In the classical unified model, blazars constitute a class of active galactic nuclei (AGNs) viewed at small angles from the jet axis (Blandford & Rees 1978; Antonucci 1993; Urry & Padovani 1995). Traditionally, blazars have been further splitted into two subclasses based on the strength of the features present in their optical spectra. While flat-spectrum radio quasars (FSRQs) show emission lines with equivalent width ≳5 Å, in BL Lacertae objects (BL Lacs) the non-thermal synchrotron radiation of the jet completely dominates the optical/UV emission, ending up in a typical featureless power-law spectrum. This makes the determination of their redshift via the detection of absorption/emission lines from the nuclear emission and/or from the host galaxy particularly challenging, even with 8–10 m class telescopes (e.g. Sbarufatti et al. 2005a, 2006, 2009; Landoni et al. 2013; Sandrinelli et al. 2013; Shaw et al. 2013; Falomo, Pian & Treves 2014; Pita et al. 2014; Paiano et al. 2016; Rosa-Gonzalez et al. 2017 for a review). In past years, several alternatives have been proposed to constrain the redshift of BL Lac objects, including the detection of intervening absorption features either from the halo of lower redshift galaxies (e.g. Shaw et al. 2013; Landoni et al. 2014) or from the neutral hydrogen in the intergalactic medium (e.g. Danforth et al. 2010; Furniss et al. 2013); the spectroscopy of galaxies in the environment where the blazars are embedded (e.g. Muriel et al. 2015; Farina et al. 2016); the detection of molecular emission lines from the host galaxy (e.g. Fumagalli et al. 2012); the study of the effect of the interaction with the extragalactic background light (EBL) in the blazar emission in the GeV and TeV domain (e.g. Prandini et al. 2010; Prandini, Bonnoli & Tavecchio 2012). In particular, the narrow distribution in luminosity of BL Lac host galaxies (Urry et al. 2000; Sbarufatti, Treves & Falomo 2005b) opened the possibility to use them as standard candles, and thus to measure their distance via broad-band imaging (e.g. Nilsson et al. 2008; Meisner & Romani 2010; Kotilainen et al. 2011). The main challenge of this approach is to accurately remove the bright central emission that typically outshine the host galaxy. Given the average 1.0 arcsec (or 3.2 kpc in the considered cosmology) effective radius calculated from the collection of z ≲ 0.6 BL Lac hosts observed with HST by Scarpa et al. (2000), it is clear that images with an exquisite spatial resolution and high contrast are necessary to unveil the faint and diffuse starlight emission around the bright, point-like emission from the active nucleus. In this paper, we exploit the capabilities of the new Advanced Rayleigh guided Ground layer adaptive Optics System (ARGOS; Rabien et al. 2010) mounted on the Large Binocular Telescope (LBT; Hill & Salinari 2004; Hill et al. 2012) to collect high-resolution near-infrared (NIR) LUCI 1 (i.e. LBT Utility Camera in the Infrared; Seifert et al. 2003; Ageorges et al. 2010) observations of HESS J1943+213. This blazar was detected by HESS in the very high energy (VHE) domain (i.e. at E >100 GeV) during a VHE galactic survey (H.E.S.S. Collaboration et al. 2011), making it the only BL Lac object known located in the Galactic plane. Broad Ks-band images gathered with the 3.5 m CAHA telescope revealed the presence of an extended emission that has been attributed to the host galaxy of HESS J1943+21 (Peter et al. 2014). A comparison with the typical size of blazar host derived by Cheung et al. (2003) allowed Peter et al. (2014) to set a lower limit on the redshift of z > 0.03. This is consistent with the z > 0.14 derived from the fit of the spectral energy distribution of HESS J1943+21 (Cerruti 2011; H.E.S.S. Collaboration et al. 2011) and with the z  0.45 limit obtained via modelling the attenuation of the VHE emission by the EBL (Peter et al. 2014). A tighter constraint on the redshift is however necessary to understand the nature of the VHE emission and to derive the EBL properties.


In the absence of dust, the spectral emission of a normal star-forming galaxy is dominated by stellar populations of different ages with superimposed nebular emission, mainly in the form of recombination lines as well as continuum. The interaction with dust has a dramatic effect, both dimming and reddening the emission from stars and ionized gas. This negatively impacts our ability to measure star formation as energetic photons produced by massive young stars are far more easily attenuated than longer wavelength photons, and even a small quantity of dust can lead to a significant attenuation in the ultraviolet (UV). In the case of particularly dust-rich galaxies, it can render their detection in the rest-frame UV especially difficult. However, as the FUV emission vanishes due to dust attenuation, this dust re-emits the absorbed energy in the mid-infrared (MIR) and far-infrared (FIR), which can in turn be exploited to trace star formation. Except for the most extreme cases (e.g., when the dust content is negligible or, conversely, when almost all of the UV photons are absorbed by dust), an attenuation correction must be carried out to retrieve the star formation rate (SFR). One of the most direct ways is to simply apply a hybrid SFR estimator combining the rest-frame UV with the IR (e.g., Hao et al. 2011; Boquien et al. 2016). The obvious downside is that this requires observations of the dust emission that are costly and difficult to obtain, and even more so at increasing redshifts, where they tend to be limited to vanishingly small samples. With the rest-frame UV emission being relatively easy to obtain from the ground from z ∼ 2 and beyond, techniques have been developed to relate the UV slope (β) to the UV attenuation (the IRX-β relation). While this approach initially appeared to work remarkably well in the case of starburst galaxies (Meurer et al. 1999), there is now ample evidence that there is no tight universal relation between the UV slope and the attenuation (e.g., Buat et al. 2005; Seibert et al. 2005; Howell et al. 2010; Casey et al. 2014). In fact, this relation relies on two strong underlying assumptions: the intrinsic UV slope of the stellar populations in the absence of dust and the exact shape of the attenuation curve. Numerous studies have analyzed their respective impact in an attempt to understand why and when such relations fail and build more reliable ones (e.g., Kong et al. 2004; Boquien et al. 2009, 2012; Popping et al. 2017, and many others). In particular, the recent study of Salim & Boquien (2019) found that the diversity of attenuation curves is a strong driver of the scatter around the IRX-β relation. This finding, which is consistent with simulations (Narayanan et al. 2018b; Liang et al. 2021), is especially important in that we can observe a broad variety of attenuation curves at all redshifts (e.g., Salmon et al. 2016; Buat et al. 2018; Salim et al. 2018). With the shape of the attenuation curve being strongly dependent on the relative geometry of stars, ionized gas, and dust (Salim & Narayanan 2020), from the disturbed morphologies observed at higher redshifts, we can only expect important variations there as well (e.g., Faisst et al. 2017). However, due to the great difficulty in measuring them and given the sparsity of the data available, our knowledge of attenuation curves beyond z = 4 remains limited. In effect, most observational studies on the attenuation properties of distant galaxies tend to concentrate on redshifts between 2 and 4 (e.g., Noll et al. 2009b; Buat et al. 2012, 2019; Reddy et al. 2012, 2015; Shivaei et al. 2015; Álvarez-Márquez et al. 2016; Salmon et al. 2016; Fudamoto et al. 2017, 2020b; Lo Faro et al. 2017; Álvarez-Márquez et al. 2019; Reddy et al. 2018; Koprowski et al. 2020). There is only a handful of examples at higher redshift (Capak et al. 2015; Scoville et al. 2015; Bouwens et al. 2016; Barisic et al. 2017; Koprowski et al. 2018). Because of the inherent limits of the observations, studies based on numerical simulations of galaxies at very high redshift (e.g., Mancini et al. 2016; Cullen et al. 2017; Di Mascia et al. 2021) are an important source of information. However, they lead to contrasted results, finding both flat (Cullen et al. 2017) and steep (Mancini et al. 2016) attenuation curves.


If the separation between the period of the planet and all the other periodic signals is large enough, and the RV signal has a similar or larger semi-amplitude, it is possible to determine the RV semi-amplitude for a USP planet without any assumptions about the number of planets in the system or the activity of the host star. Under such conditions, during a single night, the influence of any other signal is much smaller than the measurement error and, thus, it can be neglected. If two or more observations are gathered during the same night and they span a large fraction of the orbital phase, the RV semi-amplitude of the USP planet can be precisely measured by just applying nightly offsets to remove all the other signals (e.g. Hatzes et al. 2010; Howard et al. 2013; Pepe et al. 2013; Frustagli et al. 2020 for a recent example). Such an approach, also known as floating chunk offset method (FCO; Hatzes 2014), has proven extremely reliable even in the presence of complex activity signals, as shown by Malavolta et al. (2018). In our case, the shortest, next periodic signal (i. e. TOI-561 c at 10.78 d) is ≃24 times the period of TOI-561 b (i. e. the USP planet at 0.45 d), with similar predicted RV semi-amplitude, making this target suitable for the FCO approach. Thanks to our observational strategy (see Section 2.2), we could use 10 different nights for this analysis. Most notably, during two nights, we managed to gather six observations spanning nearly 5 h, i. e. more than 40 per cent of the orbital period of TOI-561 b, at opposite orbital phases, thus, providing a good coverage in phase of the RV curve. We did not include RV measurements with an associated error greater than 2.5 m s−1 (see Appendix B1). We performed the analysis with PyORBIT as specified in Section 5, assuming a circular orbit for the USP planet and including a RV jitter as a free parameter to take into account possible short-term stellar variability and any underestimation of the error bars. From our analysis, we obtained a RV semi-amplitude of Kp = 1.80 ± 0.38 m s−1, corresponding to a mass of Mp = 1.83 ± 0.39 M⊕. The resulting RV jitter is j  0.9 m s−1(84.13th percentile of the posterior). We show the phase folded RVs of the USP planet in Fig. 9. Since the greater reliability of this method over a full fit of the RV data set is counter-balanced by the smaller number of RVs, we decided not privilege one over the other. Therefore, we assumed as final semi-amplitude and mass of TOI-561 b the weighted mean of the values obtained from the two methods (FCO approach and joint photometric and RV fit), i. e. Kb = 1.56 ± 0.35 m s−1, corresponding to a mass of Mb = 1.59 ± 0.36 M⊕. Table 5 lists the above-mentioned values for TOI-561 b.


We employ two types of kinetic codes, hybrid particle-in-cell (PIC) and full PIC simulations. Both types make use of the P3D family of codes (Zeiler et al. 2002), in hybrid PIC (e.g., Parashar et al. 2011) mode, and fully kinetic PIC mode (e.g., Wu et al. 2013b). All simulations discussed here are performed in the 2.5D geometry (two-dimensional (2D) grid and all three components of field vectors). The hybrid simulation has

 (where

 is the ion inertial length, with c the speed of light and

 the proton plasma frequency),

, 200 particles per cell,

, cold isothermal electrons with

. The simulation is initialized with energy only in wavevectors

 that have

. v and b fluctuations are chosen with a specified initial spectral shape, Gaussian random phases, and only in essentially incompressive modes of the system. This simulation was also used in a recent study of variance anisotropy in kinetic plasmas (Parashar et al. 2016). The first full PIC simulation has

,

, 200 particles per cell,

,

. The initial condition is the Orszag–Tang vortex (OTV) (e.g., Orszag & Tang 1979; Dahlburg & Picone 1989; Parashar et al. 2009; Vasquez & Markovskii 2012). This simulation was performed for a recent study of transition from kinetic to MHD-like behavior (Parashar et al. 2015). The final PIC simulation (Turb812) has

,

, 400 particles per cell,

,

. The initial condition is MHD-like, and more “turbulent,” with v and b fluctuations excited in a band of wave-vectors with

 with a specified initial spectrum. This simulation was done as part of a recent study that discussed the relation of timescales at the proton gyroscale and their relation to relative proton–electron heating (Matthaeus et al. 2016). PIC codes have an inherent noise associated with them due to the finite number of particles per cell. While performing these simulations, the two most important numerical criteria that we paid attention to were: (i) excellent conservation of total energy (less than a few percent change in any fluctuation energy), and (ii) the particle noise in the spectrum was significant only at scales much smaller than the scales of interest (Debye length

 for PIC and di for hybrid PIC). On this basis, the modest number of particles employed here was considered adequate. As an additional measure, we employed filtering (e.g., Wan et al. 2012) to remove particle noise at grid scales prior to computing gradients (e.g., vorticity).


Further diagnostics are clearly needed to form firm conclusions. There are likely to be three routes through which this can come. The first is via spectroscopy of the bumps in any further examples. High quality spectroscopy, allied to detailed modeling can yield diagnostics even in the case of relatively weak or featureless spectra, as recently demonstrated in the case of the ultra-long and luminous supernovae pairing GRB 111209A/SN2011kl (Greiner et al. 2015). The unique identification of features expected in luminous SNe (e.g., turn-off due to line blanketing, absorption lines seen in SLSNe) or TDFs (e.g., blueshifted narrow lines from streams (Strubbe & Quataert 2011)) would then provide a clinching argument as to the origin of the bumps in the longest high-energy transients. A second route arises through studying the locations of the transients within their hosts. Swift J1644+57 clearly arises very close to the galactic nucleus, and Swift J2058+0516 is also consistent with the nucleus of a much fainter galaxy (Pasham et al. 2015). In the case of GRBs, approximately 1/6 of examples are consistent with a galaxy nucleus (Fruchter et al. 2006; Svensson et al. 2010); this number may be lower for SLSNe (Lunnan et al. 2015) although the origin of SLSNe in the nuclei of galaxies may be ambiguous (e.g., Dong et al. 2016). Further examples, all in the nuclei of their hosts, would rapidly remove any SNe model from consideration. Finally, we can also consider the host galaxy more globally. TDFs can be observed in quiescent, non-star-forming galaxies while SLSNe are thought to arise from massive star collapse (Gal-Yam 2012) and in principle should occur only in star forming galaxies. A prime model for SLSNe is that they arise from supernovae in which the shock wave is re-energized by the spin-down energy of a recently formed magnetar (Kasen & Bildsten 2010). While magnetars similar to those suggested to power SLSNe can be formed via accretion induced collapse of two merging white dwarfs (Usov 1992; Levan et al. 2006), and may provide a similar energy input, in the case of a white dwarf merger there would be minimal remnant to re-energize, and hence no luminous SNe. This means that the presence of an extremely long event within an quiescent elliptical galaxy would rule out SNe models, and strongly favor an origin as a relativistic tidal flare. Since a reasonable fraction (∼50%) of candidate tidal disruptions arise from passive systems, (i.e., those with little sign of star formation) (e.g., Arcavi et al. 2014) such a test should be possible with only a handful of additional examples since we would expect to observe an example in a system without star formation in the near future.


The first identification of a possible meteor shower with a radiant point in the constellation of Ursa minor was by Denning (1912), occurring around the winter solstice. However, very few observations were subsequently made. Hoffmeister recorded its activity in 1914, but its existence was not confirmed until 1945 (Becvr 1946). There are two reasons for the lack of records of the Ursids. First, the Ursids have very low activity levels in most years, its Zenith hourly rate (the number of meteors that would be observed under good observing conditions in one hour if the radiant was at the zenith) is usually ZHR 10 (Jenniskens 1994). Secondly, the weather can be bad in mid-December and many observers choose to only observe the more predictable Geminids. Ceplecha (1951) showed that the annual Ursid shower was related to comet 8P/Tuttle, a Jupiter family comet with a period of 13.6yr (JPL-HORIZONS, ssd.jpl.nasa.gov) and a perihelion distance slightly greater than 1au. This means that the comet is usually brightest (close to perihelion) and close to the Earth at roughly the same time. Hence, it has been observed at all perihelion passages since discovery apart from 1953, when observing conditions were poor throughout. These perihelion passages were in 1858, 1872, 1885, 1899, 1913, 1926, 1940, 1953, 1967, 1980, 1994 and 2008. As it can take a considerable time after being ejected from the nucleus for meteoroids to disperse away from the nucleus locality, an enhancement is generally to be expected in stream activity at the time when the comet is close to perihelion and new meteoroids are injected (see Williams, Johnson  Fox 1986 for an early discussion and mathematical formulation of this). An enhancement at some such times has also been observed in the Ursids, where the ZHR reaches around three times the normal rate (e.g. 1900, 1914, 1953, 1981 and 1996, data taken from www.meteorshowersonline.com). However, in the case of the Ursids, several perihelion passage years do not show any significant enhancement and so this is unlikely to be the explanation. Instead, Jenniskens etal. (2007) suggested that they are caused by cometary material released at very old comet perihelion passages between ad300ad1400 and appear as a wide and stretched stream (which we will call and refer to as a filament).


The lack of data at complementary wavelengths also makes resolved multiwavelength analyses applied to low-redshift galaxies, such as the Schmidt–Kennicutt relation (the correlation between galaxies’ SFR and gas mass surface densities; e.g., Schmidt 1959; Kennicutt 1989, 1998), significantly less common at high redshift. High-resolution CO observations are critical for evaluating where high-redshift galaxies fall on the true surface density version of the Schmidt–Kennicutt relation, where ΣSFR and Σgas can be compared on a pixel-by-pixel basis within individual galaxies (as done for local galaxies; e.g., Kennicutt et al. 2007; Bigiel et al. 2008, 2011; Wei et al. 2010; Leroy et al. 2013). Many high-redshift analyses use star formation and gas properties averaged over the entire galaxy (e.g., Buat et al. 1989; Kennicutt 1989, 1998; Daddi et al. 2010b; Genzel et al. 2010; Tacconi et al. 2013) or avoid the additional uncertainties in source size and scaling factors by using the total luminosities of the star formation and gas tracers (e.g., Young et al. 1986; Solomon & Sage 1988; Gao & Solomon 2004). These different methods for determining SFRs and gas masses make it difficult to compare studies that focus on different galaxy populations, leading to significant uncertainties in the power-law index of the Schmidt–Kennicutt relation and the relative placement of different galaxy types in the ΣSFR–Σgas plane. Accurately characterizing the Schmidt–Kennicutt relation is important, since offsets imply a difference in star formation efficiency (SFE), and the power-law index probes the underlying physical processes of star formation (for example, a linear correlation would imply supply-limited star formation, whereas superlinear correlations occur if star formation depends on cloud–cloud collisions or total gas freefall collapse times; e.g., Tan 2000; Krumholz & McKee 2005; Ostriker & Shetty 2011). Systematic differences in the Schmidt–Kennicutt relation between different galaxy populations would imply important differences in their star formation processes.


Within a star-forming cloud core, the protostar is the main source of luminosity and heat due to the release of gravitational energy from contraction and material accretion. The amount of protostellar heating dictates the temperature structure of the cloud core. In an idealized spherical scenario, the temperature alone would dictate the snowline locations within the cloud core. However, star-forming cloud cores are not spherically symmetric. The outflow cavity, flattened structures around the protostar (e.g., pseudo-disks and rotationally supported disks; hereafter referred to as disks for simplicity), and variations within the envelope density can all impact how heat is distributed within the cloud core. Studies have shown that heating mainly escapes through the outflow cavity in deeply embedded sources (van Kempen et al. 2009; Yıldız et al. 2015; Murillo et al. 2018a). Thus the extent of chemical richness in the outflow cavity provides insight into the luminosity of the protostar and the physical conditions of the envelope (e.g., Drozdovskaya et al. 2015; Murillo et al. 2018b; Tychoniec et al. 2019, 2020). Observations of embedded protostars (so-called Class 0 and I systems) have shown the presence of disks, both as flattened dust continuum structures (e.g., J∅rgensen et al. 2009; Enoch et al. 2011; Persson et al. 2016; Segura-Cox et al. 2018; Tobin et al. 2020) and rotationally supported disks traced in molecular gas (e.g., Murillo et al. 2013; Harsono et al. 2014; Yen et al. 2015, 2017; Maret et al. 2020). These disks show a wide range of geometries and radii ranging from a few 10 AU up to ~200 AU. Additional studies have shown that the presence of a disk can alter the temperature profile along the equator (disk mid-plane) of the cloud core (e.g., Murillo et al. 2015, 2018b; van’t Hoff et al. 2018b; Hsieh et al. 2019a). Multiplicity, that is two or more protostars within a single cloud core, can produce further asymmetries due to differences in luminosity from the multiple components and their locations with respect to each other (e.g., Chen et al. 2009; Koumpia et al. 2016; Murillo et al. 2016, 2018b). At an early evolutionary stage, protostellar luminosity is dominated by accretion, that is accretion luminosity (Hartmann & Kenyon 1996). Variability in protostellar luminosity has been detected toward several targets (V1647 Ori: Ábrahám et al. 2004; Andrews et al. 2004; Acosta-Pulido et al. 2007; Fedele et al. 2007; Aspin & Reipurth 2009; OO Serpentis: Kóspál et al. 2007; CTF93 216-2 Caratti o Garatti et al. 2011; VSX J205126.1: Covey et al. 2011; Kóspál et al. 2011; HOPS383 Safron et al. 2015; S255IR-SMA1 Safron et al. 2015; Liu et al. 2018; EC53 Herczeg et al. 2017; Yoo et al. 2017). Such variability is considered to be a product of the nonuniform accretion of material with a variable amount and frequency onto the protostar, that is to say episodic accretion (Audard et al. 2014).


In this work, we follow the method for measuring the IGM thermal state based on Voigt profile decomposition of the Ly α forest (Schaye et al. 1999; Ricotti et al. 2000; McDonald et al. 2001). In this approach, a transmission spectrum is treated as a superposition of multiple discrete Voigt profiles, with each line described by three parameters: redshift zabs, Doppler broadening b, and neutral hydrogen column density $N_{\rm H\, {\small I}}$. By studying the statistical properties of these parameters, i.e. the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution, one can recover the thermal information encoded in the absorption profiles. The majority of past applications of this method constrained the IGM thermal state by fitting the low-b-$N_{\rm H\, {\small I}}$ cutoff of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution (Schaye et al. 1999, 2000; Ricotti et al. 2000; McDonald et al. 2001; Rudie, Steidel & Pettini 2012; Boera et al. 2014; Bolton et al. 2014; Garzilli, Theuns & Schaye 2015, 2020; Hiss et al. 2018; Rorai et al. 2018). The motivation for this approach is that the Ly α lines are broadened by both thermal motion and non-thermal broadening resulting from combinations of Hubble flow, peculiar velocities, and turbulence. By isolating the narrow lines in the Ly α forest that constitutes the lower cutoff in $b-N_{{{{\rm H\, {\small I}}}}{}}$ distributions, of which the line-of-sight component of non-thermal broadening is expected to be zero, the broadening should be purely thermal, thus allowing one to constrain the IGM thermal state. However, this method has three crucial drawbacks. First, the IGM thermal state actually impacts all the lines besides just the narrowest lines. Therefore, by restricting attention to data in the distribution outskirts, this approach throws away information and reduces the sensitivity to the IGM thermal state significantly (Rorai et al. 2018; Hiss et al. 2019). Secondly, in practice, determining the location of the cutoff is vulnerable to systematic effects, such as contamination from the narrow metal lines (Hiss et al. 2018; Rorai et al. 2018). Lastly, the results from this approach critically depend on the choice of low-b cutoff fitting techniques, where different techniques might result in inconsistent T0 and γ measurements (Hiss et al. 2018; Rorai et al. 2018).


Meanwhile, the quiescence of the stellar disks (albeit possibly not entirely passive), is the first indication of the presence of an apparent “outside-in” quenching mode in high-redshift massive galaxy populations, in contradiction to the classic “inside-out” configuration (Lang et al. 2014; Tacchella et al. 2015; Breda & Papaderos 2018). We consider various possible modes of quenching. Since we observe the galaxies to be undergoing an outside-in quenching, this could not have primarily occurred due to feedback from active galactic nuclei (AGN; Alatalo et al. 2015), known to quench galaxies inside-out (Tacchella et al. 2018). We also find no evidence of AGN activity from X-ray observations (Daddi et al. 2021), although a radio excess in Galaxy-C is indicative of weak past AGN activity in that galaxy. The process of morphological quenching (Martig et al. 2009), where the formation of a stellar bulge stabilizes the disk against further star-formation, is also improbable. The galaxies are far from being bulge-dominated, essential for this mode of quenching to be applicable, based on their stellar mass distributions. Also unlikely is cosmological starvation (Feldmann & Mayer 2015) since the availability of gas has already been established in RO-1001. Finally, ram-pressure stripping (RPS; Gunn & Gott 1972) could be regarded as a possible contributor as it is known to remove gas from external regions of galaxies (Bravo-Alfaro et al. 2000; Vollmer et al. 2001; Fumagalli et al. 2009; Boselli et al. 2014; Loni et al. 2021), therefore resulting in an apparent outside-in quenching (for a review, Boselli et al. 2022). It could also lead to compression of the gas in the galaxy which could result in the lopsidedness (although the stellar morphology would not be affected). However, as shown in Appendix B, a conservative lower-limit of the radius up to which RPS can remove gas from the sample in RO-1001 would be 10–15 kpc. This is more than an order of magnitude higher than the kpc-scale cores beyond which the galaxies have suppressed star-formation. Hence we do not expect RPS to be playing a major role.


The abundances for cold and hot tracers with different Ye treatments are shown in Figure 12 for model s15_F120_R006. In general, the abundances for cold and hot tracers show a clear iron peak. The cold component is characterized by the odd–even distribution from carbon to calcium, following the progenitor composition. The hot component reaches heavier elements than the cold one with a slight dependency of the abundances on the exact electron fraction. The different assumptions for the initial Ye lead to some variability for the abundances beyond iron covering all expected possibilities for yields from neutrino-driven supernovae. The production of elements in the region of Sr, Y, and Zr is more efficient for slightly neutron-rich conditions, corresponding to RLn = 1.35 (Arcones & Montes 2011; Arcones & Bliss 2014). We observe a very similar behavior and dependency of abundances on the Ye distribution for all exploding models of the 15 M⊙ progenitor. As a summary, we show in Figure 13 the final abundances only for the narrow Ye distribution with RLn = 1 for all models. We do not find any clear correlation between the abundances and the final explosion energy, although we see slight dependency on the explosion energy at ∼1 s after bounce. The lack of correlation is probably due to our simple treatment of the neutrinos and the correction of the electron fraction, as well as to the fact that we are calculating abundances only for the 15 M⊙ progenitor. Simulations with detailed neutrino transport and for several progenitors are necessary to narrow the uncertainties in the abundances and to link those to other astrophysical conditions. Even if our results are not completely conclusive for abundances beyond iron, they indicate that there is not a strong variability for iron group elements. This may be important to estimate uncertainties in the production of 56Ni and 44Ti as shown in Figure 14 where we present an overview of all models including cold and hot components and variations of Ye.


The fields targeted by our proof-of-concept mini-survey were observed at relatively high airmasses (see Section 2). Therefore, it can be argued that our null result could be due to enhanced extinction caused by observing at such low elevations. However, this is likely not the case because the same EURONEAR collaboration carried out a nearly concurrent mini-survey looking for Atira and Vatira asteroids (see e.g. Greenstreet, Ngo & Gladman 2012) using the same instrumental setup and similar automated reduction pipeline. Atiras or Interior Earth Objects (IEOs) have aphelion distances 0.983 au and can only be observed at low solar elongations (often 70○); Vatiras have aphelia 0.718 au, are observed at very low solar elongations (typically 40○–45○), and just one such object is currently known (Bolin et al. 2020; de la Fuente Marcos & de la Fuente Marcos 2020; Greenstreet 2020), 594913 ‘Ayloi’chaxnim (2020 AV2). Although the nearly concurrent EURONEAR small-scale survey (12 nights with an average time of 1.5 h per night devoted to searching for Vatira and Atira asteroids towards the evening and early morning skies) did not find any new Vatiras or IEOs, it did observe at elevations in the range 15○–30○ and recovered known objects at apparent magnitudes close to or above 23 – for example 2017 HO20, a main belt asteroid that was observed near conjunction. Furthermore, Fig. 2, top panel, shows the r′-magnitude distribution of the detected stars from one representative pointing out of the 77 (×5) pointings intended to recover the TESS candidate in Cepheus. The histogram was produced using the matplotlib library (Hunter 2007) with sets of bins computed using numpy (van der Walt, Colbert & Varoquaux 2011; Harris et al. 2020) by applying the Freedman and Diaconis rule (Freedman & Diaconis 1981). Fig. 2, bottom panel, shows the expected S/N for WHT prime-focus imaging as a function of the exposure time from the exposure time calculator (ETC)11 for a similar camera (Red + 4, PFIP) for observations carried out under a seeing of 0${_{.}^{\prime\prime}}$9 at an airmass of 2.3 in dark time and R = 23.2 mag. TNOs have colour index V − R in the range 0.2–1.2 (see e.g. Peixinho, Delsanti & Doressoundiram 2015). Consistently, we are confident that we reached a limiting magnitude r′= 23.0 mag, which actually corresponds to $V\, \gt $23.0 mag (in fact, it could be 23.2–24.2 mag). Therefore, our distant TNO candidate survey could have detected candidates 9 and 11 in table 2 of Rice & Laughlin (2020) unless both candidates are much fainter than predicted or they are false positives in TESS data. In any case, Rice & Laughlin (2020) stated that many if not most of the high signal significances reported in their table 2 could be the result of unmodelled systematic errors. On the other hand, in the fields observed towards Cepheus, there are a few bright stars that might have hidden a putative moving object with the properties of candidate 9; we estimate that the probability of having missed the candidate as a result of it moving projected towards one of those bright stars is 1 per cent (considering the area affected by the bright stars and associated diffraction spikes).


IC 59 has a lower surface brightness than IC 63, which may be the result of both lower column densities as well as a larger physical distance from the illuminating star (Blouin et al. 1997; Karr, Noriega-Crespo & Martin 2005) compared to IC 63. Because of their rare illumination geometry and proximity to Earth, these two nebulae have been studied intensively at wavelengths ranging from the Lyman limit of hydrogen to the hydrogen line and continuum near 21 cm as ideal test cases for PDR models (Perrin & Sivan 1992; Jansen, van Dishoeck & Black 1994; Blouin et al. 1997; Luhman et al. 1997; Hurwitz 1998; Habart et al. 2004; France et al. 2005; Karr et al. 2005; Thi et al. 2009; Fleming et al. 2010; Miao et al. 2010). As a result of these studies, the physical conditions in these nebulae are exceptionally well constrained. The distances of the nebulae from the illuminating star are about 1 pc, assuming that they are located near the plane of the sky occupied by γ Cas (Friedmann et al. 1996). Thus, the incident radiation field at locations within the two nebulae is essentially unidirectional, with the contribution from γ Cas about 650 times (Habart et al. 2004) more intense than the average ISRF in the solar vicinity at the front PDR in IC 63 facing γ Cas. This leads to well-defined PDRs that are viewed essentially edge-on. This is the case particularly in IC 63. Thus, it is possible to observe radiation from different emission processes requiring photons of different energies for their excitation, such as recombination lines from ionized hydrogen and sulphur, fluorescence from photoexcited molecular hydrogen, emissions from ionized and neutral polycyclic aromatic hydrocarbons (PAHs), and dust-scattered continuum at different depths behind the front of the PDR. In this regard, IC 63 is a more ideal geometry for the morphological study of ERE than NGC 7023, where the illuminating star, HD 200775, is centrally embedded and where projection effects make it more difficult to spatially separate different emission processes (Witt et al. 2006; Berné et al. 2008). One of the prime objectives of this study is to determine the spatial distribution of the ERE in IC 59 and IC 63 in relation to other emissions with known excitation requirements. For this analysis, we take advantage of the wavelength dependence of the opacity of the ISM consisting of atomic and molecular gas and interstellar dust in the UV–optical spectral range (Ryter 1996). An added benefit of the special geometry of IC 59 and IC 63 with respect to γ Cas is that scattering by dust occurring here at large scattering angles near 90° is rather inefficient, which makes it easier to separate other UV/optical emission components from the scattered light, including the ERE. The subsequent chapters of this paper are organized as follows: In Section 2, we present new optical observations of IC 59 and IC 63 and discuss their reductions and absolute intensity calibrations. Additional archival observations obtained from the WISE, Spitzer and Herschel Space Observatories will be introduced as well. In Section 3, we present the analysis of the ERE morphology in the nebulae based on digital image subtraction and division. We will estimate the ERE intensity using the colour-difference technique and determine the wavelength region of ERE excitation. A discussion of the implications for the ERE emission process and specific ERE carrier models will follow in Section 4, with conclusions to be presented in Section 5. Data tables with the results of measurements of the relative surface brightnesses of IC59 and IC63 are presented in the appendices.


Cataclysmic variables (CVs) are strong interacting binaries. They are systems with an accreting white dwarf (WD, the primary) and a red dwarf (the donor). The donor star is on a late-type main sequence, or sometimes in a slightly evolved state. An accretion disc forms and accreted material reaches the WD in the case in which the magnetic field of the primary is too weak to interrupt the accretion flow (B  0.01 MG): such systems are referred to as non-magnetic CVs, characterized by their eruptive behaviour (Warner 1995). Mass and angular momentum transfer from the donor star to the WD drive a rich variety of variability, as well as the evolution of these systems (Knigge, Baraffe & Patterson 2011). Nova-like variables (NLs) and dwarf novae (DNs) are subtypes of non-magnetic CVs: in addition to the more frequent eruption of DNs, there are many differences between them. NLs have high accretion rates (∼10−8 M⊙ yr−1), so are in a persistent high state, and they gather above the period gap in the period distribution of CVs (Thorstensen et al. 1991); while the accretion rates of DNs are lower than those of NLs by one or two orders of magnitude (≤10−9 M⊙ yr−1), their luminosities only match those of NLs during DN outbursts and their periods are more commonly below the period gap. The possible evolutionary links between the two classes were discussed by Shara et al. (1986) as part of the hibernation scenario, in which systems are NLs immediately after a nova burst and then metamorphose into DNs if their luminosity becomes sufficiently low within several centuries. The hibernation hypothesis also predicts that CVs will experience novae, NLs, and DNs within 104−105 yr and repeat the cycle during their lifetimes. The NL system V1315 Aql was estimated to experience a nova outburst about 500–1200 yr earlier (Sahman et al. 2018): this is consistent with nova-induced cycles in hibernation theory. Kovetz, Prialnik & Shara (1988) estimated that the mass-transfer rate declines at a rate of 0.012 mag yr−1 for the century following outburst. Despite enhanced interest in long-term observations of post-novae and their final decline inspired by the hibernation hypothesis, analysis of the secular evolution of NLs is not yet well known.


Depending on the specific driver, the characteristics of turbulence will then be imprinted within the ISM mainly as three-dimensional density and velocity fluctuations, and these fluctuations have been traditionally studied via correlation functions such as the spatial power spectrum (SPS) (e.g., Crovisier & Dickey 1983), Δ-variance (e.g., Stutzki et al. 1998), and structure function (e.g., Padoan et al. 2002; Burkhart et al. 2015b). In particular, the SPS approach has been applied to observations of various Galactic and extragalactic environments (e.g., Plume et al. 2000; Dickey et al. 2001; Elmegreen et al. 2001; Burkhart et al. 2010; Combes et al. 2012; Zhang et al. 2012; Pingel et al. 2013), showing power spectral slopes β roughly ranging from −2.7 to −3.7 depending on the tracers used (e.g., H i, carbon monoxide (CO), and dust). These slopes essentially provide information on the relative amount of structure as a function of spatial scale and can be compared with theoretical models of turbulence (mainly numerical simulations) to characterize turbulence cascade (e.g., Burkhart et al. 2010), to determine the influence of shocks (e.g., Beresnyak et al. 2005), to reveal the injection and dissipation scales of turbulent energy (e.g., Kowal & Lazarian 2007; Federrath & Klessen 2013; Chen et al. 2015), and to trace the evolution of MCs (e.g., Burkhart et al. 2015a). The proximity and abundance of multi-wavelength observations make MCs in the solar neighborhood an ideal laboratory for probing the impact of turbulence on their formation and evolution. In this paper, we focus on the Perseus MC, which is a nearby (∼300 pc; e.g., Herbig & Jones 1983; Černis 1990), low-mass (∼2 × 104 M⊙; e.g., Sancisi et al. 1974; Lada et al. 2010) cloud. Its star formation activities, as well as atomic and molecular gas content, have been extensively examined over the past decade (e.g., Ridge et al. 2006; Jørgensen et al. 2007; Pineda et al. 2008; Lee et al. 2012, 2014, 2015; Mercimek et al. 2017), revealing that the cloud consists of several individual dark and star-forming regions (e.g., B5, B1, B1E, IC 348, and NGC 1333) and is actively forming low- to intermediate-mass stars (see Bally et al. 2008 for a review).


The catalogue represents a luminosity-complete sample of galaxies with r-band absolute magnitude Mr ≤ −19 in a (300h−1Mpc)3 comoving volume at z = 0. The mock contains both central and satellite galaxies, populated in dark matter haloes identified in an N-body simulation having 10243 particles with a flat ΛCDM WMAP7 cosmology (Komatsu et al. 2011; Ωm = 0.276, h = 0.7). To achieve the luminosity completeness threshold of Mr ≤ −19, haloes containing ≥40 particles are considered. Since the halo concentration cannot be reliably measured for haloes with fewer than about ∼400 particles, we use the method presented by Ramakrishnan, Paranjape & Sheth (2021) to assign concentrations cvir (assuming Navarro, Frenk & White 1996, NFW profiles) conditioned on the mass and local tidal environment of individual haloes.2 The galaxies were populated using a halo occupation distribution (HOD) model and H i-optical scaling relations calibrated by Paul, Choudhury & Paranjape (2018) and Paul, Pahwa & Paranjape (2019) using luminosity- and colour-dependent clustering measurements from the Sloan Digital Sky Survey (SDSS; York et al. 2000; Zehavi et al. 2011) and H i-dependent clustering measurements from the Arecibo Legacy Fast ALFA survey (ALFALFA; Giovanelli et al. 2005; Guo et al. 2017). Each galaxy in the mock is assigned absolute magnitudes in SDSS u, g, and r bands (with a threshold Mr ≤ −19 imposed by the SDSS clustering measurements) and a stellar mass m* using a colour-dependent mass-to-light ratio. The H i-optical scaling relation additionally leads to a fraction ${\sim}60{{\ \rm per\ cent}}$ of galaxies to be assigned an H i mass $m_{\rm{H}\,{\small I}}$. PCS21 presented extensive tests of this algorithm. We focus in this work on the population of mock central galaxies containing massive H i discs, with $m_{\rm{H}\,{\small I}}\ge 10^{9.7}h^{-2}M_{\odot }$; the resulting ∼50 000 such objects in our catalogue form a volume-complete sample of H i-selected galaxies.


In the field of GRBs, evidence of PFD jets has been collected independently in several directions. First, a prominent thermal emission component as expected in the fireball-internal-shock model (e.g., Mészáros & Rees 2000) has been seen only in a small fraction of GRBs (e.g., GRB 090902B, Ryde et al. 2010; Zhang et al. 2011). The majority of GRBs either show no evidence of a thermal component or a weak, sub-dominant thermal component (e.g., Abdo et al. 2009; Guiriec et al. 2011; Axelsson et al. 2012). These GRBs require that the GRB central engine is highly magnetized, and jet is still PFD at the emission site (Zhang & Pe’er 2009; Gao & Zhang 2015). Next, strong linear polarization was discovered during the prompt gamma-ray emission phase for some GRBs (Yonetoku et al. 2011, 2012), and during the reverse-shock-dominated early optical afterglow emission phase for some others (Steele et al. 2009; Mundell et al. 2013), which hint at the existence of globally ordered magnetic fields in the jet. Furthermore, strong PeV neutrino emission as predicted by the MFD models has not been observed from GRBs so far (Abbasi et al. 2012), which is consistent with the expectation of the PFD models (Zhang & Kumar 2013). Finally, the MFD internal shock (IS) model for GRBs also suffers some criticisms, such as low energy dissipation efficiency (Kumar 1999; Panaitescu et al. 1999), electron fast cooling (Ghisellini et al. 2000), the electron number excess (Bykov & Mészáros 1996; Daigne & Mochkovitch 1998; Shen & Zhang 2009), and inconsistency with some empirical (Amati/Yonetoku) relations (Zhang & Mészáros 2002; Liang et al. 2010). Zhang & Yan (2011) proposed a novel PFD outflow model named as “the Internal-Collision-induced MAgnetic Reconnection and Turbulence (ICMART),” which can potentially keep the merits of the IS model but alleviate the criticisms faced by the IS model mentioned above. The main idea of the ICMART model is that the GRB jets are PFD. The Poynting flux is catastrophically discharged at a relatively large distance (e.g., 1015 cm) from the central engine through collision-induced magnetic reconnection. The magnetic energy is converted to particle energy and radiation efficiently, leading to a very high radiation efficiency as demanded by the GRB data (Panaitescu & Kumar 2002; Zhang et al. 2007). A PFD jet has less leptons than the MFD model so that the electron excess problem is avoided. A large emission radius favors a moderately fast cooling, which can account for the right low-energy spectral index observed in GRBs (Uhm & Zhang 2014). It also gives a natural explanation of the seconds-duration of “slow variability component” observed in GRBs (Gao et al. 2012). The rapid “fast variability component” can be interpreted within this scenario as mini jets due to locally Lorentz boosted regions (see also Lyutikov & Blandford 2003; Narayan & Kumar 2009)3

3
Lyutikov & Blandford (2003) and Narayan & Kumar (2009) proposed that GRB variability is a consequence of mini jets due to relativistic outflow from reconnection or relativitic turbulence. There is no simple explanation to the observed slow variability component in these models. Zhang & Yan (2011) attributed the two variability components (slow and fast) as due to central engine activity and mini jets, respectively. Monte Carlo simulations by Zhang & Zhang (2014) showed that the ICMART model can indeed reproduce the observed GRB light curves.
. It is speculated that turbulent reconnection in a moderately high-σ flow can give rise to relativistic motion of mini jets within the bulk relativistic motion of the jets.


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

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

−0.33

+0.38

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


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.

Uses Uses Uses Compare/Contrast Compare/Contrast


Another possibly important cooling delay may arise from the phase separation of 22Ne during crystallization (Isern et al. 1991; Althaus et al. 2010). Our current best understanding is that at the small 22Ne concentrations typical of C/O white dwarfs (∼1% by number), the presence of 22Ne should not affect the phase diagram, except near the azeotropic point of the C/O/Ne phase diagram. Thus, the crystallization of the C/O core initially proceeds as in the case without 22Ne with no redistribution of neon ions between the solid and liquid phases. After a significant fraction of the core has crystallized, the temperature approaches the azeotropic point and the existing calculations indicate that the liquid phase is enriched in 22Ne relative to the solid (Segretain 1996; García-Berro et al. 2008). The 22Ne-poor solid is lighter than the surrounding liquid and floats upward where it eventually melts. This gradually displaces the 22Ne-rich liquid downward toward the solid–liquid interface until the azeotropic composition is reached, thereby releasing a considerable amount of gravitational energy. Given our very limited knowledge of the ternary C/O/Ne phase diagram (Segretain 1996; Hughto et al. 2012), this effect cannot be quantitatively implemented in our evolution models. However, we note that our current understanding of 22Ne phase separation is remarkably consistent with the missing cooling delay. In Fig. 2 we show the luminosity function obtained by adding an artificial 0.6 Gyr delay when 60% of the core is crystallized. These parameters are entirely consistent with those found in preliminary studies (Segretain 1996; García-Berro et al. 2008) and yield an excellent fit to the crystallization pile-up3. Based on the current (albeit limited) knowledge of the C/O/Ne phase diagram, we propose that the phase separation of 22Ne in the advanced stage of crystallization significantly contributes to the pile-up in the luminosity function of 0.9−1.1 M⊙ white dwarfs (Fig. 2).


The new sample of HSPs gave us an opportunity to see the optical IDVs of HSPs and compare its properties with optical IDVs of LSPs. We started a dedicated project to search for optical IDV in HSPs and after doing 62 nights of IDV observations of HSPs which gave us 144 LCs (41 in B band, 62 in R band, and 41 in B−R colour) of five HSPs (Mrk 421, 1ES 1426+428, 1ES 1553+113, 1ES 1959+650, and 1ES 2344+514). Interestingly, we found that, four HSPs did not show any IDV (Gaur, Gupta & Wiita 2012a; Gaur et al. 2012b,c), but only one HSP 1ES 1426+428 for which we have the least observations have shown IDV in six LCs out of eight LCs (Gaur et al. 2012c). Our this pilot project gave us 6 IDV LCs out of 144 LCs searched for IDV i.e ∼4 per cent LCs have shown IDV. We explained it by density inhomogeneities and bends in the bases of the jets by Kelvin–Helmholtz instabilities (Romero, Cellone & Combi 1999). We gave an alternative explanation i.e. since in HSPs, the optical band lies below the SED peak, hence, we should see changes in the efficiency of acceleration of, and/or in the rates at which energy is radiated by, the highest energy electrons available for synchrotron emission would have a more retarded effect on optical variability in HSPs (Gaur et al. 2012b). In LSPs, the optical band is dominated by highest energy electrons emitting synchrotron radiation and probably the X-ray emission is dominated by the comparatively lower energy electrons emitting the inverse Compton radiation, hence their X-ray variability is less pronounced than optical variability. If SED peak is really responsible for IDV properties, then we suspected that X-ray IDV LCs in LSPs should not show any IDV at all or show on rare occasions. With this motivation, here we present the X-ray IDV study of almost complete sample of 10 LSPs and 2 ISPs observed by XMM–Newton since its launch and we found that the LSPs show very less IDV 2 out of 50 LC i.e. 4 per cent in X-ray bands. We have reported above the similar finding for HSPs in optical bands.


The distances to planetary nebulae (PNe) have always faced the difficulty that nearby targets were lacking that could be reached well by direct methods. Trigonometric parallaxes have been obtained in a homogeneous long time-line campaign by the US Naval Observatory (USNO; Harris et al. 2007) and from the Hubble Space Telescope (HST; Benedict et al. 2009). Other studies (Acker et al. 1998; Smith 2015) showed that Hipparcos spacecraft parallaxes do not seem to be reliable. It was assumed that contamination by the emission of the surrounding nebulae caused these problems. Another model-independent method for distances to PNe are a cluster membership, as studied extensively by Majaess et al. (2007, 2014), and as discussed in Frew et al. (2016). In addition to these model-independent methods, a wide variety of statistical, model-dependent individual distance scales have been derived. The most frequently used of these are certainly those that are based on surface brightness versus angular sizes. They sometimes include optical depth corrections. All these methods have to be calibrated against a data set of nebulae with known distances. The older, widely used method is based on the 6 cm radio continuum flux, either using the ionized mass concept of Daub (1982) in the calibrations of Cahn et al. (1992) and Stanghellini et al. (2008), or by means of the radio continuum brightness temperature as used by van de Steene & Zijlstra (1994) and calibrated with a Galactic bulge sample. The newest model developed by Frew et al. (2016) is based on similar ideas, but makes use of the optical Hα surface brightness and a wide set of various calibrators. Moreover, they use a completely homogeneous data set for the brightness data derived earlier by themselves (Frew et al. 2013). Smith (2015) and Frew et al. (2016) described the underlying physics and assumptions for all these methods in detail. With the upcoming Gaia project (Gaia Collaboration 2016), a new era was expected to start for many classes of objects. The first step into this was described by Stanghellini et al. (2017) based on the combined Tycho + Gaia DR1 solution called TGAS (Michalik et al. 2015). With the second Data Release of Gaia (hereafter GDR2; Gaia Collaboration 2018), a complete homogeneous data set based only on Gaia measurements is available now for the first time. We present here the comparison of this new data set with common previous calibrations of PNe distances. Moreover, we compare it to the preliminary TGAS results in Stanghellini et al. (2017). Finally, we discuss possible caveats using the current GDR2.


Water ice is ubiquitous in the cold regions of the Universe, owing to the fact that hydrogen and oxygen are the two most abundant elements to form a solid such as icy dust particles and comets. It is, therefore, commonly accepted that the essential component of dust particles and planetesimals in protoplanetary discs is water ice beyond the so-called snow line, at which the temperature of gas is low enough for water vapour to condense into ices (e.g. Cyr, Sears & Lunine 1998). Reactive accretion of water ice from hydrogen and oxygen atoms on the surface of dust particles takes place in the dense core of molecular clouds where the growth of dust particles has been observed by scattering of stellar radiation (Steinacker et al. 2010). It is worthwhile noting that laboratory experiments on the coagulation growth of water-ice particles have a long history outside astronomy and planetary science, since coagulation is observed in daily life and is a plausible route to the formation of snowflakes (e.g. Faraday 1860; Hosler, Jensen & Goldshlak 1957). Recent works on laboratory measurements of cohesion between crystalline water-ice particles at vacuum conditions provided encouraging results that dust particles composed of water ice might be much more cohesive than previously believed (Gundlach et al. 2011; Gundlach & Blum 2015; Jongmanns et al. 2017). Form a theoretical point of view, Chokshi, Tielens & Hollenbach (1993) demonstrated that the JKR theory of elastic contact formulated by Johnson, Kendall & Roberts (1971) is a powerful tool for better understanding of dust coagulation. Numerical simulations incorporating the JKR theory have shown that dust aggregates consisting of submicrometre-sized water-ice particles proceed with coagulation growth even at a collision velocity of 50 m s−1 (Wada et al. 2009, 2013). As a result, the majority of recent studies on dust coagulation and planetesimal formation assume that silicate aggregates are disrupted by mutual collision at a velocity of vdisrupt ∼ 1 m s−1, but icy aggregates at vdisrupt ∼ 10 m s−1 (e.g. Birnstiel, Dullemond & Brauer 2010; Vericel & Gonzalez 2019). Such a trendy assumption led Drążkowska & Alibert (2017) to propose planetesimal formation by the ‘traffic jam’ effect at the snow line, provided that sticky water-ice particles grow faster and thus drift toward the central star faster than less-sticky bare silicate particles, implying that aggregates of the former catch up the latter at the snow line, which results in a traffic jam. However, we argue that the importance of water ice to dust coagulation is still open to debate, since water ice is not necessarily stickier than other materials such as silicates and complex organic matter (Kimura et al. 2015, 2020a; Musiolik & Wurm 2019).


The PN central white dwarf generates a significant ultraviolet (UV) radiation field during its transition from the proto-PN stage to the PN stage, typically ∼105 times that of the general interstellar medium (ISM), but decreasing to 10–100 as the remnant envelope expands and the luminosity of the white dwarf declines (Cox 1997). The copious amount of UV photons penetrating the nebula is predicted to photodissociate the remnant molecular material from the AGB stage within a thousand years (e.g., Redman et al. 2003). Indeed, the first molecular searches of PNe turned up negative (e.g., Penzias et al. 1971; Wilson et al. 1974). Subsequently, both CO and H2 have been detected in numerous PNe (e.g., Huggins & Healy 1989; Huggins et al. 1996, 2005; Hora et al. 1999; Likkel et al. 2006). More recent studies have identified other molecules in planetary nebulae with ever increasing complexity. Toward the young PNe NGC 7027 and NGC 6537, for example, HCN, HNC, CCH, CS, SO, H2CO, HCO+, and N2H+ have been identified (Zhang et al. 2008; Edwards & Ziurys 2013). In more evolved nebulae, species such as HCN, HNC, HCO+, CS, and CN have been found (e.g., Cox et al. 1992; Bachiller et al. 1997; Edwards et al. 2014). The very old Helix Nebula (age ∼12,000 years.) has an assortment of interesting molecules, including HCO+, CN, HCN, H2CO, CCH, c-C3H2, and HNC (Bachiller et al. 1997; Tenenbaum et al. 2009), and mapping data have shown that the molecular material is distributed throughout the PN (Zack & Ziurys 2013; Zeigler et al. 2013). SiO, SO, and SO2 have recently been found in M2-48 (age ∼5000 years.) as well (Edwards & Ziurys 2014). Perhaps even more striking is the identification of C60 in several PNe with low central star temperatures (Cami et al. 2010; García-Hernández et al. 2010, 2011, 2012; Otsuka et al. 2013). The presence of long-lived molecular material is believed to arise from shielding by high-density clumps (Howe et al. 1994), as seen in images of the Helix and the Ring (e.g., Meaburn et al. 1992; Speck et al. 2003; Meixner et al. 2005).


As of 2018, three multimeasurement catalogues including a substantial amount of redshift-independent extragalactic distance measurements have been released: HyperLEDA (Makarov et al. 2014), NED-D (Mazzarella & Team 2007; Steer et al. 2017), and Cosmicflows-3 (Tully, Courtois & Sorce 2016). HyperLEDA includes a homogenized catalogue for extragalactic distances in the nearby universe, with 12 866 distance measurements for 518 galaxies to date. NED-D is the NASA/IPAC Extragalactic Distance catalogue of redshift-independent distances, which compiles 326 850 distance measurements for 183 062 galaxies in its 2018 version. Here, ∼1800 galaxies (∼1 per cent) have more than 13 distance measurements, and 180 galaxies (∼0.1 per cent) have distance measurements using more than six different methods. Cosmicflows-3 is the most up-to-date catalogue, which reports distance measurements for 10 616 galaxies (all of which include errors) using up to four distance determination methods, calibrated with supernova luminosities. However, unlike HyperLEDA or NED-D, Cosmicflows-3 only reports the latest distance measurement for each method. In HyperLEDA, NED-D, and Cosmicflows-3 errors are reported as one standard deviation from the reported distance modulus. Treatment of errors for combining distance moduli across methods or across measurements is suggested by Mazzarella & Team (2007) and Tully et al. (2016) to be based on weighted estimates such as the uncertainty of the weighted mean, albeit with caution partly due to the heterogeneous origin of the compiled data and partly due to Malmquist bias. In the case of NED-D, this is additionally complicated by the fact that many errors are not reported or are reported as zero. In fact, the TF relation method has the largest number of galaxies with non-reported distance modulus errors (884 to date). Even though extragalactic distances measured using the TF relation were originally reported to have a relative error in distance modulus of 10–20 per cent (Tully & Fisher 1977), we consider that this conservative estimate can be improved upon by using a predictive model based on the distance error of galaxies that use the same distance determination method. This requires a robust estimation of the variance of extragalactic distances based on the available data.


The emission from both types of sources contaminates measurements of the Cosmic Microwave Background (CMB), which contains information on cosmological parameters. The measurement of the CMB polarization, particularly the E-mode damping tail, can help break some of the degeneracies between cosmological parameters. Measurements of the polarization damping tail are expected to become foreground-limited at a smaller angular scale (higher ℓ) than the temperature damping tail, because of the expected low polarization of dusty point sources (see below). Further, the higher contrast of the acoustic features in EE power spectrum compared to astrophysical foregrounds (Calabrese et al. 2014; Galli et al. 2014) will ultimately provide independent and tighter constraints on the standard cosmological parameters, such as the scalar spectral index ns, than those from the temperature data alone. High-resolution measurements of the E-mode polarization will improve the delensing of the primordial B-modes (Seljak & Hirata 2004), ultimately tightening the constraint on the tensor-to-scalar ratio r. As measurements of the small angular-scale fluctuations in the CMB are attaining higher sensitivity and finer resolution, ongoing and planned ground-based CMB surveys, such as Advanced ACTPol (Henderson et al. 2016), SPT-3G (Benson et al. 2014), Simons Observatory (Ade et al. 2019 (SO)), CCAT-prime (Stacey et al. 2018), and CMB Stage 4 (Abazajian et al. 2016; Abitbol et al. 2017) will be capable of extracting information from the E-mode damping tail out to ℓ ≈ 9000. However, the contribution of the extragalactic point sources to the CMB power spectrum increases towards smaller angular scales, and it is expected to be a significant fraction of the CMB polarization power. For example, extragalactic foreground sources are expected to be the predominant contaminant for angular scales smaller than 30′ (ℓ≳ 400) in the 70–100 GHz frequency range (Toffolatti et al. 1998). Hence, characterization of these sources in terms of their spectral and spatial distributions is essential for separating foregrounds from the CMB.


It has been cleared out in the observations that a coronal flux tube could consist of a twisted magnetic field (e.g. Kwon & Chae 2008; Aschwanden et al. 2012; Thalmann et al. 2014; Wang et al. 2015). In a magnetically twisted flux tube, the background magnetic field has an azimuthal component which causes the magnetic field lines to wind around the axis of the tube. The winding number (the number of twist turns around the tube axis) has been reported to have values in the range (0.11, 0.87) (Kwon & Chae 2008). The role of twisted magnetic field in the MHD waves has been studied in many theoretical works (e.g. Bennett et al. 1999; Erdélyi & Carter 2006; Erdélyi & Fedun 2006, 2007, 2010; Ruderman 2007, 2015; Carter & Erdélyi 2008; Karami & Barin 2009; Karami & Bahari 2010, 2012; Terradas & Goossens 2012; Ruderman & Terradas 2015; Ebrahimi & Karami 2016; Ebrahimi et al. 2017; Terradas et al. 2018). Sakurai et al. (1991a) studied resonant absorption of MHD waves in presence of a twisted magnetic field and obtained jumps of the perturbations around the resonance point (see also Sakurai et al. 1991b; Goossens et al. 1992). Ebrahimi et al. (2017) investigated resonant absorption of kink MHD waves and phase mixing of the perturbations in twisted magnetic flux tubes. They showed that depending on the profile of the azimuthal component of the magnetic field and the azimuthal mode number of the global kink wave (m = ±1) magnetic twist can enhance or suppress the decay rate of the kink wave and the rate of phase mixing of the perturbations. Ebrahimi et al. (2017) concluded that even a small amount of twist can have a large impact on the generation of small spatial scales and transferring the wave energy from the global mode to the local Alfvénic oscillations. However, Ebrahimi et al. (2017) neglected the dissipation effects in their analysis. It is known that dissipation could affect the generation of small scales due to phase mixing (McLaughlin et al. 2011; Ebrahimi et al. 2020; Howson et al. 2020).


Based purely on quality of fits of atmosphere model spectra to observed spectra obtained here, one composition is not preferred over another for the three older CCOs. The primary differences in fit results when the atmosphere is composed of carbon instead of hydrogen are a ∼40 per cent lower temperature and ∼3 times larger emission radius (to maintain nearly constant $R_{\rm em}^2T^4$). The larger Rem could be an argument in favour of carbon because it is closer to the neutron star radius R, which would imply that the entire surface is essentially at a single temperature and would explain non-detection thus far of pulsations from each of these three CCOs. However, a hot region with radius 3–4 times smaller than R can still produce a pulsed fraction below current limits of 20–40 per cent in the spin period range 0.1–0.4 s of known CCOs (see Section 1; for pulsed fraction dependence on spot size, see, e.g. Psaltis, Özel & DeDeo 2000; DeDeo, Psaltis & Narayan 2001; Weinberg, Miller & Lamb 2001; Bogdanov, Grindlay & Rybicki 2008; Lamb et al. 2009; Bauböck, Psaltis & Özel 2015; Elshamouty et al. 2016). For example, Gotthelf, Perna & Halpern (2010) find that a model which includes a hotspot with Rem/R ∼ 0.4 (and a second smaller spot) is able to produce a pulsed fraction that matches the 11 per cent measured for the CCO in Puppis A. Also of note is the stronger limit on the Cassiopeia A CCO pulsed fraction of 12 per cent for P > 0.01s compared to the other CCOs (see Table 1). Meanwhile, a hydrogen atmosphere is a natural consequence of even a very low-level of accretion from the interstellar medium on to a relatively cool neutron star surface several hundred years after neutron star formation (see Section 5.1 for further discussion). Thus from an evolution standpoint, a hydrogen atmosphere for the older CCOs studied here might be preferred. Future measurements of pulsations or improvements to pulsation constraints could provide stronger indications of their atmosphere composition.


With all this in mind, our last question is: What powers soft X-rays and [O III] in LINERs? This has no clear answer, but both are not tracing the same mechanism, since none of them match in morphologies. This is a clear difference between type-2 Seyferts and LINERs. In favour of the soft X-ray emission being originated by AGN photoionization, the RGS spectra studied by Gonzalez-Martin et al. (2010b) showed that in at least 30 per cent of their sample, a contribution of photoionization by the AGNs is required due to the presence of radiative recombination continua (RRC) from CV emission line. However, this does not guarantee a dominance of this emission mechanism. Moreover, cone-like morphologies at soft X-rays in some objects in this study point out again to the photoionization by the AGNs being responsible for the soft X-ray emission. Nevertheless, this assumes that we are seing LINERs with an LOS perpendicular to the accretion disc, which might not be the case. Indeed, the ultraviolet and X-ray variability detected for many of these LINERs (Maoz et al. 2005; Hernández-García et al. 2015) is in favour of a direct view of the AGNs (i.e. perpendicular to the disc under the UM). This is consistent with the fact that most of the [O III] morphologies found for LINERs are spheroids, if we assume that the [O III] traces the NLR. In addition, the fact that we detected a clear correspondence between soft X-ray and [O III] morphologies only in objects with log (LHX)>40, and also that all the objects where soft X-rays and [O III] match their morphologies seem to better follow the previously found relation between the size of the region and the hard X-ray luminosity (see Fig. 2 and Section 5.2), may argue in favour of the scenario in which the AGNs do not have enough thrust to ionize in the low-luminosity regime (Elitzur & Shlosman 2006; Elitzur & Ho 2009), ruling out photoionization by the AGNs at both soft X-ray and [O III] emissions. In this case, the most reasonable explanation for the [O III] is the host galaxy emission, which, anyhow, could also be on top of the AGNs, preventing its detection and erasing the connection (González-Martín et al. 2014). The host galaxy can contribute either as star formation or shocks to the total [O III] emission. Regarding the soft X-ray origin, Mingo et al. (2014) confirmed that jets are the main responsible for soft X-ray emission from their sources. In our sample, jets are identified in NGC 1052 (Kadler et al. 2004), where the jet position angle would be consistent with the extended soft X-ray emission shown here.


In addition, we also perform two new simulations changing the type I migration recipes from those of Tanaka et al. (2002) to those of Paardekooper et al. (2011) and Jiménez & Masset (2017). With this, we want to analyze whether or not the planet migration trap could be a robust result even using more sophisticated type I migration recipes, which were derived for nonisothermal disks. We remark that despite our simplifications in the computation of the thermodynamics of the disk, we compute the time evolution of the radial profiles of all the quantities needed to calculate the migration recipes mentioned above, that is, we compute the time evolution of the radial profiles of the density, pressure, opacity, and so on while the temperature radial profile remains fixed in time. Explicitly, the simplification lies in the fact that the evolution of the temperature is not linked self-consistently with the evolution of the gas surface density. We can see in Fig. 8 that the density and pressure maximum also acts as a planet migration trap using the type I migration recipes from Jiménez & Masset (2017). However, using the type I migration prescriptions from Paardekooper et al. (2011), the migration trap is broken close to the mass needed for the planet to open a gap in the disk. This happens because now the normalized torque is not only a function of the local gradient of the gas surface density (as in the isothermal case) but also of the local gradient of the temperature, the viscosity, and the mass of the planet (these last two dependencies through the corotation torque). Thus, the combination of such quantities breaks the migration trap at some moment. Guilera et al. (2019) showed that the main differences between the migration recipes from Jiménez & Masset (2017) and Paardekooper et al. (2011) lie in the computation on the corotation torque. Thus, in this case, when the planet reaches a mass of a several tens of Earth masses, the migration trap is broken. At this moment, the planet quickly migrates inwards (due to the fact that it has a mass of ~ 80 M⊕) until it opens a gap at ~1.15 au. We note that the time evolution of the mass of the core and the mass of the envelope for the simulations using the type I migration recipes from Paardekooper et al. (2011) and Jiménez & Masset (2017) are very similar to those of the fiducial simulation. In Fig. 9, we emphasize this by plotting the planet formation tracks as a function of time. Simulations also stopped when the planets opened a gap in the disk. This happens when the total mass of the planet is about 110 M⊕ for the case where we used the migration recipes from Paardekooper et al. (2011) and about 95 M⊕ for the case where we adopt the migration recipes from Jiménez & Masset (2017). The differences in the total mass at which the planet opens the gap are due to the fact that this mass depends on the viscosity of the disk. Inside the ice line, the viscosity is larger (because of the larger α-parameter), and therefore the total mass of the planet has to be higher to open a gap. For the second case, the planet opens the gap in the α transition region between 10−5 (outside the ice line) and 10−3 (inside the ice line). We note that if the thermodynamics of the disk are computed self-consistently, the migration trap can break at a different planet mass depending mainly on the viscosity and thermal diffusivity of the disk (see Morbidelli 2020).


In particular, two main scenarios have emerged: the first one attributes differences in radio morphology to the large-scale (i.e., host galaxy and environment, see also below in this Section) properties of radio-AGN which influence the interaction between the radio jet and the external medium (e.g., Kaiser and Best 2007; Wing and Blanton 2011; Miraghaei and Best 2017; Mingo et al. 2019, 2022), with those between HERGs and LERGs being instead dictated by different fuelling mechanisms as discussed earlier. According to this framework, HERGs are powered by accretion of cold gas, provided by e.g., a recent merger with a gas-rich galaxy, while LERGs accrete hot intergalactic gas from dense environments at a low rate (e.g., Best and Heckman 2012), with fuelling from major mergers strongly disfavoured by recent observations (e.g., Ellison et al. 2015). On the other hand, other works do not observe any difference in the host and/or environmental properties of FRI and FRII galaxies, except in the rare cases of FRII HERGs (e.g., Lin et al. 2010; Capetti et al. 2017b; Jimenez-Gallardo et al. 2019; Massaro et al. 2019, 2020; Vardoulaki et al. 2021) or even between those of HERGs and LERGs (e.g., Fernandes et al. 2015), so that an alternative mechanism for their large-scale radio behaviour has to be invoked. In this case, ageing processes can be thought as the main driver for the observed morphological differences, with an evolutionary pattern that proceeds from FRII HERGs that switch from efficient to inefficient accretion due to gas starvation and transform themselves into FRII LERGs, sources that still maintain their large radio structures thanks to the past nuclear activity at high efficiency (e.g., Ghisellini and Celotti 2001; Tadhunter 2016; Macconi et al. 2020; Grandi et al. 2021). The switch off/change in accretion mode will eventually show in the radio morphology with the delay needed to reach Kpc-to-Mpc distances, and the source will ultimately turn into an FRI galaxy.


In our simulations, we assumed that the growth of dust grains and planetesimals occurred during the first stages of planetary accretion. Thus, we used a bimodal disc composed of embryos (60 per cent of the disc’s mass) and planetesimals (40 per cent of the disc’s mass; Izidoro et al. 2015). It was assumed that embryos are formed by oligarchic growth and are thus spaced randomly by 5–10 mutual Hill radii (Kokubo & Ida 1998, 2000) with a density of 3 g cm−3. The mass of each planetesimals is ≈ 0.002 M⊕. In the numerical integrations, the planetesimals do not have gravitational interactions with themselves but only with stars, planets, and protoplanetary embryos. The protoplanetary embryos masses scale as M ≈ r3(2 − x)/2Δ3/2 (Kokubo & Ida 2002; Raymond, Quinn & Lunine 2005; Raymond et al. 2009; Izidoro et al. 2015), where Δ is the mutual Hill radii separations between embryos orbits. As we are using distinct systems with different parameters, the number of embryos and planetesimals are not the same among the systems; see Table 4. Fig. 5 shows the initial conditions of x = 1.5 and 2.5, for all our simulations. Discs with x = 2.5 have embryos more massives in the inner region of the disc, and with 1.5 in the outer region. We chose these two values of the parameter x, besides being used frequently in some works (Raymond, Quinn & Lunine 2004; Raymond et al. 2005; Izidoro et al. 2014a,2015; Izidoro, Morbidelli & Raymond 2014b; Izidoro & Raymond 2018), to study the dynamic evolution in discs that have mass growing as a function of the orbital radius of the bodies and in cases where the mass decreases as a function of the orbital radius (see Fig. 5). This is an important point because we have some systems where the giant planet is in the inner region of the disc and others in the outer region. So we needed to consider the two cases for all systems. The orbital inclination of the embryos and planetesimals is chosen randomly between $10^{-4}\, ^{\circ }$ and $10^{-3}\, ^{\circ }$ with respect to the binary plane, and the eccentricity is chosen between 0 and 0.01.


The specific radiance received from the optically thin dust plume can be expressed as
(1)
\begin{equation}
L_\lambda =f_{\rm plume}\frac{p}{\pi } \frac{\phi (\alpha )}{\phi (0)} \frac{f_{\lambda }}{r_{\rm h}{^2}}
\end{equation}
where p is the geometric albedo of the dust particles at wavelength λ, ϕ(α) is the phase function at phase angle α, fλ is the solar irradiance (in W m−2 nm−1 at 1 au), rh is the heliocentric distance in au and fplume is the dust filling factor (e.g. the fraction of a pixel covered by dust). Assuming that the geometric albedo of the dust particles is similar to that of the nucleus, the geometric albedo and specific solar flux are 0.068 and 1.513 W −2 nm−1 for the orange (648.6 nm) filter, and 0.027 and 0.23 W −2 nm−1 for the UV (270.7nm) filter (Fornasier et al. 2015), respectively. The flux ratio ϕ(α)/ϕ(0) can be derived by using the dust phase function (Kolokolova & Kimura 2010). By integrating the radiance over the image area (e.g. within the boxes in Fig. 7) containing the dust from a difference outburst plume, the total cross-section from difference images of the dust jet from within a given time interval can be determined. Then, we used a power-law index g = 3.7 for the size distribution with a constant bulk density of 1000 kg m−3 for all ejected particles. The ejected mass in size interval of a1  a  a2 (i.e. 1 μm to 1 mm) is given by
(2)
\begin{equation}
M=\frac{({4}/{3})\pi \rho N}{4-g} \left(a_2^{4-g}-a_1^{4-g}\right),
\end{equation}
where N is the total number of dust particles in the size interval 1 μm to 1 mm. The estimated dust cross-section and ejected mass are given in Table 2. The uncertainty of the ejected mass is typically of the order of 5–10 per cent, depending on the uncertainty on the brightness integration of the selected box. The averaged mass ejection rate for the outbursts can be estimated from the ejected mass (M) by dividing by the time interval between the difference images. Note that our calculation is based on the chosen time intervals and hence produces lower limits on the mass ejection rates. For example, the estimation of the ejected mass for a major outbursts on July 29 is about 4550 kg. Given a time interval of 18 min, the average mass ejection rate would be of the order of 4 kg s−1. However, if this outburst lasted for a time interval of 5 min only, which is the cadence for the outburst sequence, the corresponding mass ejection rate would be as much as 15 kg s−1.


The plethora of cosmological observations has turned cosmology into a quantitative science. From combining several probes that observe the Universe at different epochs and have different systematics and statistics, emerged the ‘concordance model’ of cosmology, a six parameter model, most of them measured to the accuracy of a per cent. Among these probes, Type Ia supernovae (SNe) are a powerful cosmological tool to directly measure the expansion history of the Universe (see e.g. a recent review of Weinberg et al. 2013). The type Ia SNe are known to be standard candles and one can measure the luminosity distances to them accurately. Several SNe surveys have set strong constraints on cosmological models from the distance–redshift relation (e.g. Riess et al. 1998; Perlmutter et al. 1999; Riess et al. 2007; Sullivan et al. 2011; Campbell et al. 2013). However the measured apparent magnitudes, have a residual scatter arising from its intrinsic scatter and effects due to line-of-sight (LOS) structures. The intrinsic scatter (∼0.4 mag) can be significantly reduced to ∼0.1 mag by empirically calibrating the luminosity curves. The scatter due to photon deflection along the LOS is composed of many different physical effects. The dominant effects are peculiar velocities at z  0.1 and gravitational lensing at z ≳ 0.3. Within the realm of cosmological perturbation theory and the stochastic nature of the LOS structures, all effects are expressed as an integral over the power spectrum with appropriate kinematical factors (Ben-Dayan et al. 2012). The lensing effects create residuals from the best-fitting curve in the magnitude–redshift relation. The lensing magnifications of SNe can be extracted by correlating the residuals with the surface densities of nearby foreground galaxies. The lensing dispersion is roughly proportional to the SNe redshift z, (e.g. Holz & Linder 2005; Ben-Dayan et al. 2013), and specifically for the concordance model, the predicted value is ∼0.06z mag.


The results of Ivanova et al. (2003) are somewhat closer to ours. A remaining key difference is that Ivanova et al. (2003) find that their calculated mass-transfer rates for systems with initial orbital periods, Porb, i  0.4 d sometime exceed a critical mass-transfer rate, $\dot{M}_{\rm crit}$ related to the location of the so-called trapping radius (e.g. Begelman 1979; Chevalier 1993; MacLeod & Ramirez-Ruiz 2015b). In systems with very large super-Eddington mass-transfer rates, matter presumably piles up around the NS and forms a growing, bloated cloud engulfing a large fraction of the accretion disc. A system will only avoid a CE if it manages to evaporate the bulk of the transferred matter via the liberated accretion energy at a distance from the NS larger than the trapping radius. Otherwise, the incoming material has too much negative binding energy to be ejected. At the same time, this trapping radius must be located inside the Roche lobe of the NS in order to avoid a CE (King & Begelman 1999). The exact location of the trapping radius, and thus the value of $\dot{M}_{\rm crit}$, is difficult to calculate because it also depends on the cooling processes of the infalling gas (Narayan & Yi 1995; Blandford & Begelman 1999). Nevertheless, in all of our models presented in Table 1 with Porb, i > 0.06 d we find that $|\dot{M}_{\rm He}^{\rm max}|\le \dot{M}_{\rm crit}$, where $\dot{M}_{\rm crit}$ is calculated from equation 15 in Ivanova et al. (2003), and varies from about 3.7 × 10−3 M⊙ yr−1 (for Porb, i = 2.0 d) to 4.3 × 10−4 M⊙ yr−1 (for Porb, i = 0.08 d). Only for Porb, i = 0.06 d, we find a couple of systems where $|\dot{M}_{\rm He}^{\rm max}|> \dot{M}_{\rm crit}$. However, these systems are anyway found to result in a runaway mass transfer and thus formation of a CE. Therefore, our calculated mass-transfer rates from the helium stars donors must be slightly smaller than those calculated by Ivanova et al. (2003). The reason for this, besides from using different stellar evolution codes, is perhaps that our mass-transfer rates are calculated using the prescription by Ritter (1988) whereas Ivanova et al. (2003) adopted the prescription by Tout & Eggleton (1988). To summarize, we caution that all numerical calculations of Case BB RLO could potentially be affected by uncertain accretion processes at high mass-transfer rates exceeding the Eddington limit by ∼4 orders of magnitude.


Utilizing the full range of peak absolute magnitudes observed in LBV stars [M ≃  (−13)–(−9) mag; e.g. Smith et al. 2011b] provides a range of peak apparent magnitudes of m ≃  16.5–20.5 mag, for a distance of D ≃ 8 Mpc (Table 1). Hence, if the transient source (m ≈ 21.0 mag; Section 2.1.2) is an LBV star, it must have been observed a short time after its peak (Fig. 2; left-hand column; rows 4–5); quiescent LBV stars can have absolute magnitudes as low as M ≃ −6 mag (e.g. Smith et al. 2011b), or m ≃ 23.5 mag (for a distance of D ≃ 8 Mpc; Table 1). An LBV star provides an adequate explanation for the transient time-scale, the isolation (e.g. Smith & Tombleson 2015; Smith 2016), the lack of a host H ii region (Fig. 2 and 3; see below, however), and the transient/main source offset (d ≈ 0.3 kpc, for D ≃ 8 Mpc; Table 1; see below, however). In addition, (net) fading of the LBV peak event by Δm ≲ 3 mag (over a period of approximately 40 yr) may possibly produce an apparent brightness centroid shift/morphology variation in the main source (Sections 2.1.2 and 2.1.3). However, this scenario has its caveats. First, it is difficult to interpret the flux variability of the main source (Sections 2.1.4 and 2.3.1) within such a context. Secondly, although a fraction of LBV stars are isolated (e.g. Smith & Tombleson 2015; Smith 2016), in the only XMP with a documented LBV star, the LBV star appears embedded within an H ii region (DDO 68; Pustilnik et al. 2017); no clear H ii region at the location of the transient source is discernible in the HST images (Fig. 3; top), although it should be detectable given the typical lifetime of an H ii region (few Myr; e.g. Alvarez, Bromm & Shapiro 2006). Thirdly, a (net) magnitude variation of Δm ≲3 mag of the transient over a period of approximately 60 yr would result in a quiescent LBV source (m ≲ 23.5 mag) that should have been detectable in the HST images (Fig. 3; top). Lastly, as LBV stars brighten, they become redder (e.g. Sterken 2003), which appears to contradict the POSS data (Table 2; Fig. 2; rows 2–5). Consequently, as the LBV scenario explains some of the observables challenged by other scenarios (e.g. transient timeline), it remains a contender for the observed phenomenon.


In particular, the presence of slow magneto-acoustic-gravity waves (MAG waves, hereafter) guided by the magnetic field is supported by increasingly observational evidence in different atmospheric structures, e.g. photospheric flux tubes (Roberts & Ulmschneider 1997), sunspots (Jess et al. 2013; Freij et al. 2014; Khomenko & Collados 2015; Madsen, Tian & DeLuca 2015), coronal loops (King et al. 2003), and coronal plumes (Nakariakov 2006). These oscillations are also used to estimate the formation heights of different emission spectral lines. As a result of the analysis of 3 min oscillations detected in observations from the Atmospheric Imaging Assembly instrument (AIA; Lemen et al. 2012) on-board the Solar Dynamic Observatory (SDO; Pesnell, Thompson & Chamberlin 2012), Deres & Anfinogentov (2015) found that the formation heights of the corresponding spectral lines are consistent with models of the sunspots umbra involving strong temperature gradients of the type used in this paper (e.g. Fontenla et al. 2009). Meanwhile the lower atmospheric magnetic structure is frequently believed to be mostly formed by small magnetic flux tubes of circular cross-section emerging from the photosphere and expanding upwardly in the corona (Solanki, Inhester & Schüssler 2006). The photosphere and chromosphere are known to be dominated by acoustic-gravity waves with observed short periods of ∼[3–5] min. Whereas in the lower corona a wider range of periods are present (up to about 80 min – e.g. Sakurai et al. 2002–), short periods ([3–5] min) have also been detected in certain coronal structures, e.g. coronal loops and intense magnetic flux tubes (Srivastava & Dwivedi 2010; Jess et al. 2012; Reznikova et al. 2012). A rich range of periods are found in sunspots, the periods becoming larger as the distance from the sunspot umbra increases; a likely result of the influence of the magnetic field (Bogdan & Judge 2006; Jess et al. 2013; Yuan et al. 2014; Madsen et al. 2015).


Understanding how inertial waves interact with co-rotation resonances is thus a key issue in quantifying tidal dissipation, especially since waves may deeply interact with the background flow at this particular location, which in turn may alter the background flow (as was proposed first by Eliassen & Palm 1961, for terrestrial mountain waves). In binary systems and for late-type stars, Goldreich & Nicholson (1989) showed that the angular momentum transported by gravity waves and exchanged at co-rotation can lead to the successive synchronisation of the layers, from the base to the top of the radiative envelope. More generally, a body of work in various domains, from astrophysical disks (e.g. Goldreich & Tremaine 1979; Baruteau & Masset 2008; Latter & Balbus 2009; Tsang & Lai 2009) to geophysical fluid dynamics (e.g. Bretherton 1966; Yamanaka & Tanaka 1984), has tried to understand the properties of wave propagation and dissipation around co-rotation and, more generally, at all special locations in fluids that correspond to singularities in the linear wave propagation equation. We will refer to them as ‘critical levels’ in the following (Maslowe 1986), or as ‘critical layers’ in the case of a viscous medium. This distinction is analogous to the distinction between shear layers and attractors of characteristics that are kinds of singularities for the governing equation of inertial waves in a spherical shell. The aforementioned singularities can act very differently, with either severe absorption at the critical level (as in Booker & Bretherton 1967, for stratified vertical shear flows) or no attenuation if the wave propagates in a peculiar direction (Jones 1967; Acheson 1972; Grimshaw 1975a, for stratifiedvertical shear flows with rotation and magnetism). In other cases, a critical level may even give rise to wave amplification under certain conditions related to the first and second derivatives of the mean flow velocity (Lindzen & Tung 1978; Lindzen & Barker 1985, for barotropic and stratified shear flows, respectively). These studies all used an invariant quantity (the Reynolds stress or thewave action for rotating or magnetic flows) as a diagnostic tool to interpret the role of the critical level in terms of energy transmission and to quantify exchanges between the wave and the mean flow (Eliassen & Palm 1961; Bretherton 1966).


The chemical composition of protostellar envelopes and their properties along the evolutionary stage of protostars is an important topic in astrochemistry. Since the pioneering work by Cazaux et al. (2003) and Sakai et al. (2008), systematic chemical studies of solar-type protostars (see Ceccarelli et al. 2007; Caselli & Ceccarelli 2012 for a review; also Lefloch et al. 2018) have identified two classes of objects. The first class corresponds to the so-called “hot corinos”, that is, sources which display a rich content in complex organic molecules (COMs) in the central inner regions of the protostellar envelope (see Ceccarelli et al. 2007 for a review; also Taquet et al. 2015). Only a few hot corinos have been identified so far either with single dish or interferometric observations: IRAS16293-2422 (Cazaux et al. 2003; Bottinelli et al. 2004b; Jørgensen et al. 2011, 2016), IRAS2, IRAS4B (Bottinelli et al. 2007), IRAS4A (Bottinelli et al. 2004a; Taquet et al. 2015), HH212 (Codella et al. 2016), L483 (Oya et al. 2017), B335 (Imai et al. 2016), SVS13A (Bianchi et al. 2017), Serpens SMM1, and SMM4 (Öberg et al. 2011). We note that very few sources were investigated in a systematic manner meaning that the COM budget in hot corino sources is very inhomogeneous, making a general picture difficult to come by. Hot corinos share some similarities with the hot cores observed around high-mass stars but they are not scaled-down versions of these. Bottinelli et al. (2007) showed that the abundances of O-bearing species scaled to methanol are higher than those measured in hot cores by one to two orders of magnitude or more. The second chemical class of protostars corresponds to the so-called Warm Carbon Chain Chemistry (WCCC) sources, which have a rich content in C-chains but are poor in COMs. A recent survey of a sample of 36 Class 0/I protostars of the Perseus molecular cloud complex by Higuchi et al. (2018) shows that the majority of the sources observed have intermediate characters between these two distinct chemistry types.