boldsymbol{k}_{j})+f \mu _{ij}^2 G_2(\boldsymbol{k}_{i}, \boldsymbol{k}_{j})+\frac{f \mu _{ij} k_{ij}}{2}\nonumber\\
&&\times \,\left[\frac{\mu _i}{k_i} Z_1(\boldsymbol{k}_{j})+\frac{\mu _j}{k_{j}} Z_1(\boldsymbol{k}_{i})\right] + \frac{b_2}{2},
\end{eqnarray*}$$where $\boldsymbol{k}_{ij} = \boldsymbol{k}_{i} + \boldsymbol{k}_{j}$ and $\mu _{ij} = \boldsymbol{k}_{ij}\cdot \hat{{\bf z}}/k_{ij}$. F2 and G2 denote the second-order kernels for the real-space density and velocity fields and are given by
(12)$$\begin{eqnarray*}
F_2(\boldsymbol{k}_{i}, \boldsymbol{k}_{j}) = \frac{5}{7} + \frac{m_{ij}}{2}\left(\frac{k_i}{k_{j}} + \frac{k_{j}}{k_i}\right) + \frac{2}{7} m_{ij}^2,
\end{eqnarray*}$$(13)$$\begin{eqnarray*}
G_2(\boldsymbol{k}_{i}, \boldsymbol{k}_{j}) = \frac{3}{7} + \frac{m_{ij}}{2}\left(\frac{k_i}{k_{j}} + \frac{k_{j}}{k_i}\right)+\frac{4}{7} m_{ij}^2 ,
\end{eqnarray*}$$where $m_{ij} = (\boldsymbol{k}_{i}\cdot \boldsymbol{k}_{j})/(k_i k_{j})$. The final term in equation (10), DFoG, is a phenomenological factor to address some non-linear RSD effects not sufficiently modelled by the redshift kernels alone. On smaller scales, internal motion inside virialized structures produces a radial smearing to the density field in redshift space, known as the fingers-of-god (FoG) effect (Jackson 1972). It is common to include a term which describes the FoG (Taruya, Nishimichi & Saito 2010), even when including higher order perturbation theory terms and should be seen as a phenomenological damping required to correct for non-linear effects (Verde et al. 1998; Gil-Marín et al. 2014). For our choice of model, this factor is given by (Gil-Marín et al. 2015)
(14)$$\begin{eqnarray*}
D_\text{FoG}(\boldsymbol{k}_{1},\boldsymbol{k}_{2},\boldsymbol{k}_{3},\sigma _\text{B}) = \left[1 + \frac{1}{2}\left(k_{1}^2 \mu _1^2 + k_{2}^2\mu _2^2 + k_{3}^2\mu _3^2\right)^2 \sigma _\text{B}^2\right]^{-2} . \nonumber\\
\end{eqnarray*}$$It is worth noting that it is necessary for galaxy surveys to also include modelling of shot noise caused by discreteness effects in their bispectra analyses. However, for H i IM, where unresolved signal is integrated over, this should not be a limiting factor (Spinelli et al. 2020). We therefore do not consider any treatment of shot noise in our analysis, making the assumption that this should be very low in H i IM observations.


Another binary parameter is the stellar mass ratio distribution. The choice of the mass ratio can be called the pairing function, which is combining stars into binary systems. When random pairing is used (i.e., binary companions are randomly chosen from a given IMF), we find similar mass segregation results to those for star clusters containing only single stars. However, random pairing is ruled out observationally, and there is also a lack of theoretical backing for a random pairing function (Shatsky & Tokovinin 2002; Kouwenhoven et al. 2005, 2007a, 2007b). Indeed, massive stars preferentially choose other massive stars as their binary companions (Kouwenhoven et al. 2010). This implies that both the geometric average and the median MST method may be biased by the short MST edges from binary systems, although the LnND method is less influenced. An alternative binary pairing function is the so-called ordered pairing (i.e., mass ratio of the binary star components ∼1, in particular for massive stars; see e.g., Kouwenhoven et al. 2009; Oh & Kroupa 2012), which matches stars in order of their mass distribution. We re-pair our test model using ordered pairing and find some extremely high values of the mass segregation degree when using the MST method. This is illustrated in Figure 5, where we see that the mass segregation degree for ordered pairing functions is biased toward very high values for relatively small massive-star samples. These extremely high degrees of mass segregation are not physical, because they are mainly produced by the short MST edges in the binary systems. This is illustrated by the sharp steps in the solid curves, which greatly deviates from the non-mass-segregation distribution equal to unity. Therefore, the gmMST and mMST methods should not be considered as a global compactness measure of massive stars in cases where binary fractions are significant, i.e., >10%. Massive stars may have much shorter MST edges than low-mass stars, due to the preferential presence of binaries among massive stars (e.g., Sana et al. 2014).


Due to the high luminosity and seemingly long-term flux stability, the Crab pulsar and its pulsar wind nebula (PWN) is one of the most studied sources in the very high energy (VHE, $\rm {E} \gt 100$ GeV) regime. For many years, Crab has been used as a standard candle in X- and gamma-ray astronomy (Hester 2008). The Crab nebula was the first TeV gamma-ray source discovered (in 1989 by the Whipple 10-m telescope; Weekes et al. 1989), and soon after detected by numerous facilities above 100 GeV (Smith et al. 2000; Aharonian et al. 2006; Abdo et al. 2012; Aleksić et al. 2015; Meagher & VERITAS Collaboration 2015; Abeysekara et al. 2017). It has a (energy-dependent) angular size of ∼0.1° and its distance has been estimated to be ≈2.2 kpc, corresponding to a physical size of ≈3.8 pc (Trimble 1973; Davidson & Fesen 1985; Kaplan et al. 2008). The nebula non-thermal spectrum can be described by two components, a synchrotron component extending from radio to high energy gamma-rays and a second component emerging above 1 GeV (Atoyan & Aharonian 1996). The latter is interpreted as inverse Compton scattering (IC) of the same particles against soft background photons: cosmic microwave background (CMB), far-infrared (FIR), and near-infrared (NIR) background, and the synchrotron photons of the nebula itself or Synchrotron Self-Compton (SSC). The pulsar has a spin period of $\rm {P} = 33$ ms, a spin-down rate of $\rm {\dot{P}} = 4.21\times 10^{-13}$ and a spin-down luminosity of $\rm {L_{spin}} = 3.8\times 10^{38}\ \rm {erg}\ \rm {s^{-1}}$. The pulsed emission between 0.1  and 100 GeV is believed to be due to synchrotron-curvature radiation (Abdo et al. 2010; Ansoldi et al. 2016) and its spectrum is well parametrized by a power law with a sub-exponential cut-off function of spectral index γP = 1.59, the break located at an energy of about 500 MeV and curvature index of κ = 0.43. In addition, a power-law component emerges above the cut-off extending above 100 GeV (Aliu et al. 2011; Aleksić et al. 2012; Ansoldi et al. 2016).


Disk galaxies typically reveal out-of-equilibrium features due to incomplete equilibration. These may appear in the form of bars and spiral arms, which are large-scale perturbations in the radial and azimuthal directions, responsible for a slow, secular evolution of the disk. In the vertical direction, disks often reveal warps (Binney 1992). In the case of the Milky Way (MW) disk, which can be studied in much greater detail than any other system, recent data from astrometric and radial velocity surveys such as SEGUE (Yanny et al. 2009), RAVE (Steinmetz et al. 2006), GALAH (Bland-Hawthorn et al. 2019), LAMOST (Cui et al. 2012), and above all Gaia (Gaia Collaboration et al. 2016, 2018a, 2018b) have revealed a variety of additional vertical distortions. At large galactocentric radii (>10 kpc) this includes, among others, oscillations and corrugations (Xu et al. 2015; Schönrich & Dehnen 2018), and streams of stars kicked up from the disk that undergo phase mixing, sometimes referred to as “feathers” (e.g., Price-Whelan et al. 2015; Thomas et al. 2019; Laporte et al. 2022). Similar oscillations and vertical asymmetries have also been reported in the solar vicinity (e.g., Widrow et al. 2012; Williams et al. 2013; Yanny & Gardner 2013; Gaia Collaboration et al. 2018b; Quillen et al. 2018; Bennett & Bovy 2019; Carrillo et al. 2019). One of the most intriguing structures is the phase-space spiral discovered by Antoja et al. (2018) and studied in more detail in subsequent studies (e.g., Bland-Hawthorn et al. 2019; Li 2021; Li & Widrow 2021; Gandhi et al. 2022). Using data from Gaia DR2 (Gaia Collaboration et al. 2018a), Antoja et al. (2018) selected ∼900,000 stars within a narrow range of galactocentric radius and azimuthal angle centered around the Sun. When plotting the density of stars in the (z, v

z
)-plane of vertical position, z, and vertical velocity, v

z
, they noticed a faint, unexpected spiral pattern, which became more enhanced when color-coding the (z, v

z
)-“pixels” by the median radial or azimuthal velocities. The one-armed spiral makes two to three complete wraps, resembling a snail shell, and is interpreted as a signature of phase mixing in the vertical direction following a perturbation, which Antoja et al. (2018) estimate to have occurred between 300 and 900 Myr ago. More careful analyses in later studies (e.g., Bland-Hawthorn et al. 2019; Li 2021) have nailed down the interaction time to ∼500 Myr ago.


Several studies that analyzed the metallic content in the atmospheres of evolved stars hosting planets have been published in the last decade. The first results were based on small samples and/or the abundances were not obtained with a homogeneous technique. Schuler et al. (2005) derived the metallicity for one GWP and gathered abundances from the literature for another seven. They reported that, on average, GWP were metal-poor compared with planet hosting dwarfs. Similar results were found by Sadakane et al. (2005) analyzing 4 GWP. In 2007, Pasquini et al. studying 14 GWP (4 from the literature), concluded that in contrast to the distribution of main-sequence stars with planets, the GWP distribution does not favor high metallicity objects. Conversely, Hekker & Meléndez (2007), analyzing a sample of 380 GK giant stars including 20 with planets (15 from the literature), found an enhancement for GWP of 0.13 dex compared with stars without planets. Takeda et al. (2008), with a sample of 322 giants, including 10 planet-hosts, did not find any metallicity offset. Ghezzi et al. (2010a) found that the metallicity distribution of 16 GWP displays an average that is 0.17 dex more metal-poor than the sample of 117 planet-hosting dwarfs and, furthermore, that the subgiant sample is more metal-rich by 0.12 dex. Johnson et al. (2010) ruled out a flat metallicity relationship among their sample of 246 subgiants (36 with planets, including unpublished candidates). More recently, with larger samples, Mortier et al. (2013) did not find any metallicity enhancement in 71 evolved stars with planets in comparison with 733 evolved stars without planets, with metallicity values gathered from the literature. Finally, Maldonado et al. (2013) found a metallicity enhancement in 16 subgiants with planets relative to 55 without planets (50 from literature). These authors did not find evidence of a metallicity offset between giants with and without planets, analyzing 43 GWP and 67 GWOP. However, for stars with masses above 1.5 M⊙, they reported a slight metallicity enhancement for giants with planets relative to the control sample.


When a galaxy is isolated, star formation quenching is mostly driven by internal processes (Larson 1974; Dekel & Silk 1986; Vulcani et al. 2021). Active galatic nuclei (AGNs) feedback create an outflow of gas preventing further hot gas accretion from the circumgalactic medium (Dalla Vecchia & Schaye 2008; Bongiorno et al. 2016; Trussler et al. 2020). Star formation depends on gravitational instabilities, which may be prevented due to a transition from a stellar disc to a spheroid (‘morphological quenching’; Martig et al. 2009). Bars in spiral galaxies may drive gas inflows, which enhance central star formation (bar-driven evolution; Spinoso et al. 2017). However, in the local Universe most of the galaxies live in groups/clusters (Geller & Huchra 1983). Even before crossing the virial radius, infalling galaxies can stop accreting new gas (‘Starvation’; Larson, Tinsley & Caldwell 1980; Balogh, Navarro & Morris 2000; van de Voort et al. 2017). For instance, Trussler et al. (2020) suggest galaxy quenching has an extended phase (∼5 Gyr) of starvation. In addition, infalling galaxies can lose gas, stars and even dark matter via gravitational tides (‘tidal mass-loss’ - TML; Johnston, Sigurdsson & Hernquist 1999; Read et al. 2006). Within the virial radius, the hot gas in the intracluster medium (ICM) exerts pressure on galaxies moving within the cluster and may remove gas via Ram Pressure Stripping (RPS; Gunn & Gott 1972; Abadi, Moore & Bower 1999). Clusters provide a suitable environment for both direct and indirect galaxy interactions, especially in its core. Direct encounters may lead to galaxy mergers and cause a starburst event over a short time-scale and quickly exhaust a galaxy’s gas supply (Springel & Hernquist 2005; Cox et al. 2008; Teyssier, Chapon & Bournaud 2010), whereas repeated indirect encounters may leave interacting galaxies with disturbed morphologies. At last, it is important to note that clusters are built up by the accretion of galaxy groups. Cluster galaxies may therefore be affected by ‘pre-processing’, in which galaxy properties were altered even before entering the cluster (Fujita 2004; Mahajan 2013; Sarron et al. 2019).


Figure 2 shows solar wind plasma and magnetic field measurements for a CIR that occurred between July 26 and 27, 2003 (days of year 207–208). Following Chotoo et al. (2000), Richardson et al. (1993), we marked four regions in the plot: the slow wind region (S), the compressed slow wind region (S′), the compressed fast wind region (F′), and the fast wind itself (F). Throughout four regions, the mean charge states of iron measured by ACE/SWICS lies around 11+, consistent with typical values in the solar wind (Lepri et al. 2001). The stream interface (S′-F′) is indicated by the vertical line in Fig. 2 and is characterized by a drop of the O7+/O6+ abundance ratio measured with SWICS in the bulk solar wind (Wimmer-Schweingruber et al. 1997, 1999). The leading (S-S′) and trailing edge (F′-F) of the CIR were determined by the total pressure (Jian et al. 2006). Bučík et al. (2009) found that CIR boundaries can be well defined when the total pressure exceeds 50 pPa (indicated by the horizontal dashed line in Fig. 2), which is slightly higher than that in the background solar wind, which typically is 20−30 pPa, according to Jian et al. (2006). The total pressure P was obtained from the sum of plasma and magnetic field pressure, that is, \hbox{$P=n_{\rm p}v^{2}_{\rm th}m+B^2/2\mu_0$}P=npvth2m+B2/2μ0, where np and vth are the proton density and thermal speed, respectively, and B is the magnitude of the magnetic field. Because SOHO has no magnetometer, we used magnetic field data from ACE/MAG (which is also around L1). Comparing plasma parameters (bulk speed, thermal speed, and proton density) measured by PM with those of SWEPAM, we see that the physical conditions at SOHO and ACE were almost the same, and that the time difference between passages of the CIR boundaries is less than ten minutes. The CIR shown in Fig. 2 was bounded by a reverse shock (vertical line separating F′ from F). We clearly see that the suprathermal He++ intensity peaks inside the decelerated and compressed fast-wind region (F′), close to the reverse shock. In contrast, suprathermal particles are very rare in the S and S′ regions. After passage of the reverse shock, suprathermal particles continue to be observable for more than one day. They are commonly believed to be the sunward particles accelerated by the reverse shock far beyond the Earth orbit. In other words, the observer saw the duration of the CIR particle event, which was longer than that of the CIR compression region itself. The background level shown in green was estimated using the method described above. The signal-to-noise ratio (S/N) in the F and F′ regions is higher than 100, confirming that our observations are due to real He++ particles.


Since the free-fall time-scale tff depends on the gravity law, we study how changing the gravity law affects the value of n in the KS law. Our main aim in this paper is to derive for the first time the KS law from a basic description in the framework of Milgromian dynamics (MOND; Milgrom 1983; Famaey & McGaugh 2012). MOND is an alternative approach to a cold dark matter-dominated universe deduced from the flattening of observed rotation curves of spiral galaxies under the assumption of Newtonian dynamics. In MOND, these dynamical discrepancies are addressed by a generalization of Newtonian gravity (for a thorough review, see e.g. Famaey & McGaugh 2012). Within the classical MOND framework, the Newtonian gravitational acceleration gN is replaced in the spherically symmetric case by $g=\sqrt{g_{\rm {N}} a_0}$ when the gravitational acceleration is far smaller than the critical acceleration a0 = 1.2 × 10−10 m s−2 (Begeman, Broeils & Sanders 1991; Gentile, Famaey & de Blok 2011). In less symmetric configurations, the equations of motion are derived from a Lagrangian, yielding standard equations of motion but with a generalized Poisson equation for the gravitational field (Bekenstein & Milgrom 1984; Milgrom 2010). MOND predicted the very tight radial acceleration relation (RAR) between the gravity g implied by disc galaxy rotation curves and the Newtonian gravity gN, resulting from their baryonic distribution (Lelli et al. 2017; Li et al. 2018). The RAR is also evident in stacked galaxy–galaxy weak lensing measurements that probe out to larger radii (Milgrom 2013; Brouwer et al. 2021). The external field effect (EFE) predicted by MOND (Bekenstein & Milgrom 1984) and required for consistency with data on Solar neighbourhood wide binaries (Banik & Zhao 2018c; Pittordis & Sutherland 2019) has recently been confirmed at high significance by comparing galaxies in isolated and more crowded environments (Haghi et al. 2016; Chae et al. 2020). Detailed numerical simulations of disc galaxy secular evolution in MOND have recently been conducted for the case of M33 (Banik et al. 2020) and for a Milky Way or M31-like surface density (Roshan et al. 2021), while star formation has also been explored with high-resolution simulations (Renaud, Famaey & Kroupa 2016). The possible cosmological context has been explored in e.g. Haslbauer, Banik & Kroupa (2020) and Asencio, Banik & Kroupa (2021). The MOND corrections to Newtonian gravity might be capturing effects of the quantum vacuum (Milgrom 1999; Smolin 2017; Verlinde 2017; Senay, Mohammadi Sabet & Moradpour 2021).


The most commonly used technique to create a mock lens system from simulated galaxies is to extract a mass map from a particle-based simulation and use it to calculate lensing quantities (i.e. lensing potential and its first and second derivatives) needed to emulate the gravitationally lensed images. For this purpose, galaxies from high resolution hydrodynamical simulations, including, for example, EAGLE (Evolution and Assembly of GaLaxies and their Environments, Schaye et al. 2015; Crain et al. 2015) or Illustris (Vogelsberger et al. 2014b,a), have been widely used. Different types of software, such as lenstronomy (Birrer & Amara 2018) and GLAMER (Gravitational Lensing Simulations with Adaptive Mesh Refinement, Metcalf & Petkova 2014), can handle the inference of lensing quantities from mass maps using fast Fourier transform convolution. Fast Fourier is a commonly used technique to speed up the calculation of lensing quantities, which imply computationally expansive numerical integration but it remains a demanding procedure (Metcalf & Petkova 2014; Plazas 2020). One could wonder what mass map resolution should be used and what size of map is relevant to be sufficiently precise in the mock creation while minimising the computational time. One generally considers that a strongly lensed system is determined by the projected mass inner to the lensed images. This would suggest that a region extending over a few Einstein radii (θE) is sufficient for the simulations. However, this consists in effectively ignoring any source of shear, and/or perturbations caused by substructures and/or anisotropy in the mass distributions. Moreover, depending on the symmetry of the problem, cutting the mass distribution at a given radius not only automatically removes the mass beyond that radius, but it may also introduce numerical artefacts that could wrongly be attributed to properties of the examined lens mass distribution. In this paper we focus on this latter point and quantify the impact of the shape (and size) of the integration domain on the lensing quantities inference.


We derived the mean values of the 13CO/C18O abundance ratio for the three star-forming regions, obtaining values of 13CO/C18O = 10.9 ± 7.5 for Taurus, 13CO/C18O = 17.3 ± 11.5 for Perseus, and 13CO/C18O = 23.7 ± 10.4 for Orion. The expected value is 13CO/C18O = 7.5−9.8, assuming 12C/13C = 57−67 and 16O/18O = 500−600 (Gerin et al. 2015; Langer & Penzias 1990; Wilson & Rood 1994). As mentioned in Sect. 5.7, the 13CO/C18O abundance ratio increases in regions of enhanced UV field (Shimajiri et al. 2014; Ishii et al. 2019; Areal et al. 2018). This variation is interpreted in terms of the selective photodissociation and isotopic fractionation (see Bron et al. 2018; Fuente et al. 2019). This effect is produced because the more abundant CO isotopolog shields itself from the effect of UV photons more efficiently than less abundant isotopologs (Stark et al. 2014; Visser et al. 2009). Our data confirm this trend in Orion, although the observed positions are located at a distance >1 pc from the ionized nebula M 42, which shows that the whole cloud is illuminated by a strong UV field emitted by young massive stars in the Trapezium cluster (Pabst et al. 2019). In contrast to X(C18O), which presents uniform abundance in the three regions, the mean 13CO abundance is a factor of approximately two higher in Orion than in Taurus. One interesting question pertains to whether the observed variation in the 13CO abundance is related to a variation in the 12CO/13CO ratio (Roueff et al. 2015; Colzi et al. 2020) or is revealing variations for a higher 12CO abundance in Orion. Because of the higher gas temperature and incident UV field in Orion, selective photodissociation would work in the direction of increasing N(12CO)/N(13CO) in Orion with respect to Taurus. Therefore, a higher 12CO abundance in Orion stands as the most likely explanation. Our results are based on significant approximations (one single phase, gas-dust thermalization), and therefore a detailed multi-transition study of these compounds is required to confirm this result.


As done by Le Fèvre et al. (2020), we visually inspect the ancillary data, the intensity maps, the velocity and velocity dispersion fields presented in Sect. 3.1 to search for the presence of multiple components or disturbed morphology near the position of the targets. The channel maps, the spectra and the PVDs are checked together searching for consistent emission features. By taking into account the results of the initial qualitative classification by Le Fèvre et al. (2020) and of the more recent quantitative analysis of a subsample of the ALPINE targets by Jones et al. (2021), we proceed with a more in-depth characterization of the [CII]-detected galaxies aimed at obtaining a robust merger fraction at z ∼ 5. Adopting the same criteria described in Sect. 2 to differentiate the targets and considering the S/N of the minor merger component as described in Sect. 3.1, we find a slightly lower fraction (∼31%, 23 out of 75 [CII]-detected sources) of mergers7 if compared to the 40% found by Le Fèvre et al. (2020), with 12, 20 and 7% of the sample made by rotating, extended and compact dispersion dominated sources, respectively. To be more conservative in the classification of the galaxies (especially for obtaining a more robust merger statistics), we define the remaining 30% of the sample as ‘uncertain’, a new category that includes the weak galaxies (as described in Le Fèvre et al. 2020) and also objects that, by visual inspection, present features that are intermediate to those of various classes. This category is similar to the ‘uncertain’ (UNC) class introduced in Jones et al. (2021) that, based on the results of the 3DBarolo fits, contains sources they are unable to classify because of the low S/N and/or spectral resolution, or contrasting evidence in their classification criteria. Although the uncertain category is populated by a significantly larger fraction of sources with respect to the weak class (∼16%) in Le Fèvre et al. (2020), we recover the same qualitative morpho-kinematic distribution of the previous analysis, confirming the high fraction of rotators and mergers at these early epochs.


For these four remaining FHSC candidates (L1451-mm, MC35-mm, SM1N, and Oph A-N6) that have been observed at intermediate scales (few 100 au to few 1000 au) a final confirmation of their true evolutionary state requires higher resolution observations. For L1451-mm, the compact outflow needs to be resolved to investigate its morphology and kinematics, as a higher velocity component (an indication of protostellar nature) could be revealed by observations with a beam smaller than 100 au, similar to the case of B1b-N (Hirano 2019). An additional goal of high-resolution observations for L1451-mm and the remaining youngest candidates should be to investigate the temperature and density profiles of the envelope at scales from few au to 100 au. This is because simulations show that the temperature remains lower than ∼30 K even at several tens of au up to 100 au from the centre (Bate et al. 2014; Tomida et al. 2015; Hincelin et al. 2016; Young et al. 2019) during the FHSC stage. On the other hand, Class 0 sources show temperatures of 20–30 K or higher at scales of several 100 au (sufficient for thermal evaporation of CO) that results in the inner envelope and disc being easily detected using C18O observations (Yen et al. 2015, 2017; Stephens et al. 2018). This holds even in very low luminosity objects, for which the unexpected large extent of C18O is interpreted as evidence of a previous burst of accretion (Frimann et al. 2017; Hsieh et al. 2018). As for the density profile, simulations of the FHSC stage show a flat inner region, corresponding to the FHSC structure and extending up to ∼10 au (Tomida et al. 2013; Bate et al. 2014). For a protostar, on the other hand, the density profile should increase towards the central ∼1 au region (Young et al. 2019). Observations of the continuum emission with a resolution better than a few tens of au are likely required to model the emission and provide a density and temperature profile that can probe the relevant scales. Additional line observations with a similar resolution can also help to further distinguish between the different models. We note that, as pointed out in Young et al. (2019), distinguishing a dense core with only an FHSC and one that has recently formed a protostar but in which the FHSC structure is still present is likely not possible, even with high-resolution observations. Given the optically thick nature of the FHSC core, it is difficult to probe the physical properties within the FHSC structure. Despite this, finding a source with density and temperature profiles as well as with outflow properties consistent with the theoretical predictions will provide convincing evidence in support of a bona fide FHSC.


Hydrodynamical simulations of evolving galaxies allow us to calibrate these diagnostics by measuring their observability given a set of formation scenarios and physical processes (e.g. Jonsson et al. 2006; Rocha et al. 2007; Lotz et al. 2008a; Bush et al. 2010; Narayanan et al. 2010; Hayward et al. 2013; Snyder et al. 2013; Lanz et al. 2014). The quality and breadth of these experiments are limited by the availability of computational resources and the fidelity of models for galaxy physics such as star formation, supernovae, and the interstellar medium (ISM). It has only recently become widespread to model the formation of galaxies ab initio (e.g. Governato et al. 2004; Agertz, Teyssier & Moore 2011; Guedes et al. 2011; Marinacci, Pakmor & Springel 2013; Ceverino et al. 2014), and the realism continues to improve (Stinson et al. 2012; Hopkins et al. 2014; Torrey et al. 2014), albeit with still widely varying physics models (e.g. Scannapieco et al. 2012; Kim et al. 2014). Prior to these advances, studies were limited to small numbers of isolated galaxies or mergers to inform common diagnostics of galaxy evolution, an approach with a significant limitation: they do not fully account for cosmological context, such as gas accretion and the breadth of assembly histories. In addition to mergers, models of high-redshift galaxy formation (e.g. Dekel, Sari & Ceverino 2009; Dekel et al. 2013) have recently appreciated the tight coupling between gas accretion and disc evolution (e.g. Cacciato, Dekel & Genel 2012; Danovich et al. 2012; Dekel & Krumholz 2013), as well as bulge and super-massive black hole (SMBH) growth mediated by turbulent motions or violent disc instability (e.g. Bournaud et al. 2011; Porter et al. 2014) and the evolution of giant clumps (Dekel & Burkert 2013). These important processes likely complicate interpretation of a given observation, and recent studies of galaxy morphology have begun to exploit simulations including them (e.g. Scannapieco et al. 2010; Pedrosa, Tissera & De Rossi 2014).


Located in the star-forming region ρ-Ophiuchi, inside the dark cloud L1689N and at a distance of 141 pc (Dzib et al. 2018), IRAS16293−2422 is a well-studied Young Stellar Object (YSO) classified as a Class 0 source with less than 104 yr (Andre, Ward-Thompson & Barsony 1993), and represents one of the very early stages of low-mass star formation. It was the first source identified as a hot corino (Blake et al. 1994; van Dishoeck et al. 1995) based on the detection of Complex Organic Molecules (COMs) in the source, which was later supported by follow-up studies (Ceccarelli et al. 1998, 2000; Schöier et al. 2002; Crimier et al. 2010; Jørgensen et al. 2011, 2016; Pineda et al. 2012; Oya et al. 2016; Jacobsen et al. 2018; van der Wiel et al. 2019). Higher resolution observations revealed that IRAS16293−2422 is in fact a triple system, composed of sources A1 and A2, separated by 54 au from each other (Maureira et al. 2020) and source B, 738 au (5 arcse; Wootten 1989) away from source A. Due to this larger separation, tidal truncation between the three protostars is discarded and therefore source B is considered to have evolved as an isolated source (Rodríguez et al. 2005). It was initially proposed to be either an evolved T Tauri star (Stark et al. 2004; Takakuwa et al. 2007) or a very young object (Chandler et al. 2005), however, Chandler et al. (2005) suggested that source B has large-scale infalls based on SO line emission. Pineda et al. (2012) confirmed the infall of an inner envelope, with mass accretion rates of 4.5 × 10−5 M⊙yr−1, based on ALMA detections of inverse P-Cygni profiles in CH3OCHO-E, CH3OCHO-E-A and H2CCO, ruling out the possibility of it being a T Tauri star. The interpretations of infall from these profiles was also suggested by Jørgensen et al. (2012) and Zapata et al. (2013). Unlike the A1 and A2 protostars, source B has not shown clear signs of outflow launching, explained by the lack of free–free emission at low frequencies (Chandler et al. 2005; Rodríguez et al. 2005; Loinard et al. 2007; Rao et al. 2009; Liu et al. 2018; Hernández-Gómez et al. 2019b) and also based on molecular lines (Loinard et al. 2002; van der Wiel et al. 2019).


In recent years, numerous low-mass and ELM WDs have been detected in the context of relevant surveys, such as the SDSS, ELM, SPY and WASP (see, e.g., Koester et al. 2009; Brown et al. 2010, 2016, 2020; Kilic et al. 2011, 2012; Gianninas et al. 2015; Kosakowski et al. 2020). The discovery of their probable precursors, namely, the so-called low-mass pre-WDs, has triggered an interest in these types of objects because of the possibility of studying the evolution of the progenitors that lead to the WD phase. Even more interestingly, the detection of multi-periodic brightness variations in low-mass WDs (Hermes et al. 2012, 2013a,b; Kilic et al. 2015, 2018; Bell et al. 2017, 2018; Pelisoli et al. 2018), and low-mass pre-WDs (Maxted et al. 2013, 2014; Gianninas et al. 2016; Wang et al. 2020) has brought about new classes of pulsating stars known as ELMVs and pre-ELMVs, respectively (ELM and pre-ELM variables, respectively). It has allowed for the study of their stellar interiors using the tools of asteroseismology, similarly to the case of other pulsating WDs such as ZZ Ceti stars or DAVs –pulsating WDs with H-rich atmospheres – and V777 Her or DBVs – pulsating WDs with He-rich atmospheres (Winget & Kepler 2008; Fontaine & Brassard 2008; Althaus et al. 2010; Córsico et al. 2019). The pulsations observed in ELMVs are compatible with global gravity (g)-mode pulsations. In the case of pulsating ELM WDs, the pulsations have large amplitudes mainly at the core regions (Steinfadt et al. 2010; Córsico et al. 2012; Córsico & Althaus 2014a), allowing for the study of their core chemical structure. According to nonadiabatic computations (Córsico et al. 2012; Van Grootel et al. 2013; Córsico & Althaus 2016), these modes are probably excited by the κ − γ (Unno et al. 1989) mechanism acting at the H-ionization zone. In the case of pre-ELMVs, the nonadiabatic stability computations for radial (Jeffery & Saio 2013) and nonradial p- and g-mode pulsations (Córsico et al. 2016; Gianninas et al. 2016; Istrate et al. 2016b) revealed that the excitation is probably due to the κ − γ mechanism, acting mainly in the zone of the second partial ionization of He, with a weaker contribution from the region of the first partial ionization of He and the partial ionization of H. The presence of He in the driving zone is crucial to having the modes destabilized by the κ − γ mechanism (Córsico & Althaus 2016; Istrate et al. 2016b).


Over time, the data releases have treated the Balmer line regions in different ways. The presence of the artificial curvature was first reported by Busca et al. (2013) in the context of the DR9 data release. To minimize this effect, a different scheme was used in DR12 (Alam et al. 2015, see their table 2) by using a linear function (instead of an iterative b-spline procedure) to interpolate the flux over the masked regions. Surprisingly, we observe that this data reduction change was only applied to the Balmer β, γ, and δ lines but not applied to the Balmer α line. For the latter one, the original iterative spline interpolation scheme has been used all along. As a result, an absorption-like feature at the location of Balmer α is found in SDSS data releases 9 up to now, i.e. the latest data release 14 (Abolfathi et al. 2018). To illustrate this, we show examples of calibration vectors for SDSS BOSS DR9 (Ahn et al. 2012; Dawson et al. 2013), DR12 (Alam et al. 2015), eBOSS DR14 (Dawson et al. 2016; Abolfathi et al. 2018) data release as well as calibration vectors for the MaNGA survey (Bundy et al. 2015) DR14 data release (Abolfathi et al. 2018) in Fig. 6. In the upper panel, we show small-scale features in calibration vectors from the same plate (number 3647) processed by the DR9 (blue), DR12 (green), and DR14 (red) pipelines. The spectra are obtained by normalizing the large-scale features in calibration vectors with a cubic b-spline with break points separated by 50 Å. The three spectra are mostly identical while the smooth curving features at the wavelengths of Balmer series in DR9 disappear in DR12 and DR14. From DR12, the pipeline corrects the features with linear interpolation across wavelength regions with Balmer β, γ, and δ lines (Alam et al. 2015). One can also observe the change in the median residual spectra of DR9 and DR12 in Fig. 1. However, the Hα feature remains uncorrected from DR9 to DR14. We also show a DR7 calibration vector (black) in which most of the wiggles are absent. As pointed previously, this is due to the fact that the DR7 pipeline interpolates the calibration vectors using an effective scale larger than that used in subsequent data releases.


An example of a low [14N/15N] value is potentially interesting for understanding the origins of material in our own solar system. The observed value in N2 of ∼200 is lower than values measured for both atmospheres of Earth and Venus (∼270; Junk & Svec 1958; Hoffman et al. 1979) and inferred for the protosolar nebula (∼440; Owen et al. 2001; Fouchet et al. 2004; Meibom et al. 2007; Marty et al. 2010). It is more similar to the extremely low values of [14N/15N] found in primitive solar system material, like cometary CN and HCN (∼140; Arpigny et al. 2003; Bockelée-Morvan et al. 2008; Manfroid et al. 2009) and in organic material in chondritic meteorites (∼50–150; Briani et al. 2009; Bonal et al. 2010), and that recently observed in HCN in a sample of T Tauri and Herbig disks (Guzmán et al. 2017). Low [14N/15N] values are seen to be correlated with high D abundances in carbonaceous chondrites, “cluster” interplanetary dust particles, and comets Wild2 and Hale-Bopp (Messenger 2000; Busemann et al. 2006; Floss et al. 2006; Aléon 2010), an enrichment that occurred either in the protosolar disk or in the precursor cloud core. Recent ISM modeling suggests that this correlation may not occur in the core stage, as a correlation between D and 15N is not expected (due to, e.g., sensitive dependence of chemistry on ortho-to-para variations in collisional partners like H2; Wirström et al. 2012; De Simone et al. 2018). This is supported by observations showing a hint of anticorrelation between the abundances of D and 15N using N2H+ in a sample of massive prestellar cores (Fontani et al. 2015b). However, the potential presence of simultaneously high 15N and D in N2 suggests that it could still be possible for this to occur in an individual core, allowing for an interstellar origin for this solar system feature. As the solar system is suggested to have formed in a rich stellar cluster experiencing a nearby supernova (Adams 2010; Dukes & Krumholz 2012; Pfalzner 2013), the environment of a massive protocluster like Sgr B2 may actually be quite relevant for understanding the neighborhood of the protosolar nebula.


To overcome these limitations, in our previous paper (Chatzistergos et al. 2018b, Paper I, hereafter) we introduced a novel approach to process the historical and modern Ca II K observations, to perform their photometric calibration, to compensate for the intensity centre-to-limb variation (CLV, hereafter), and to account for various artefacts. By using synthetic data, we also showed that our method can perform the photometric calibration and account for image artefacts with higher accuracy than other methods presented in the literature. More importantly, we showed that, as long as the archives are consistent with each other, for example, they are centred at the same wavelength and employing the same bandwidth for the observations, the method can be used to derive accurate information on the evolution of plage areas without the need of any adjustments in the processing of the various archives (Chatzistergos et al. 2019b, Paper II, hereafter). In Paper II, we applied our method to 85 972 images from 9 Ca II K archives to derive plage areas and produce the first composite of plage areas over the entire 20th century. In particular, we analysed the Ca II K archives from the Arcetri, Kodaikanal (8-bit digitisation), McMath-Hulbert, Meudon, Mitaka, Mt Wilson, Rome/PSPT, Schauinsland, and Wendelstein sites. Five out of the nine analysed archives were amongst the most studied and prominent ones, while the remaining archives were from less studied data sources. There are, however, many other Ca II K archives that are available and still remain largely unexplored. These archives harbour the potential to fill gaps in the available plage series as well as to address inconsistencies among the various archives and within individual archives (e.g. change in data quality, or in the measuring instrument with time). Moreover, since the work presented in Paper II, more data from various historical and modern archives became available in digital form. In particular, historical data that have been made available in the meantime include those from the latest 16-bit digitisation of the Kodaikanal archive, Catania, Coimbra, Kenwood, Kharkiv, Kyoto, Manila, Rome, Sacramento Peak, and Yerkes observatories, as well as additional data from the Meudon and Mt Wilson archives. In this light, here we present results from the most comprehensive analysis to date of historical and modern Ca II K observations taken between 1892 and 2019 from 43 different datasets for the purposes of producing a composite plage area series.


RFs can propagate from the magnetotail to Earth over a long distance more than 10 R
E together with BBFs behind them (Runov et al. 2009; Cao et al. 2010). Studies have suggested that RFs are crucial regions for particle acceleration, pitch-angle evolution, wave–particle interactions, and electromagnetic energy conversion during their Earthward propagation. For instance, rapid increases in energy fluxes of electrons and ions from tens to hundreds of keV are a typical feature of RF events (Khotyaintsev et al. 2011; Liu et al. 2013, 2018c, 2021a, 2022b; Zhou et al. 2018; Liu & Fu 2019; Gabrielse et al. 2021), pitch-angle distribution of suprathermal electrons can evolve dramatically around RFs (Runov et al. 2013; Liu et al. 2020), strong particle and wave activity can occur in the vicinity of RFs (Ono et al. 2009; Zhou et al. 2009, 2014; Fu et al. 2014; Breuillard et al. 2016; Greco et al. 2017; Yang et al. 2017), and RFs are associated with energy conversion from electromagnetic fields to particles (Sitnov et al. 2009; Huang et al. 2015; Khotyaintsev et al. 2017; Liu et al. 2018a, 2022a). The energetic plasma in the vicinity of RFs plays a key role in connecting the magnetotail with the inner magnetosphere because they carry a large amount of energy and can be injected into the inner magnetosphere to affect the ring current and radiation belt (Gabrielse et al. 2012; Duan et al. 2014; Turner et al. 2014). Possible mechanisms responsible for the energization of particles around RFs have been widely investigated based on both spacecraft observations and numerical simulations during the past decade. The strong convection electric field induced by the strong magnetic field gradient of RFs provides significant adiabatic acceleration of the ambient particles (Birn et al. 2004, 2013, 2015; Gabrielse et al. 2012, 2014, 2016; Ganushkina et al. 2013; Liu et al. 2016; Turner et al. 2016). Nonadiabatic effects, caused by particle reflection ahead of the RFs (Zhou et al. 2018), resonance with RFs (Ukhorskiy et al. 2013, 2017), and scattering by wave emissions (Zhou et al. 2009; Greco et al. 2017), are also significant for particle energization. These above studies usually assumed that the RF surface has a planar boundary at a typical thickness comparable to the ion gyroradius and below (Nakamura et al. 2002; Sergeev et al. 2009; Zhou et al. 2009; Schmid et al. 2011; Liu et al. 2013; Vapirev et al. 2013). Divin et al. (2015b) revealed that the RF surface is unstable to instabilities ranging from electron scales to ion scales. Simulation studies found that RFs can be unstable to interchange instability and that finger-like structures on ion–electron hybrid scales can develop at the RF (Vapirev et al. 2013). Such finger-like structures are found to play a role in modulating the electron acceleration process (Wu et al. 2018). Bai et al. (2022) also reported significant ion trapping acceleration at the RF with ion-scale ripples. Unlike these surface structures with ion or ion–electron hybrid scales, Liu et al. (2018b) recently reported that the RF layer has electron-scale density gradients, currents, and electric fields, based on the MMS mission, which consists of four spacecraft separated by 30 km. Such electron-scale ripple structure can be generated by lower hybrid drift instability (Divin et al. 2015b; Pan et al. 2018). Liu et al. (2021c) presented a detailed investigation of energy flux densities at two RFs with/without the electron-scale surface ripples and indicated that surface ripples may play an important role in the particle dynamics. But how such electron-scale RF structure impacts the electron energization and transport still remains unknown. In this paper, with the aid of observation-based test-particle simulation, we aim to investigate in detail the effect of the front surface ripples on the local electron dynamics.