While these similar characteristics suggest that the OA and C could have a relationship, the nature of this relationship is not clear. Kawata, Thom & Gibson (2003) used numerical simulations to investigate whether Complex C could have been produced by the passage of a satellite galaxy through the Milky Way disc, and while they found that such an event could produce a structure with the general properties of Complex C and the OA, they did not favour this hypothesis because they could not identify compelling evidence of the putative satellite. However, subsequently several stellar streams and structures have been discovered in this region of the outer Galaxy, and the progenitor(s) of these stellar structures could potentially also explain the origin of Complex C and the OA in a scenario like the one investigated by Kawata et al. (2003). The most well-known stellar stream in this region is the Monoceros Ring (e.g. Newberg et al. 2002; Peñarrubia et al. 2005), but surveys such as the Sloan Digital Sky Survey (SDSS; York et al. 2000) and the Gaia Survey (Gaia Collaboration 2016) have revealed additional stellar streams in this part of the Galaxy. Table 1 summarizes some properties of stellar streams in this direction including Monoceros ‘North’, the Anticentre Stream, Hríd, Gaia 9, and GD1. It is intriguing to note that some of the metallicities and locations of these stellar streams are similar to the published metallicities of Complex C and the OA, but as we will see in this paper, the metallicities of these HVCs are not securely measured – there are degeneracies in the ionization models used to derive metallicities, and it is possible that these HVCs have significantly higher metallicities than the published abundances. It is also worth noting that some of these stellar streams, including the northern Monoceros Ring, Hríd, and GD1, have similar velocities to the HVCs. The Anticentre Stream, on the other hand, exhibits significantly different kinematics with mean velocities of $\it {v}_{\rm LSR} = +48$ and +78 km s−1 in two directions studied by Grillmair, Carlin & Majewski (2008). However, spatially overlapping streams with different kinematics could lead to a roiled, turbulent region, which in turn could make precipitation more likely (Voit 2021). To more visually show the spatial correspondence of the stellar structures and the gas clouds, Fig. 1 shows a schematic map of the projected locations of the streams and clouds from Table 1. Note that Fig. 1 is centred and zoomed in on a set of active galactic nuclei employed in this paper (see below) and does not show the full extent of the HVCs and streams.


Discovered in 1977 from its bright H α emission (Stephenson & Sanduleak 1977), SS433’s defining characteristics are undoubtedly the helical motion of highly collimated jets of plasma launched from its innermost regions, and mass-loaded, non-polar outflows (Fabian & Rees 1979; Margon et al. 1979) which together inflate the surrounding W50 supernova remnant. Knots in SS433’s jet can be resolved at radio frequencies using very long baseline interferometry (VLBI) and indicate the presence of highly relativistic electrons (Vermeulen et al. 1987), while the baryon content is revealed by emission lines ranging from H and He lines in the optical through to highly ionized Fe lines in the X-rays (Kotani et al. 1994; Marshall et al. 2013). The Doppler shifts of the lines indicate precession of the accreting system with a period of ≈ 162 d, also seen in optical (He ii) emission lines originating from the non-polar wind (Fabrika 1997). Both the jets and winds carry a large kinetic luminosity (>1038 erg s−1, e.g. Marshall et al. 2002), which requires extraction of energy via accretion on to a compact object. While the nature of the compact object in SS433 remains somewhat unknown (although dynamical arguments suggest the presence of a black hole – Blundell, Bowler & Schmidtobreick 2008), the rate of mass transfer from the companion star, as inferred from the IR excess (Shkovskii 1981; Fuchs et al. 2006), is thought to be ∼1 × 10−4 M⊙ yr−1, orders of magnitude in excess of the Eddington limit for any plausible stellar remnant (>300 times the Eddington mass accretion rate for a typical stellar mass black hole of around 10 M⊙). Classical theory and radiation magnetohydrodynamic (RMHD) simulations agree that such ‘super-critical’ rates of accretion will lead to a radiatively supported, large scale height (H/R ≈ 1, where H is the height of the disc at distance R from the compact object) accretion disc with powerful winds launched from the surface at mildly relativistic speeds (Shakura & Sunyaev 1973; Poutanen et al. 2007; Ohsuga & Mineshige. 2011; Takeuchi et al. 2013; Jiang et al. 2014; Sadowski et al. 2014).


In Fig. 9, we show the total galactic star formation rate as a function of simulation time t for each isolated disc galaxy. Following the initial vertical collapse of the disc and the subsequent star formation ‘burst’ from t ∼ 30 Myr to t ∼ 250 Myr, the SFR settles down to a rate of ∼2–4 M⊙ yr−1. We make absolutely sure to consider each isolated disc in its equilibrium state by examining the cloud population during a later time interval, between t = 600 Myr and t = 1 Gyr (grey-shaded region). Over this period, the SFR declines only gradually, by a total of around 0.5 M⊙ yr−1. These values are consistent with the current observed SFR in the Milky Way (Murray & Rahman 2010; Robitaille & Whitney 2010; Chomiuk & Povich 2011; Licquia & Newman 2015). We may also consider the resolved star-forming behaviour on scales of 750 pc, as studied in nearby galaxies by Bigiel et al. (2008). In Fig. 10, we display the star formation rate surface density as a function of gas surface density for each of our simulated galaxies, at a simulation time of 600 Myr. The top row shows the 2D projection maps of the CO-bright molecular gas column density $\Sigma _{{\rm H}_2}$. These are computed via the total gas column density in equation (35) and degraded using a Gaussian filter of FWHM = 750 pc. The corresponding projections of the star formation rate surface densities ΣSFR are displayed in the central row. Details for the production of all maps are given in Appendix A. In the bottom row, the values of $\Sigma _{{\rm H}_2}$ and ΣSFR in each pixel of the spatially degraded projection maps are compiled to produce a single histogram. The loci of our simulation data fall close to the observed star formation relations obtained by Bigiel et al. (2008), denoted by the orange contours, though with a population of points at lower densities and star formation rates than are reached by the observations. These points arise because we consider all CO-emitting gas down to a molecular hydrogen surface density of $\Sigma _{{\rm H}_2} = 10^{-3.5} \: {\rm M}_\odot {\rm pc}^{-2}$ (see Fig. 4). This avoids taking an arbitrary cut on $\Sigma _{\rm H_2}$, but also captures much lower levels of CO emission than could be detected by current observatories.


Compared with BNS mergers, which would definitely eject a certain amount of materials to produce EM signals, some NSBH binaries may not tidally disrupt the NS component and, hence, would not make bright EM counterparts such as sGRBs and kilonovae.
9

9
During the final merger phase for plunging NSBH binaries, some weak EM signals may be produced because of the charge and magnetic field carried by the NS (e.g., Dai 2019; Pan & Yang 2019; Zhang 2019; D’Orazio et al. 2022; Sridhar et al. 2021). The tidal disruption probability of NSBH mergers and the brightness of NSBH EM signals are determined by the BH mass, BH spin, NS mass, and NS equation of state (EoS; e.g., Belczynski et al. 2008; Kyutoku et al. 2011, 2013, 2015; Fernández et al. 2015; Kawaguchi et al. 2015, 2016; Foucart 2012; Foucart et al. 2018; Barbieri et al. 2019; Krüger & Foucart 2020; Fragione & Loeb 2021; Fragione 2021; Zhu et al. 2020, 2021c, 2021e; Raaijmakers et al. 2021; Li & Shen 2021; Tiwari et al. 2021). An NSBH merger tends to be a disrupted event and produces bright EM signals if it has a low-mass BH with a high projected aligned spin and a low-mass NS with a stiff EoS. The parameter space in which an NSBH merger can undergo tidal disruption may be very limited. Recently, LIGO–Virgo–KAGRA (LVK) Collaboration reported three high-confidence GWs from NSBH candidates, i.e., GW190814, GW200105_162426, and GW200115_042309 (Abbott et al. 2020, 2021a; Nitz et al. 2021). In spite of many efforts for follow-up observations of these three events, no confirmed EM counterpart candidate has been identified (e.g., Coughlin et al. 2020; Gompertz et al. 2020; Kasliwal et al. 2020;Page et al. 2020; Thakur et al. 2020; Alexander et al. 2021; Anand et al. 2021; Dobie et al. 2022; Kilpatrick et al. 2021). Abbott et al. (2021a), Zhu et al. (2021c), and Fragione (2021) showed that the parameter space of these GW candidates mostly lies outside the disrupted parameter region, so these candidates are likely plunging events with a high probability. There are many mysteries surrounding NSBH binaries, such as the proportion of disrupted events in cosmological NSBH mergers, their cosmological contribution to elements heavier than iron, the formation channel of NSBH binaries, and so on. Systemic research on the population properties of NSBH binaries can help us address these mysteries and unveil the nature of cosmological NSBH binaries.


To investigate the emission-line properties in the blue system, we employed the photoionization code Cloudy (Version 17.01, Ferland et al. 2017) and applied the measured emission-line ratios to these models to simulate the possible physical conditions and processes in the medium. The simple model is a slab-shaped gas with a unique density and homogeneous chemical composition of solar values, irradiated directly by the central ionization continuum source. For the BLR around one of the hypothesized binary black holes, such primordial models can be simply described using parameters such as density nH, hydrogen column density NH, ionization parameter U, and spectral energy distribution (SED) of the incident radiation. A typical AGN ionization continuum is applied as the incident SED, which is a combination of a blackbody “Big Bump” and power laws.6

6
See details in Hazy, a brief introduction to Cloudy; http://www.nublado.org.
 The component peaks at ≈1 Ryd and is parameterized by TBB = 1.5 × 105 K. The slope of the X-ray component, the X-ray to UV ratio, and the low-energy slope are set as αx = −2 (beyond 100 keV) and −1 (between 1.36 eV and 100 keV), αox = −1.4, and αUV = −0.5, respectively. This UV-soft SED is regarded as more realistic for radio-quiet quasars than the other available SEDs provided by Cloudy (see the detailed discussion in Section 4.2 of Dunn et al. 2010). We calculated a series of photoionization models with different ionization parameters, densities, and hydrogen column densities. The ranges of these parameters are −4.0 ≤ log10 U ≤ 1.0, 3.0 ≤ log10 nH (cm−3) ≤ 11.0, and 19.0 ≤ log10 NH (cm−2) ≤ 24.0, with a step of 0.2 dex, which could well cover the possible parameter space of the broad-line and narrow-line regions. In Figure 3, the flux ratios of He iλ10830/Hα are presented in the log U–log NH space for the five densities (log nH (cm−3) = 3, 5, 7, 9, and 11). The extensive parameter space is almost enough to cover all the routine possibilities of the AGN “normal” emission-line regions. However, the typical BLR gases with nH ∼ 109–1010 cm−3, NH ∼ 1022 cm−2 and U ∼ 10−2–10−1 present the relatively strong He i λ10830 emission. If the blue system of SDSS J1536+0441 is also compared, the observed ratio of He i10830/Hα6564 is at least larger than 0.1, which is two times the 3σ upper limit. Further extensive calculation in a larger parameter space suggests that a parameter combination range of UnH ≈ 1011.5 cm−3 with an exceedingly high density of nH ≥ 1012 cm−3 would reproduce the observed flux ratios of the hydrogen and helium lines. If the blue system emits from such a high-density medium, the size would be 50 times less than that of the red system BLR (based on the sub-parsec binary hypothesis, in which both BLRs are illuminated by the same ionizing flux), and the number ratios of ions in the blue system and red system would be only approximately five per thousand. Even accounting for the higher emission efficiency (within an order of magnitude), the high-density medium is not sufficient to emit blue system lines comparable to those of the red system.


In addition to the wind models of λ And, we also present here the first full surface magnetic field observations of this star, finding a strong magnetic field for such an evolved star. These observations, carried out with the NARVAL spectropolarimeter, allow us to constrain the surface magnetic field of λ And. These derived surface magnetic fields can constrain the lower boundary of the 3D magnetohydrodynamic wind simulations that we run. Usually, we see a decay in magnetic field strength as solar-type stars evolve, as their activity decreases along with their rotation (Skumanich 1972; Vidotto et al. 2014b; Booth et al. 2020). However, this subgiant star seems to have a relatively strong large-scale magnetic field compared to the Sun. The exact process through which this star would reach this stage in its evolution with such a magnetic field is yet unknown. Potential reasons are that it began with a much stronger dynamo in its past than anticipated, or perhaps the secondary companion had some effect on the primary star at a point in the past. λ And differs from the Sun as it is an RS Canum Venaticorum (RS CVn) variable, meaning it is a variable binary system. The variability on this star is likely due to magnetic spots coming in and out of view due to stellar rotation (Baliunas & Dupree 1979, 1982; Donati, Henry & Hall 1995; Henry et al. 1995; O’Neal et al. 2001; Sanz-Forcada, Brickhouse & Dupree 2001; Frasca et al. 2008; Drake et al. 2011). RS CVn systems, in particular, can present observed levels of chromospheric and coronal activity that are orders of magnitude higher than in single stars with similar spectral types (Ayres & Linsky 1980; Walter & Bowyer 1981). This is likely caused by the increase in activity when the two stars interact with each other, which can lead to rotational synchronization of the system (e.g. Lanza & Rodonò 2004; an analogous process has been inferred to take place in close-in planet–star systems, Cuntz, Saar & Musielak 2000). For the purposes of this work, we assume the binarity of this system does not affect our wind models. Compared to the Sun, λ And is metal-poor ([Fe/H] = −0.46 ± 0.04 dex, Maldonado & Villaver 2016). We do not include the effects of different metal abundances on the stellar wind and stellar evolution, but the effects of which have been examined in other works (Suzuki 2018).


The typical value of the mass outflow rate for sources accreting below or close to the Eddington limit is $\dot{M}_{\rm out} \gtrsim 5\!-\!10{{\ \rm per\ cent}} \,\dot{M}_{\rm acc}$, for both UFOs and non-UFOs (Tombesi et al. 2012). In this scenario, even for the UFOs with the lowest allowed velocity, the mechanical power is enough to exercise a significant feedback impact on the surrounding environment. Looking at the comparison between mass accretion rate and mass outflow rate for our source (see Table 3), the upper limit on the mass outflow rate for Wind 1 is extremely high, but the values for Wind 2 and Wind 3 are still comparable with the values of quasars and Seyfert galaxies (Tombesi et al. 2012). If we consider the lower limits instead, their values are well below the average. Theoretical works (Di Matteo, Springel & Hernquist 2005; King 2010; Ostriker et al. 2010; Debuhr, Quataert & Ma 2011) showed that, in order to have a significant feedback impact in the environment surrounding an AGN, it is required a minimum ratio between the mechanical power of the outflow and the bolometric luminosity of ${\sim}0.5{{\ \rm per\ cent}}$. Tombesi et al. (2012) showed that actually the lower limit of this value for UFOs is ${\sim}0.3{{\ \rm per\ cent}}$ and for non-UFOs is ${\sim}0.02 \!-\! 0.8{{\ \rm per\ cent}}$. According to what found for the ratio between the mass outflow rate and the mass accretion rate, looking at the upper limits on $\dot{K}/L_{\rm b,out}$ of our source, i.e. multiphase and multiscale X-ray winds, IRAS 04416+1215 fits well in this scenario in which the outflowing winds can impress a feedback. Indeed, the upper limits on $\dot{K}/L_{\rm b,out}$ is comparable with the kinetic coupling efficiency, defined as the ratio of the kinetic luminosity of outflows to the AGN radiative luminosity (Eout/Lrad), calculated with the feedback model for hyper-Eddington accretion by Takeo, Inayoshi & Mineshige (2020), using the outflow velocities and the $\dot{M}/\dot{M}_{\rm acc}$ values of IRAS 04416+1215. Instead, the lower limits are below the minimum value required to generate at least a weak feedback. Considering only the values derived from the lower limits on the distance, i.e. the situation in which the X-ray winds are cospatial, we would be in a scenario in which the source loses much luminosity due to advection inside the disc, resulting in a much lower efficiency for wind production as most of the radiation remains trapped inside the disc. This deduction is supported also by the results of the lower limits on the ratio between the momentum rate of the outflows and the momentum of the radiation. Outflows accelerated through the continuum radiation pressure are expected to have a $\dot{p}_{\rm out}/\dot{p}_{\rm rad}\sim 1$ (King & Pounds 2015). The median value of this ratio for UFOs is ∼0.96 after the relativistic correction and ∼0.64 without the relativistic corrections (Luminari et al. 2020). The values we found for the lower limits on $\dot{p}_{\rm out}/\dot{p}_{\rm rad}$ of IRAS 04416+1215 are again well below the median. Thus, the outcoming luminosity of the source is not enough to accelerate the material to the escape velocity, which is required for a wind to leave the system, suggesting that likely in the scenario of the cospatial winds the outflows observed in IRAS 04416+1215 could be accelerated by other mechanisms such as magnetohydrodynamic processes.


We also examine our

 measurement of NGC 3504 in the context of the empirical compilations of

 and

 scaling relations (Kormendy & Ho 2013; McConnell et al. 2013; Scott et al. 2013; Saglia et al. 2016) in Figure 16. The stellar-bulge velocity dispersion of NGC 3504 is determined from Ho et al. (2009), while the bulge mass of

M⊙ was derived from Section 2.2. For a sanity check, we estimate the bulge mass of NGC 3504 using our H-band MGE model and adapting the effective radius of the bulge derived from the bulge-disk-bar decomposition model (Laurikainen et al. 2004). Accounting for the dynamical M/LH (Section 5.2), we obtain

M⊙. Our result shows that the best-fit

 of NGC 3504 is fully consistent with the empirical

 and

 relations of Kormendy & Ho (2013), McConnell et al. (2013), and Saglia et al. (2016), but outside

 uncertainty of the Scott et al. (2013) and Savorgnan et al. (2016) empirical

 relations for “Sérsic” galaxies (those without central cores). Compared with the theoretical predictions of the bimodality in the BH accretion efficiency model (e.g., Pacucci et al. 2015, 2018), our measurement is consistent with the

 correlation, but a positive outlier is the

 relation up to 1σ. At the mass of

 M⊙, the SMBH of NGC 3504 lies within the same mass regime as the BHs derived in the Combes et al. (2019) sample and lies between the samples of lower- and higher-mass galaxies previously and currently studied with ALMA (Davis et al. 2013, 2017, 2018; Onishi et al. 2015, 2017; Barth et al. 2016a, 2016b; Boizelle et al. 2019; Nagai et al. 2019; North et al. 2019; Smith et al. 2019, T. Davis et al. 2020, in preparation, D. Nguyen et al. 2020, in preparation), respectively. All of these works prove that the cold gas-dynamical method observed with ALMA at high spatial resolution now can work well in a wide range of BH masses covering six orders of magnitude from 105 to

.


In addition, the graduated cylindrical shell (GCS) model, which was developed by Thernisien et al. (2006, 2009) and Thernisien (2011), is applied to obtain the three-dimensional parameters of these CMEs. Figure 5 shows the fitting results of these CMEs. Seen from these images, the GCS model can well represent the topology of these CMEs. The last three columns in Table 1 show the fitting results of these CMEs, including the propagation directions, velocities and face-on angular widths. Assuming a constant velocity and considering the influence of the propagation direction and angular width on the prediction of the arrival time suggested by Shen et al. (2014), CME-1 would arrive at the Earth around the time of September 6 22:27 UT. However, previous results show that fast CME would decelerate during their propagation in interplanetary space (e.g., Gopalswamy et al. 2001a, 2005; Vršnak 2001; Vršnak & Žic 2007; Temmer et al. 2011; Lugaz & Kintner 2012, and reference therein). Such deceleration may make the CME-1 arrive at the Earth later than September 6 22:27 UT. Thus, CME-1 is more likely to be the solar source of ICME-1. Seen from the Figure 3, the front edge of the CME-2 is lower than the front edge of CME-1 indicating that CME-2 would arrive at the Earth later than CME-1. Thus, CME-2 was the solar source of the ICME-2. It should be noted that, based on the fitting results of GCS model, CME-2 is faster than CME-1 and their propagation directions are close to each other. Thus, these two CMEs are expected to interact in interplanetary space. Seen from the in situ observations, possible interaction region signatures were detected between these two ICMEs with lower magnetic field, higher velocity, high density, and higher plasma beta. Furthermore, similar analysis shows that CME-3 might arrive at Earth after September 7 19:21 UT. Considering the long duration of Ejecta-4 and the larger angular width of CME-3, we verify that CME-3 is the solar source of ICME-4 and the driver of the second shock. It should be noted that, no obvious Earth-directed CME could be identified as the solar source of Ejecta-3. A possible explanation is that this ejecta structure is formed in the sheath region of ICME-4 during its propagation outward (e.g., Zheng & Hu 2018, and reference therein).


As a prototypical Seyfert 2 galaxy with starburst at a distance of 14.4 Mpc (1″ = 72 pc, Bland-Hawthorn et al. 1997), NGC 1068 was observed at radio (Greenhill et al. 1996), millimeter (Schinnerer et al. 2000), infrared (Jaffe et al. 2004), optical (Antonucci & Miller 1985), UV (Antonucci et al. 1994), and X-ray (Kinkhabwala et al. 2002). High spatial resolution CO (1–0) observations show two molecular spiral arms with a diameter of ~40″ and a northern half-bar, while a CO (2–1) map reveals a nuclear ring with two bright knots in the CND region (Schinnerer et al. 2000). The dense gas fraction as traced by HCN (1–0) (Tacconi et al. 1994; Helfer & Blitz 1995) and CS (2–1) (Tacconi et al. 1997; Takano et al. 2014) in the nuclear region is higher than the two arms. Observations of CO (3–2) (Krips et al. 2011; Tsai et al. 2012; García-Burillo et al. 2014) showed that the difference of molecular gas temperatures between the nuclear region and the two arms was not as large as that of densities. Dozens of molecular lines at millimeter wavelength were detected at CND with single-dish observations (Usero et al. 2004; Nakajima et al. 2011, 2013; Aladro et al. 2013). Moreover, several molecules were detected and resolved toward NGC 1068 with interferometers in the past few years (Tosaki et al. 2017; Kelly et al. 2017; Furuya & Taniguchi 2016; Izumi et al. 2016; Imanishi et al. 2016; Nakajima et al. 2015; Viti et al. 2014; Takano et al. 2014; García-Burillo et al. 2014, 2016). The molecular gas in the CND region was denser and hotter than that in the starburst ring, while chemical properties in the two regions were also different (Viti et al. 2014). The highest molecular gas temperature was higher than 150 K, and the gas density was above 105 cm−3 in the CND region (Viti et al. 2014). The distribution of different species of molecules were also different: CO isotopic species, for instance, were enhanced in the starburst ring, while the shock/dust related molecules were enhanced in the CND region (Nakajima et al. 2015). The spatially resolved observations showed that the CND region was a complex dynamical system. For instance, the east and west dots were dominated by a fast shock and a slower shock (Kelly et al. 2017), while the dust torus also showed complex kinematics (García-Burillo et al. 2016). Gas inflow was driven by a past minor merger (Furuya & Taniguchi 2016), while the outflow was AGN driven (García-Burillo et al. 2014). We conducted adeeper survey of millimeter lines toward the CND region of NGC 1068 with the IRAM 30 m telescope, with the goal to quantify the gas properties in the CND. Compared to previous single-dish observations, our data probe weaker transition lines, which could place more constraints on the physical and chemistry properties of the CND.


C-statistic (e.g. Jang & Miller 1997) is the most commonly used and the one-way analysis of variance (ANOVA; de Diego 2010) the most powerful test for verifying the presence of variability in a DLC. However, we did not employ either of these tests because, de Diego (2010) has questioned the validity of the C-test by arguing that the C-statistics does not have a Gaussian distribution and the commonly used critical value of 2.567 is too conservative. On the other hand, the ANOVA test requires a rather large number of data points in the DLC, so as to have several points within each sub-group used for the analysis. This is not feasible for our DLCs which typically have no more than about 30–45 data points. Therefore, we have instead used the F-test which is based on the ratio of variances, F = variance(observed)/variance(expected) (de Diego 2010; Villforth, Koekemoer & Grogin 2010), with its two versions : (i) the standard F-test (hereafter Fη-test, Goyal et al. 2012) and (ii) scaled F-test (hereafter Fκ-test, Joshi et al. 2011). The Fκ-test is preferred when the magnitude difference between the object and comparison stars is large (Joshi et al. 2011). Onward Paper II, we have only been using the Fη-test because our objects are generally quite comparable in brightness to their available comparison stars. An additional gain from the use of the Fη-test is that we can directly compare our INOV results with those deduced for other major AGN classes (Goyal et al. 2013). An important point to keep in mind while applying the statistical tests is that the photometric errors on individual data points in a given DLC, as returned by the algorithms in the iraf and daophot softwares are normally underestimated by the factor η which ranges between 1.3 and 1.75, as estimated in independent studies (e.g. Gopal-Krishna, Sagar & Wiita 1995; Garcia et al. 1999; Sagar et al. 2004; Stalin et al. 2004a; Bachev, Strigachev & Semkov 2005). Recently, using a large sample, Goyal et al. (2013) estimated the best-fitting value of η to be 1.5, which is adopted here. Thus, the Fη statistics can be expressed as

\begin{equation*}
F_{1}^{\eta } = \frac{\sigma ^{2}_{({\rm q-s1})}}{ \eta ^2 \langle \sigma _{{\rm q-s1}}^2 \rangle }, \hspace{5.69046pt} F_{2}^{\eta } = \frac{\sigma ^{2}_{({\rm q-s2})}}{ \eta ^2 \langle \sigma _{{\rm q-s2}}^2 \rangle }, \hspace{5.69046pt} F_{{\rm s1-s2}}^{\eta } = \frac{\sigma ^{2}_{({\rm s1-s2})}}{ \eta ^2 \langle \sigma _{{\rm s1-s2}}^2 \rangle },\end{equation*}

 where $\sigma ^{2}_{({\rm q-s1})}$, $\sigma ^{2}_{({\rm q-s2})}$ and $\sigma ^{2}_{({\rm s1-s2})}$ are the variances of the ‘quasar–star1’, ‘quasar–star2’ and ‘star1–star2’ DLCs and $\langle \sigma _{{\rm q-s1}}^2 \rangle =\sum _{\boldsymbol {i}=0}^{N}\sigma ^2_{i,{\rm err}}({\rm q-s1})/N$, $\langle \sigma _{{\rm q-s2}}^2 \rangle$ and $\langle \sigma _{{\rm s1-s2}}^2 \rangle$ are the mean square (formal) rms errors of the individual data points in the ‘quasar–star1’, ‘quasar–star2’ and ‘star1–star2’ DLCs, respectively. η is the scaling factor (= 1.5) as mentioned above.


Several laboratory experiments have been performed to determine the mechanical properties of possible building blocks of comets. In particular, Güttler et al. (2009), Schräpler et al. (2015), Lorek et al. (2016), and Katsuragi & Blum (2017) investigated how the compressibility of ice layers and different dust structures created by random ballistic deposition as well as pebble sub-structures (with scales of centimeters, millimeters, and 0.1 mm) depend on the volume filling factor. The respective results are summarized in Fig. 6. Remote observations lead to multiple independent estimates for the volume filling factor. Kofman et al. (2015) derived values of 0.15–0.25, Pätzold et al. (2016) estimated 0.25–0.30, and a study by Fulle et al. (2016) resulted in 0.21–0.37. The corresponding range is depicted in Fig. 6 by the horizontal bar shaded in blue. As thevolume filling factor is known, the laboratory measurements can be used to determine the most likely material of the surface. For the observed volume filling factor, dust and ice layers have a compressive strength above 103 Pa. A surface made up of such dust or ice layers is therefore inconsistent with the results of Groussin et al. (2015) or the compressive strength derived as part of this work. In contrast, a surface consisting of layers of dust and ice aggregates could explain all observations, except for the MPa range derived by Spohn et al. (2015). This is strong evidence for the presence of aggregate layers on the surface of 67P, that is, a surface composed of sub-decimeter-sized aggregates, as inferred from the gravitational collapse scenario. This conclusion can be drawn without precise knowledge of the actual value of the compressive strength, as the upper limit derived as part of this work and by Groussin et al. (2015), even considering all possible errors, is well below 103 Pa for different parts of 67P. The presence of such aggregate layers can only be explained by a formation dominated by relatively low-velocity collisions. Hierarchical agglomeration would cause a significantly higher compressive strength as a result of impact-compaction of the pebbles and possible break-up of aggregates (Blum 2018). The derived mechanical properties combined with the available laboratory models therefore suggest that the gentle collapse of aggregate ensembles played a major role in the formation ofcomets like 67P.


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


The process of planet formation is strongly dependent on the stellar birth environment. The majority of stars exist in clusters or associations within their first few Myr of evolution (Lada & Lada 2003; Longmore et al. 2014; Krumholz, McKee & Bland-Hawthorn 2019), during which time they also host protoplanetary discs (PPDs – e.g. Haisch, Lada & Lada 2001; Ribas et al. 2014). Multiple feedback mechanisms influence disc evolution. In sufficiently dense environments, star–disc encounters can truncate the disc and induce increased accretion rates (Clarke & Pringle 1993; Ostriker 1994; Hall, Clarke & Pringle 1996; Pfalzner et al. 2005a; Olczak, Pfalzner & Spurzem 2006; Pfalzner, Olczak & Eckart 2006; de Juan Ovelar et al. 2012; Breslau et al. 2014; Rosotti et al. 2014; Winter et al. 2018a). Recent studies indicate that in the solar neighbourhood such interactions only have a significant effect in the early stages of cluster evolution due to enhanced stellar multiplicity and substructure, and therefore set initial conditions rather than destruction time-scales (Bate 2018; Winter et al. 2018b; Winter, Booth & Clarke 2018c). However, in regions with massive stars, external photoevaporation by far-ultraviolet (FUV) and extreme-ultraviolet (EUV) photons can rapidly disperse PPDs (Johnstone, Hollenbach & Bally 1998; Störzer & Hollenbach 1999; Armitage 2000; Clarke 2007; Fatuzzo & Adams 2008; Adams 2010; Facchini, Clarke & Bisbas 2016; Ansdell et al. 2017; Haworth et al. 2018b; Winter et al. 2018b). Additionally, before the dispersal of the parent giant molecular cloud (GMC), ram pressure stripping can truncate PPDs (Wijnen et al. 2017a) or additional material can be accreted (Moeckel & Throop 2009; Scicluna et al. 2014), leading to the destruction and reforming of discs during the embedded phase (Bate 2018). If a PPD is destroyed quickly by feedback in dense stellar environments, planets may be unable to form, depending on the efficiency of the formation mechanisms (Youdin & Goodman 2005; Johansen & Lambrechts 2017; Ormel, Liu & Schoonenberg 2017; Haworth et al. 2018a). Given the apparent ubiquity of grouped star formation, quantifying the destruction time-scales for PPDs due to neighbour feedback is of great relevance for understanding the demographics of PPDs and exoplanetary systems.


Studies of SEP events are important for different reasons. On one hand, solar eruptive events are well-observed processes of energetic-particle acceleration (Vainio & Afanasiev 2018), which can be studied in detail using a multi-messenger approach, complementing particle data with observations in different wavelengths (e.g., Plainaki et al. 2014; Cliver 2016; Kocharov et al. 2017). For this purpose, the peak flux intensity and detailed temporal variability of the particle flux are important as signatures of the acceleration process in the solar corona and the interplanetary medium (e.g., Desai & Giacalone 2016; Kong et al. 2017). Accordingly, numerous studies were focused on peak fluxes of SEPs and corresponding acceleration and transport processes (e.g., Kouloumvakos et al. 2015; Kocharov et al. 2017). On the other hand, enhanced fluxes of energetic particles affect the radiation environment near the Earth (e.g., Webber et al. 2007; Mishev et al. 2015), making not only the peak fluxes but also the fluence (event-integrated flux) and its spectral shape of significant importance, especially for extreme events (e.g., Cliver et al. 2020). We emphasise that SEP fluences can not be used for the detailed study of SEP acceleration processes, because (i) the observations at 1 AU are also modified by transport, and (ii) different energies in the fluence spectrum can be dominated by different acceleration mechanisms or by the same mechanism operating under different conditions. It is evident from the proton time-intensity profiles alone that the fluence at MeV and 10 MeV energies is often dominated by acceleration at interplanetary shocks (e.g., Reames 1999). However, the question is more open at 100 MeV and GeV energies peaking much earlier, with possible contributions from flares and/or coronal shocks as the main candidates to account for the acceleration (see Cliver 2016, and references therein). Even if the same CME-driven shock were responsible for the acceleration of 10 MeV and 1 GeV protons, the former would typically be accelerated mainly in the solar wind and the latter in the corona, and there is no reason to suggest that the spectral form of the fluence would reveal something common about the accelerator properties.


Low- and intermediate-mass stars are formed by the gravitational collapse of the parental giant molecular cloud (GMC), followed by the accretion process (Palla 1996). During the accretion phase, material is ejected as well via collimated bipolar jets. However, when a YSO reaches 8 M⊙, the radiative flux becomes so intense (using ϕ = L/4πd2, the ratio between the radiative fluxes of an O5 and a B3 star – masses of ∼40 and ∼8 M⊙, respectively – is ≈250) that it may interrupt the accretion flow. A process that constrains the outcoming radiation field to narrower angles may leave some room for the accretion process to continue in some directions. This seems to be the case for the outflows driven by young stars from a very broad mass range, as previous reported by several authors (Bachiller 1996; Bontemps et al. 1996; Shepherd & Churchwell 1996; Beuther et al. 2002; Wu et al. 2004). Outflows associated with high-mass objects are expected to be more energetic than the outflows observed in lower mass YSOs (Beuther et al. 2005; Zhang et al. 2005; López-Sepulcre et al. 2009), with velocities greater than ∼100 km s−1 (Martí, Rodríguez & Reipurth 1998). Some authors have found evidences that outflows associated with massive stars are scaled up versions of their low-mass counterparts (Vaidya et al. 2011; Codella et al. 2013) while other works have reported that no well-collimated outflows have been found towards MYSOs (Shepherd, Testi & Stark 2003; Sollins et al. 2004). Massive YSO outflows mapped in high-velocity CO lines have collimation factors R = length/width ∼2.05 ± 0.96 as compared to R ∼ 2.81 ± 2.16 for low-mass stars (Wu et al. 2004), indicating a weak tendency that outflows associated with massive stars are less collimated than those from low-mass stars as previously thought (Richer et al. 2000). Besides the degree of collimation, these massive outflows would work removing mass from the plane of the accretion disc, lowering the density on the plane and, therefore, facilitating the accretion flow to reach the stellar core as shown in the recent 3D simulations presented by Krumholz et al. (2009). Although these authors have not included the outflow activity on their simulations, they argue that the presence of outflows would decrease the star formation efficiency from 70 per cent (considering purely radiation effects) to 50 per cent.


W51e2 is the strongest and best-studied HC HII region in the W51 Main cluster, and it is believed to be powered by an O8-type young star (e.g., Shi et al. 2010a). A number of interferometric studies conducted with varying angular resolutions, at centimetre (cm) and (sub)millimetre (mm) bands, identified molecular and ionized gas undergoing infall and rotation toward W51e2. VLA observations of the NH3 inversion lines (1, 1) and (2, 2) seen in absorption (1\hbox{$\farcs$}.̋1 beamsize) revealed radial infall on scales larger than 5000 AU toward the W51e2 core (Zhang & Ho 1997). Higher angular resolution observations of the (3, 3) NH3 absorption line (0\hbox{$\farcs$}.̋3 beamsize) showed signatures of rotation within 2000 AU based on a position-velocity (pv) diagram (Zhang & Ho 1997). Zhang et al. (1998) identified a velocity gradient in a CH3CN transition at 2 mm, deriving a position angle (PA) of 20 ± 20°. Keto & Klaassen (2008) imaged the H53α radio recombination line (RL) with the VLA (0\hbox{$\farcs$}.̋45 beamsize) and they claimed rotation in the ionized gas along the axis of a molecular bipolar outflow (oriented NW-SE) imaged with the SMA in the CO (2−1) line (1′′ beamsize), suggesting a simple inflow/outflow picture in a single high-mass young stellar object (YSO). However, higher resolution observations, using the SMA at the wavelengths of 0.85 mm (0\hbox{$\farcs$}.̋3 beamsize) and 1.3 mm (0\hbox{$\farcs$}.̋7 beamsize), revealed a more complex picture, by resolving W51e2 into three subcores (Shi et al. 2010a): W51e2-W, corresponding to the HC HII region, W51e2-E, located about 1′′ east of the HC HII region and corresponding to the brightest dust continuum source, and W51e2-NW, the weakest continuum component, located about 1′′  NW of the HC HII region. Shi et al. (2010b) imaged the CO (3−2) line (with a 0\hbox{$\farcs$}.̋7 beamsize) and established that the driving source of the powerful molecular outflow in this region is the protostellar core W51e2-E, and not the HC HII region W51e2-W, challenging the scenario proposed by Keto & Klaassen (2008). Etoka et al. (2012) used MERLIN to image the Class II 6.7 GHz CH3OH masers (typical signpost of HMSF), and found that the bulk of maser emission is indeed concentrated toward W51e2-E, and not the HC HII region W51e2-W. This further supports the scenario proposed by Shi et al. (2010a), where the ongoing star formation activity in the region is not concentrated on the HC HII region but toward its companion 1′′ to the east.


Cepheus X-4 was discovered as a transient source using the X-ray telescope of the OSO-7 satellite during 1972 June–July (Ulmer et al. 1973). Ginga observed the source during the 1988 March outburst and detected a spin period of 66.25 s for its neutron star for the first time (Koyama et al. 1991). Spectroscopic studies from the same Ginga observations led to the detection of a cyclotron resonance scattering feature corresponding to a centroid energy at 30.5 ± 0.4 keV (Mihara et al. 1991). The ROSAT observations during the 1993 June outburst refined the source coordinates and also determined its pulsar spin period (Schulz et al. 1995). The observations by BATSE during 1993 June–July and during the subsequent outburst of 1997 June–July, which was also followed by RXTE, determined the pulse characteristics of Cepheus X-4. Additionally, a possible range of its orbital period from 23 to 147.3 days was suggested using RXTE data (Wilson et al. 1999). From observed characteristic features and outburst activities, it was predicted that Cepheus X-4 could possibly have a massive early-type Be star with its circumstellar disk as a companion, which was thought to be the most likely cause of its long outburst of about 40 days, as seen for other Be binaries. Optical observations of Cepheus X-4 subsequently confirmed it as a Be binary system and estimated its location at a distance of 3.8 ± 0.6 kpc (Bonnet-Bidaud & Mouchet 2005). But this distance estimate was later challenged by Riquelme et al. (2012), who proposed a distance of either 7.9 kpc or 5.9 kpc according to whether the stellar type of the companion is a B1 or B2 star, respectively. The distance of Cepheus X-4 was later reported by Gaia to be

10.2

−
1.6

+
2.2

 kpc (Malacaria et al. 2020). Luminosity dependent changes in the pulse profile of Cepheus X-4 were studied during the declining phase of the 1997 outburst (Mukerjee & Agrawal et al. 2000) by combining observations by the Indian X-ray Astronomy Experiment (Agrawal et al. 1996) and RXTE (Rothschild et al. 1998). The RXTE observed another outburst in 2002 and re-established its cyclotron resonance feature corresponding to a centroid energy at 30.7 ± 1.8 keV (as established earlier by Ginga), which did not show a significant dependence on X-ray luminosity, although the continuum became harder with increasing source luminosity (McBride et al. 2007). The source went into outburst again in 2014 and was observed with the Nuclear Spectroscopic Telescope Array (NuSTAR; Harrison et al. 2013) and Suzaku (Mitsuda et al. 2007). The Suzaku observation of the 2014 outburst overlapped with the second observation with NuSTAR on 2014 July 1–2, and detected an additional absorption feature at ≈45 keV in the phase resolved spectra of the pulsar, which was identified as the first harmonic of the fundamental cyclotron line detected at ≈28 keV (Jaiswal & Naik 2015). The source spectra obtained from the NuSTAR observations in 2014 were well fitted by a Fermi–Dirac cutoff (FD-cutoff) model along with an iron emission line, and a cyclotron absorption feature was clearly detected in both of the observations at

30.39

−
0.14

+
0.17

 keV and

29.42

−
0.24

+
0.27

 keV, respectively. Although, the averaged source luminosity differed by a factor of about 3 between these two observations, it only showed a marginal variation in its centroid energy (Furst et al. 2015). Using the same NuSTAR observations of the 2014 outburst, Vybornov et al. (2017) reported that the spectrum of Cepheus X-4 showed two cyclotron resonance scattering features, with the fundamental line at ≈30 keV and its harmonic at ≈55 keV. They also showed that the energy of the fundamental cyclotron absorption feature increases and the continuum becomes harder with increasing X-ray luminosity. Pulse phase resolved spectroscopic studies of Cepheus X-4 were conducted by Bhargava et al. (2019) at these two different intensities of the source using the same two NuSTAR observations of the 2014 outburst. It was found that the observed cyclotron line profile of Cepheus X-4 had an asymmetric shape in the phase averaged spectrum. However, for phase resolved spectra, a single symmetric cyclotron profile fitted the data well. The spectral continuum and the parameters of the cyclotron line showed some variations with respect to the pulse phase only within a limited pulse phase (Bhargava et al. 2019).


It is still unclear whether this incompatibility is evidence against the spatially flat ΛCDM model or is caused by unidentified systematic errors in one of the established cosmological probes or by evolution of the parameters themselves with the redshift (Dainotti et al. 2021b, 2022). Newer, alternate cosmological probes could help alleviate this issue. Recent examples of such probes include reverberation-mapped quasar (QSO) measurements that reach to redshift z ∼ 1.9 (Czerny et al. 2021; Khadka et al. 2021a,b; Yu et al. 2021; Zajaček et al. 2021), H ii starburst galaxy measurements that reach to z ∼ 2.4 (Mania & Ratra 2012; Chávez et al. 2014; González-Morán et al. 2019, 2021; Cao, Ryan & Ratra 2020, 2022a; Cao et al. 2021a; Johnson, Sangwan & Shankaranarayanan 2022; Mehrabi et al. 2022), QSO angular size measurements that reach to z ∼ 2.7 (Cao et al. 2017, 2020, 2021a; Ryan, Chen & Ratra 2019; Lian et al. 2021; Zheng et al. 2021), QSO flux measurements that reach to z ∼ 7.5 (Risaliti & Lusso 2015, 2019; Khadka & Ratra 2020a,b, 2021, 2022; Lusso et al. 2020; Yang, Banerjee & Ó Colgáin 2020; Li et al. 2021; Lian et al. 2021; Luongo et al. 2021; Rezaei, Solà Peracaula & Malekjani 2021; Zhao & Xia 2021),1 and the main subject of this paper, gamma-ray burst (GRB) measurements that reach to z ∼ 8.2 (Amati et al. 2008, 2019; Cardone, Capozziello & Dainotti 2009; Cardone et al. 2010; Samushia & Ratra 2010; Dainotti et al. 2011, 2013a,b; Postnikov et al. 2014; Wang, Dai & Liang 2015; Wang et al. 2016, 2022; Fana Dirirsa et al. 2019; Khadka & Ratra 2020c; Hu, Wang & Dai 2021; Dai et al. 2021; Demianski et al. 2021; Khadka et al. 2021c; Luongo et al. 2021; Luongo & Muccino 2021; Cao et al. 2021a). Some of these probes might eventually allow for a reliable extension of the Hubble diagram to z ∼ 3–4, well beyond the reach of Type Ia supernovae. GRBs have been detected to z ∼ 9.4 (Cucchiara et al. 2011), and might be detectable to z = 20 (Lamb & Reichart 2000), so in principle GRBs could act as a cosmological probe to higher redshifts than 8.2.


When we now compare the photodesorption yields at 541 eV between fluences  5 × 1015 photon cm−2 and at 3 × 1017 photon cm−2 in Fig. 2, the CO2 photodesorption first increases from 2.6 × 10−2 molecule/photon to 7.3 × 10−2 molecule/photon. We also observed this phenomenon for CO photodesorption yield (the data are not shown for more clarity), which increased from 1.9 × 10−2 molecule/photon to 3.5 × 10−2 molecule/photon. Second, the estimated yield for the X-ray photodesorption of CH3OH from pure methanol ice decreased by almost one order of magnitude from 9.0 × 10−3 molecule/photon to 1.3 × 10−3 molecule/photon. This indi- cates that the photodesorption of CH3OH is higher for a lower fluence received by the ice when more intact methanol molecules are present in the ice. This aging process favors the photodesorption of simpler molecules such as CO2 or CO. Laffon et al. (2010) estimated with NEXAFS spectroscopy (at the C K-edge) that X-ray irradiation at 150 eV of pure methanol ice at 20 K leads to a survival rate of 50% for methanol after an absorbed dose of 1.1 MGy. In our fixed-energy experiments, we irradiated pure methanol ice with fluences between 5 × 1015 photon cm−2 and 2 × 1016 photon cm−2. Because we irradiated a volume of 0.1 cm2 × 100 ML, with a meanenergy of ~550 eV, and when we consider a volumic mass of condensed methanol of ~ 0.64 g cm−3 (at 20 K; Luna et al. 2018) and an X-ray absorption cross section of ~ 0.6 Mbarn (Ishii & Hitchcook 1988), the absorbed doses used in our fixed energy experiments change from ~ 2 to ~ 15 MGy, whichis quite similar to the absorbed doses in Laffon et al. (2010). This indicates that we could expect a methanol destruction rate of about 50% for our low-fluence experiments. In similar experiments, when irradiating a H2 O:CH4:NH3 (2:1:1) ice mixture covered by a layer of CO:CH3OH (3:1) with 250–1250 eV X-rays during 120 min with a flux of 7.6 × 1014 photon s−1, higher by almost two order of magnitudes than our experiments, Ciaravella et al. (2020) did not detect a desorption signal on the mass channel 31 (attributed to methanol desorption) and estimated that only ~ 20% of methanol molecules remained intact in the first minutes of the irradiation. The irradiation flux therefore appears to be critical for detecting methanol desorption in X-ray irradiation experiments of methanol-containing ices. A lower X-ray flux appears to favor methanol desorption because the methanol destruction rate is lower. This destruction of methanol molecules could also have a significant effect on the formation and desorption of more complex molecules.


Recent studies have shown that one can use energy balance arguments that include the large-scale magnetic field, ${\mathrm{{\boldsymbol {\mathit {B}}}}_0}$, to derive scaling laws between the Alfvénic and kinetic fluid quantities (Federrath 2016; Beattie et al. 2020; Skalidis & Tassis 2021; S+2021). The dimensionless magnetic energy density, by which we mean the magnetic energy density normalized to the mean thermal pressure3$\rho _0 c_{\rm s}^2$, is
(5)$$\begin{eqnarray}
{e_{\mathrm{ mag}}}= \frac{B^2}{8\pi c_{\rm s}^2 \rho _0} = \frac{1}{8\pi c_{\rm s}^2 \rho _0}\Bigg (B_0^2+ \underbrace{2\delta \mathrm{{{\mathit {B}}}}\cdot \mathrm{{{\mathit {B}}}}_0}_{{\substack{\text{coupling} \\\text{term}}}} {} + \delta B^2 \Bigg),
\end{eqnarray}$$where $B_0^2$ is the large-scale field contribution to the total energy, δB2 is the turbulent field contribution, and $2\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot \mathrm{{\boldsymbol {\mathit {B}}}}_0$ is the coupling term between the two field components. In the linear perturbation theory limit of the MHD equations, δB2 includes contributions from shear Alfvén, fast and slow magnetosonic compressive eigenmodes (e.g. Landau & Lifshitz 1959). Because $\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot \mathrm{{\boldsymbol {\mathit {B}}}}_0 = \delta B_{\parallel }B_0$, the coupling term only contains the component of magnetic field fluctuations that are parallel to the large-scale field. In linear theory, both fast and slow magnetosonic compressible modes are able to perturb the field variables parallel to ${\mathrm{{\boldsymbol {\mathit {B}}}}_0}$, so under the lens of linear theory, the coupling term is the fluctuation contribution from the compressible modes in the turbulence scaled by B0 (Bhattacharjee, Ng & Spangler 1998). Furthermore, for sub-Alfvénic turbulence Beattie et al. (2021b) showed that converging, shocked flows along magnetic field lines excite strong δB∥ fluctuations, which travel roughly at the theoretical fast Alfvén mode speed. Therefore, it is likely, assuming that δB∥/B0 ≪ 1 (this is indeed the case for ${\mathcal {M}_{\text{A0}}}\lt 1$ plasmas; see left panel of fig. 5 in Beattie et al. 2022) where a linear theory may be valid for the magnetic field, the coupling term contains significant energy contributions from fast magnetosonic modes excited by shocked gas that converges and forms dense filaments perpendicular to magnetic field lines.


The scenario presented above has been formulated in various flavors to individually explain several of the properties reported here. The main addition of this work, namely the excitation of CO in distant main-sequence and starburst galaxies, fits in the general picture that we sketched. The ensemble of properties and correlations that we reported here can be also used to revisit the definition of what a starburst is. A standard operational classification is based on the distance from the observed empirical M⋆-SFR correlation, the main sequence. This proved to be a useful distinction and an excellent predictor of several trends (e.g., Sargent et al. 2014), but recent results, including our present and previous analysis (Puglisi et al. 2019), show that the demarcation between starburst and main-sequence galaxies is more blurred that we previously considered. We do detect starburst-like behaviors in galaxies on the main sequence (Elbaz et al. 2018), likely linked to the existence of transitional objects (Popping et al. 2017; Barro et al. 2017b; Gómez-Guijarro et al. 2019; Puglisi et al. 2019, and in prep. to limit the references to recent works based on submillimeter observations). Such transition might well imply an imminent increase of the SFR, driving the object in the realm of starbursts (e.g., Barro et al. 2017b), or its cessation, bringing the system back onto or even below the main sequence (Gómez-Guijarro et al. 2019; Puglisi et al. 2019), with the CO properties potentially able to distinguish between these two scenarios. Regardless of these transitional objects, a definition of starburst based on ΣSFR, rather than ΔMS, would naturally better account for the observed molecular gas excitation properties, dust temperatures and opacities, or SFE (see also Elbaz et al. 2011; Rujopakarn et al. 2011; Jiménez-Andrade et al. 2018; Tacconi et al. 2020). As an example, in Fig. 8 we show the mean SLED of the subsample of galaxies with both CO (2 − 1) and CO (5 − 4) coverage, split at its median ΣSFR. While only tentative at this stage, this suggests a trend of increasing CO excitation with ΣSFR, consistently with Fig. 7 and what mentioned above.


To tackle this problem, one must study the recent star formation history (SFH) of galaxies. This information is embeddedin their spectral energy distribution (SED). However, recovering it through SED modeling is complex and subject to many uncertainties and degeneracies. Although an average SFH of galaxies can be derived assuming that they follow the MS (Heinis et al. 2014; Ciesla et al. 2017), galaxies are expected to exhibit complex SFHs, with short-term fluctuations, requiring sophisticated SFH parametrizations to model them (e.g., Lee et al. 2010; Pacifici et al. 2013; Behroozi et al. 2013; Pacifici et al. 2016). However, implementation of these models is complex and a large library is needed to model all galaxies properties. Instead, numerous studies have used simple analytical forms to model galaxies SFH (e.g., Papovich et al. 2001; Maraston et al. 2010; Pforr et al. 2012; Gladders et al. 2013; Simha et al. 2014; Buat et al. 2014; Boquien et al. 2014; Ciesla et al. 2015; Abramson et al. 2016; Ciesla et al. 2016, 2017). Furthermore, SFH parameters are known to be difficult to constrain from broadband SED modeling with a general agreement on the difficulty to constrain the age of the galaxy, here defined as the age of the oldest star, from broad-band SED fitting (e.g., Maraston et al. 2010; Pforr et al. 2012; Buat et al. 2014; Ciesla et al. 2015, 2017). To understand the origin of the scatter of the MS, we need to use an analytical SFH that is able to recover recent variations of the SFR with a precision better than the scatter of the MS itself, that is, 0.3 dex. Recently, Ciesla et al. (2017) showed that a delayed SFH to which we add a flexibility on the recent SFH provides SFRs that are more accurate than those estimated by other typical analytical SFHs (τ models, delayed, etc.). This SFH was tested in Ciesla et al. (2016). Studying a sample of local galaxies from the Virgo cluster, that is, galaxies known to have undergone a fast drop of star formation activity due to ram pressure stripping, we showed that the amplitude of the flexibility can be constrained by broadband SED modeling as long as ultraviolet (UV) rest frame and near-IR data are available.


Flows with

Rem≪1

 and

N∼(1)

 have the distinct property that the induced magnetic field is quickly diffused away, yet the Lorentz force is not negligible. This limit is referred to as the quasi-static approximation to MHD (which we call “QMHD” henceforth; Moffatt 1967; Sommeria & Moreau 1982; Davidson 1995; Knaepen & Moreau 2008; Davidson 2013), and has been studied mainly in metallurgy and in MHD experiments due to the typically low conductivity of liquid metals (Alemany et al. 1979; Sommeria 1988; Gallet et al. 2009; Klein & Pothérat 2010; Pothérat & Klein 2014; Baker et al. 2018), although recent numerical studies on its turbulent properties and anisotropy have been done as well (Zikanov & Thess 1998; Burattini et al. 2008; Favier et al. 2010, 2011; Reddy & Verma 2014; Verma 2017). After nondimensionalizing the equations of MHD using the uniform density ρ, ℓ, and u, and taking the limits above, one is left with a single dynamical equation for the velocity
2

∂v∂t+v·∇v=−∇p*−Ro−1xˆ∥Ω×v−N∇−2(xˆ∥B0·∇)2v+F,

where p
* is the total pressure modified by rotation and magnetic pressure, Ro
−1 ≡ 2Ωℓ/u is the inverse Rossby number (quantifying the relative strength of the Coriolis force),

xˆ∥Ω

 and

xˆ∥B0

 are unit vectors in the direction of rotation and the background magnetic field, respectively, and
F
 is a generic forcing term that can include dissipation such as viscosity and a body force (to be specified in Section 3). The background magnetic field is fixed in time and is uniform in space, such that

∇×B0=B0∇×xˆ∥B0=0

. Care must be taken if considering a spatially dependent background magnetic field
B

0
(
x
), as the resulting equation will not be the same. See the discussion in Section 5. This equation is accompanied with the incompressibility condition ∇ ·
v
 = 0. The induced magnetic field can be found using a diagnostic relation
3

b=−∇−2xˆ∥B0·∇v,

which would be

b=−∇−2B0·∇v/η

 in dimensional variables.


This work, which focuses on mass reconstruction from gravitational lensing, is only the first in a series, which will exploit our mesh-free numerical techniques. Two regimes are typically distinguished in lensing mass reconstruction. Strong lensing is usually confined to the inner-most core of the gravitational lens and produces spectacular observational constraints such as multiple images of the same source, gravitational arcs or even rings. The domain of weak lensing is further away from the centre of the lens but spans large areas and manifests itself by the weak distortion in the shape of background galaxies behind the lens. Reconstruction techniques are divided into two classes, although this distinction is by no means unique or even consistent in some cases. Parametric techniques (e.g. Kneib et al. 1996; Broadhurst et al. 2005; Smith et al. 2005; Halkola, Seitz & Pannella 2006; Jullo et al. 2007; Zitrin et al. 2009; Oguri 2010; Newman et al. 2013; Jullo et al. 2014; Monna et al. 2014; Johnson et al. 2014, for some recent examples) assume a parametric form of the underlying mass density distribution for the lens and typically make the assumption that light traces mass in the positioning of these parametric forms. On the other hand, free-form1 methods (see e.g. Broadhurst, Taylor & Peacock 1995; Bartelmann et al. 1996; Abdelsalam, Saha & Williams 1998; Bridle et al. 1998; Seitz, Schneider & Bartelmann 1998; Bradač et al. 2005a; Cacciato et al. 2006; Liesenborgs, De Rijcke & Dejonghe 2006; Diego et al. 2007; Jee et al. 2007; Coe et al. 2008; Bradač et al. 2009; Merten et al. 2009; Williams & Saha 2011; Merten et al. 2011, 2015; Diego et al. 2015, for some recent examples) usually do not make this assumption and purely rely on the input data either based on weak lensing, strong lensing or a combination of the two. This is possible while using a reconstruction mesh and directly inverting the underlying equations describing lensing on this mesh. In the following, we introduce a free-form method combining weak and strong lensing, which uses our new mesh-free numerical framework. This method translates original ideas by Bartelmann et al. (1996), Seitz et al. (1998), Bradač et al. (2005a), Cacciato et al. (2006) and Merten et al. (2009) into the flexible and efficient mesh-free numerical domain. Alternative implementations of such ideas can e.g. be found in Bradač et al. (2009).


Magnetic reconnection (MR) may occur in various space and astrophysical plasma environments, among which the planetary magnetopause boundaries separating the solar wind and magnetospheric origins of plasmas and magnetic field are some of the most likely sites for the occurrence of MR. Due to the easy access to the in situ spacecraft observations the Earth’s magnetopause is the most widely studied space plasma environment for MR (Paschmann et al. 1979; Vaivads et al. 2004; Graham et al. 2014). In particular, the Magnetospheric Multiscale (MMS) mission has contributed greatly to the kinetic physics of magnetopause reconnection (Burch et al. 2016; Hasegawa et al. 2017; Zhong et al. 2020). Many studies have shown that an initial Harris type equilibrium profile with constant total pressures

 and antiparallel magnetic field with or without a guide field (Harris 1962) may tend to develop MR geometry. In particular, two major categories of MR have been proposed: the steady state model with a single X line and the outflow approaching the Alfvén speed (Petschek 1964), and the tearing mode instability with a series of X and O lines and mild plasma velocity (Furth et al. 1963). Numerous fluid and kinetic simulations have been carried out to examine the various aspects of MR processes for the past 50 yr (Hau & Chiou 2001; Guo et al. 2015; Landi et al. 2015). In particular, the effects of pressure or temperature anisotropy on MR have been examined by a number of authors (Chen & Palmadesso 1984; Shi et al. 1987; Birn & Hesse 2001; Chiou & Hau 2002, 2003; Hung et al. 2011). In the MHD models the double-polytropic (DP) laws are widely adopted as the energy closures to study the effects of temperature anisotropy and energy closures on MR and tearing mode instability (Chiou & Hau 2002, 2003; Hung et al. 2011). It is shown that the mirror type temperature anisotropy of

 may greatly enhance the growth rate of tearing mode instability and the merging rate of single X-line reconnection. In particular, the coupling of tearing and mirror instabilities may lead to relatively larger magnetic islands as compared to the cases with isotropic pressure and the mirror waves with anticorrelated density and magnetic field may be present in the vicinity of X lines.


The kinetic energy stored in the CO shell can be estimated as $E_{\rm kin} = 0.5\, M_{\rm shell}\, V^2_{\rm exp}$, where Vexp is the expansion velocity of the shell and Mshell is the total (molecular, atomic, and ionized) shell mass. Adopting an expansion velocity equal to half the velocity interval where the structure is observed, Vexp = 7.0 ± 1.3 km s− 1 , the molecular mass given in Table 1 and the atomic and ionized masses estimated by Cichowolski et al. (2001), 1450 and 3000 M⊙, respectively, we obtain Ekin = (2.5 ± 1.0) × 1049 erg, assuming a 40 per cent error for the masses.. Although Cichowolski et al. (2001) concluded that WR 130 could have alone created the observed structure, it is important to note that they did not take into account the molecular mass present in the shell, which considerably increases the kinetic shell energy. Thus, we can compare now the new value obtained for Ekin with the mechanical energy deposited in the ISM by the wind of the WR star, Ew = (0.7–2.2) × 1050 erg (Cichowolski et al. 2001). We obtain ϵ = Ekin/Ew = 0.007–0.5. The ratio ϵ measures the energy conversion efficiency in the shell, and according to evolutionary models ϵ ≤ 0.2 (Koo & McKee 1992). Thus, not all the possible values of ϵ are compatible with the scenario where the energy injected during the WR phase is enough to create the structure. In this case, the contribution of the energy injected during the O-star phase and/or other massive stars, should be considered. As mentioned in the Introduction, WR 130 is a WNH star, and according to Smith & Conti (2008) its age would be of about 2–3 Myr and its initial mass of at least 60 M⊙. A rough estimation of the energy injected by such a star during its main sequence yields Ew = (2.5–3.5) × 1050 erg (de Jager, Nieuwenhuijzen & van der Hucht 1988), which would be enough to create the observed structure. We have nevertheless looked for the presence of other massive stars in the region. We queried the available catalogues such as the Galactic O-Star Catalog (Maíz Apellániz et al. 2013), the Early-Type Emission-Line Stars Catalogue (Wackerling 1970), the Catalogue of Be stars (Jaschek & Egret 1982), the H-alpha Stars in the Northern Milky Way Catalogue (Kohoutek & Wehmeyer 1997), and the Catalog of Galactic OB Stars (Reed 2003), for early-type and emission stars. No stars were found in any catalogue. The only massive star located nearby is, as mentioned by Cichowolski et al. (2001), an OB star, which has an uncertain spectral type and no distance estimate (Stock, Nassau & Stephenson 1960). It is located in projection not in the centre of the structure but on to the shell (there is a second OB star mentioned by Cichowolski et al. 2001 but its location is actually outside the structure, see fig. 1 of Cichowolski et al. 2001). Although we cannot completely rule out the possibility that the OB star may be playing a role in creating the shell structure, we think that the action of WR 130 is sufficient and most likely dominant in the region.


Energy flows induced into magnetically dominated relativistic magnetospheres of compact objects are commonly modelled by numerical simulations in the force-free electrodynamics (FFE) limit. Fueled by the track record of observations in the era of multimessenger astrophysics, current targets for such simulations include the magnetospheres of rapidly spinning black holes, spiraling neutron stars, magnetars, and pulsars. The tenuous, magnetically dominated atmosphere (magnetosphere) of pulsars is an active field of scientific interest. They fascinate both observers (e.g. Lorimer et al. 1995; Ransom et al. 2005; Abdo et al. 2013; Jankowski et al. 2018) and theorists (e.g. Kennel & Coroniti 1984; Lyubarskii 1996; Contopoulos, Kazanas & Fendt 1999; Goodwin et al. 2004; Timokhin 2006; Timokhin & Arons 2013; Contopoulos 2019; Pétri 2020). With the remarkable progress in scientific computing, their rotating magnetosphere has captured designers of numerical methods that integrate FFE and magnetohydrodynamics (MHD) with ever-improving accuracy (e.g. Komissarov 2006; Spitkovsky 2006; Tchekhovskoy, Spitkovsky & Li 2013; Parfrey, Spitkovsky & Beloborodov 2017; Carrasco & Shibata 2020). Recently, particle-in-cell (PIC) simulations were able to resolve a broad range of scale separations and allow for unprecedented insight into the microphysics of pulsar magnetospheres across the global scale (Cerutti et al. 2015; Philippov, Spitkovsky & Cerutti 2015a; Kalapotharakos et al. 2018; Philippov & Spitkovsky 2018; Guépin, Cerutti & Kotera 2020). In this fascinating flurry of outcomes, only few references scrutinized whether the results from ideal plasma simulations are the best possible model for the pulsar magnetosphere that contains an inherently non-ideal region, namely the equatorial current sheet (ECS) beyond the closed zone (Contopoulos 2016; Contopoulos 2019; Contopoulos, Pétri & Stefanou 2020). Here, we study with rigorous technical depth how this non-ideal region can affect the global dynamics of the force-free aligned rotator magnetosphere – effectively serving as a blueprint for force-free magnetospheres of other compact objects.


Work in recent years has shown that rotation is a key ingredient in shaping the evolution of massive stars with very low metallicities (Z  SMC metallicity down to Population III stars; see Meynet & Maeder 2017, and references therein). Fast rotators (with initial vrot ≳300 km s−1) are expected to lead to chemically homogeneous evolution (CHE) in which the star becomes brighter and hotter, and thus more ionizing photons, specially in the extreme UV, are emitted than in the corresponding non-rotating case (e.g. Brott et al. 2011; Levesque et al. 2012; Yoon, Dierks & Langer 2012). Presently, although we still know little about rotation velocities of massive stars and their variation with environment, observations seem to favor fast rotators at low Z (e.g. Martayan et al. 2007; Hunter et al. 2008). Model predictions suggest that the effects of rotation, like CHE, should be enhanced at lower metallicities. There is an increase of theoretical and observational evidence which supports the significant role of rotation among the generations of first stars, with Z=0 or extremely low metallicities, and fast rotating massive stars were likely common phenomena in the early Universe (e.g. Leitherer 2008; Chiappini et al. 2008; Maeder & Meynet 2012; Yoon et al. 2012). Modern models for low-metallicity massive fast-rotating single stars which undergo CHE have been published by Szécsi et al. (2015); the authors called them transparent wind UV intense stars (or TWUIN stars). Considering all this and the extremely low-Z of SBS 0335 − 052E, we compare our observations with the TWUINs predictions,6 following the same approach that we used previously for non-rotating WCE and massive O stellar models. Taking the computed Q(He ii)=7.37 × 1048 photon s−1 for the most massive 294 M⊙ TWUIN, we require that ∼430 (∼300) such stars are necessary to explain the Q(He ii)Int (Q(He ii)$_{\rm He\, \small {II}-MB}$). Again, hundreds of these super-massive TWUINs do not match the M⋆, SSCs of SBS 0335 − 052E. If we instead, apply the same approach using lower mass TWUIN models, it makes even harder to account for the observations. Besides the Q(He ii) budget, we have measured values of He ii λ4686/Hβ as high as 0.06 within the He ii λ4686 main body region. Under ionization-bounded conditions, even the most massive TWUIN models cannot reproduce these values of He ii λ4686/Hβ (see table B.1 from Szécsi et al. 2015).


A pulsar rotates at an angular velocity Ω with inertial moment I and magnetic moment $\boldsymbol {\mathcal {M}}$. It is described by the canonical rotation-down equation in the magnetic dipole model:
(4)
\begin{eqnarray*}
\dot{\Omega } = - K \Omega ^3,
\end{eqnarray*}
where $K = \frac{\mu _0 | \boldsymbol{\mathcal {M}} |^2 \sin ^2 \theta }{6 \pi c^3 I}$, μ0 is vacuum permeability, and c is speed of light. θ is inclination angle, namely, the angle between $\boldsymbol {\mathcal {M}}$ and $\boldsymbol {\Omega }$. The possible change of macroscopic magnetic moment of pulsars at the moment of a glitch occurring was discussed by Link and Epstein (Link et al. 1992; Link & Epstein 1997). Namely, K and Ω changed while the rotation-down equation remains the same at glitches,
(5)
\begin{eqnarray*}
\frac{\Delta \dot{\Omega }}{\dot{\Omega }} \approx \frac{\Delta K}{K} = 2 \frac{\Delta (| \boldsymbol{\mathcal {M}} | \sin \theta)}{| \boldsymbol{\mathcal {M}} | \sin \theta } - \frac{\Delta I}{I} .
\end{eqnarray*}
From observations, we know $\frac{\Delta \dot{\Omega }}{\dot{\Omega }} \sim 10^{-3}$. Merely variation of orbit angular momentum cannot describe the magnetic moment changing, as $- \frac{\Delta I}{I} = \frac{\Delta \Omega }{\Omega } \lesssim 10^{-6} \ll \frac{\Delta \dot{\Omega }}{\dot{\Omega }}$. It motivates us to consider the origin of the equation (5) related with conservation of total angular momentum. As Einstein-de Haas effect suggests that $\boldsymbol {S}$ and $\boldsymbol {\Omega }$ can transfer into each other caused by the total angular momentum conservation,
(6)
\begin{eqnarray*}
\Delta \boldsymbol {J} = \Delta (\boldsymbol {S} + I \boldsymbol {\Omega }) = \boldsymbol {T} \Delta t \approx 0,
\end{eqnarray*}
where $\boldsymbol {S}=(1/\gamma)\boldsymbol {\mathcal {M}}$, Δt is the duration of a glitch, and $\boldsymbol {T}$ is the torque. The total angular momentum conservation would turn to be reasonable, when glitches regarding as instantaneous processes, namely Δt → 0, as the traditional glitch model (Baym et al. 1969) does. In principal, $\boldsymbol {T} \Delta t \ne 0$ is permitted in our model. For the first step, we wish to obtain approximated results with the simplest case of equation (6).


We begin with our results from global DNS MHD simulations of the MRI in cylindrical (r, ϕ, z) geometry using the DEBS (Schnack et al. 1987; Ebrahimi et al. 2009) initial-value code to solve the non-linear, viscous and resistive MHD equations

(1)

\begin{eqnarray}
\frac{\mathrm{\partial} \boldsymbol A }{ \mathrm{\partial} t } &=& -{\boldsymbol E} = S\boldsymbol V\times \boldsymbol B - \eta \boldsymbol J
\end{eqnarray}

(2)

\begin{eqnarray}
\rho \frac{\mathrm{\partial} \boldsymbol V }{ \mathrm{\partial} t } &=& -S \rho \boldsymbol V\cdot \ \nabla \boldsymbol V + S\boldsymbol J \times \boldsymbol B +P_{\rm m} \nabla ^2 \boldsymbol V -S \frac{\beta _0}{2}\nabla P
\end{eqnarray}

(3)

\begin{eqnarray}
\frac{\mathrm{\partial} P }{ \mathrm{\partial} t } &=& -S\nabla \cdot (P \boldsymbol V) - S (\Gamma -1) P \nabla \cdot \boldsymbol V
\end{eqnarray}

(4)

\begin{eqnarray}
\frac{\mathrm{\partial} \rho }{ \mathrm{\partial} t } &=& -S\nabla \cdot (\rho \boldsymbol V)
\end{eqnarray}

(5)

\begin{eqnarray}
\boldsymbol B &=& \nabla \times \boldsymbol A
\end{eqnarray}

(6)

\begin{eqnarray}
\boldsymbol J &=& \nabla \times \boldsymbol B,
\end{eqnarray}

where the variables, ρ, P, V, B, J, and Γ are the density, pressure, velocity, magnetic field, current, and ratio of the specific heats, respectively. We use the same normalization (Schnack et al. 1987; Ebrahimi et al. 2009; Ebrahimi & Bhattacharjee 2014), where time, radius and velocity are normalized to the outer radius a, the resistive diffusion time τR = a2/μ0η, and the Alfvén velocity $V_{\rm A} = B_0/\sqrt{\mu _0 \rho _0}$, respectively. The dimensionless parameters, S = τRVA/a and Pm, are the Lundquist number and the magnetic Prandtl number (the ratio of viscosity to resistivity), respectively. the initial state satisfies the equilibrium force balance condition $\frac{\beta _0}{2}\nabla p = \rho V_{\phi }^2/r$, where $\beta _0 \equiv 2 \mu _0 P_0/B_0^2$ is normalized to the axis value, and the initial pressure and density profiles are assumed to be radially uniform and unstratified. Pressure and density are evolved, however, they remain fairly uniform during the computations. A no-slip boundary condition is used for the poloidal flow and flow fluctuations. The inner and outer radial boundaries are perfectly conducting so that the tangential electric field, the normal component of the magnetic field, and the normal component of the velocity vanish. The tangential component of the velocity is the rotational velocity of the wall. The azimuthal (ϕ) and axial (z) boundaries are periodic. We assume a radial pressure gradient balances the centrifugal force in equilibrium, but radial gravity and a radial pressure force are interchangeable for our incompressible, unstratified circumstance. The pressure gradient, rather than gravity, is what balances the centrifugal force in cylindrical laboratory experiments designed to test the MRI (Goodman & Ji (2002)).


While these early studies demonstrated the viability of neutron star mergers as a major r-process site, they identified only one ejection channel: ‘dynamical ejecta’ that are tidally flung out by gravitational torques. Since they are never substantially heated, these ejecta carry their original β −equilibrium electron fraction from the original neutron star, Ye ≈ 0.05, and this enormous neutron-richness allows them to undergo a ‘fission cycling’ process (Goriely, Bauswein & Janka 2011; Korobkin et al. 2012), which produces a very robust r-process abundance distribution close to the solar pattern for A ≥ 130, but hardly any lighter r-process elements. Oechslin, Janka & Marek (2007) pointed out that there is a second channel of mass ejection that also happens on a dynamical time-scale: shock-heated matter from the interface where the stars come into contact. As of today, many more mass ejection channels have been discussed: matter that becomes unbound on secular time-scales (∼1 s) from the post-merger accretion torus (Beloborodov 2008; Metzger, Piro & Quataert 2008; Fernandez & Metzger 2013; Fernandez et al. 2015; Just et al. 2015; Siegel & Metzger 2017, 2018; Fernandez et al. 2019; Miller et al. 2019a), as MHD-driven winds (Siegel & Ciolfi 2015) and by viscous effects (Shibata, Kiuchi & Sekiguchi 2017; Radice et al. 2018a; Shibata & Hotokezaka 2019) from a long-lived neutron star merger remnant. Similar to the case of proto-neutron stars, the enormous neutrino luminosities (>1053 erg s−1) after a neutron star merger can also drive substantial matter outflows (Ruffert et al. 1997; Rosswog & Ramirez-Ruiz 2002; Dessart et al. 2009; Perego et al. 2014; Martin et al. 2015; Radice et al. 2018b). The secular torus ejecta contain approximately 40 per cent of the initial torus mass and, although the latter may vary substantially from case to case, they likely contribute the lion’s share to the total ejecta mass. Due to their different thermal histories and exposure times to neutrinos, the ejecta channels can have different electron fractions Ye and therefore different nucleosynthesis yields.1 For electron fractions below a critical value, $Y_{\rm e}^{\rm crit}\approx 0.25$ (Korobkin et al. 2012; Lippuner & Roberts 2015), lanthanides and actinides are efficiently produced, which, due to their open f-shells, have particularly high bound–bound opacities (Barnes & Kasen 2013; Kasen, Badnell & Barnes 2013; Tanaka & Hotokezaka 2013; Tanaka et al. 2020) and therefore lead to red transients that peak days after the merger. Ejecta with electron fractions above $Y_{\rm e}^{\rm crit}$, in contrast, only produce ‘lighter’ elements with lower opacities and thus result in bluer transients that peak after about 1 d. Opaque, low-Ye ejecta blocking the view on high-Ye ejecta can lead to a ‘lanthanide curtaining’ effect (Kasen, Fernández & Metzger 2015; Wollaeger et al. 2018), which will efficiently block blue light. Therefore, it is important to understand the layering, dynamics, interaction and potential mixing of different ejecta channels.


Figure 1 shows that in the regions where activity was detected visually, i.e., Hapi, Seth, and Ma’at pits have lower (8–13%/100 nm) spectral slopes than the rest of the comet surface (13–22%/100 nm). In addition to those places, Seth alcoves, the wall of the large Anuket alcove, around the circular features, both clustered and isolated bright features (see Thomas et al. 2015b; Auger et al. 2015; Pommerol et al. 2015b, for definitions) show similar lower spectral slopes than the rest of the surface, even though there was no visual detection of activity features rising from them at the time of the observations used in this study4. This may be because the observing geometry was not suited for their detections during the observations. In the regions we investigated, the Hapi region displays the lowest spectral slopes 8–11%/100 nm (see also Fornasier et al. 2015) together with the isolated bright features (IBFs) and the clustered bright features in the Imhotep region. The locations of the bright features on the Imhotep image (image #4) are shown in Fig. B.4. According to the spectral slope values, the IBFs of Imhotep seem to be more similar to the Hapi region than the active pits of Seth and Ma’at regions. Active pits, alcoves, and the large alcove of Anuket have slope values of typically 10–13%/100 nm. The Ma’at region, which is located on the smaller lobe (head) of the comet, displays higher spectral slope values than the Seth region, which is located on the larger (body) lobe of the comet. In the investigated regions, the highest slope values are detected in the Imhotep region (see Fig. 1d). Here it should be mentioned that the comparison of spectral slopes is performed under the assumption of no spectral reddening between the phase angles of the images we investigated, although the spectral slopes show reddening by phase as presented in Fornasier et al. (2015). Unfortunately, the previous work does not cover all the phase angles of the images we investigated, but the spectral slope variation between 35–54° (Fig. 3 of  Fornasier et al. 2015) is small so that we can make this comparison. However, if we follow the linear trend of the phase reddening, for the image taken in 70.45° phase angle (image #4), the spectral slopes would vary from 15%/100 nm to 18%/100 nm in the observations we used.


Progress in this field will require large statistical samples of metal-poor stars in a variety of environments within the Local Group. Unfortunately, metal-poor stars are exceedingly rare and difficult to find, being overwhelmed by the more numerous metal-rich populations in the Galaxy. Examination of the Besançon model of the Galaxy (Robin et al. 2003), which is guided by a theoretical framework for the formation and evolution of the main stellar populations, suggests that a typical halo field has only one in ∼2000 stars with [Fe/H]  −3 between 14  V  18 (Youakim et al. 2017). Enormous effort has gone into the discovery and study of extremely, ultra, and hyper metal-poor stars with [Fe/H]  −3.0, −4.0, and −5.0, respectively. Most of the known metal-poor stars have been found in dedicated surveys, such as objective prism surveys (the HK survey and Hamburg-ESO survey, Beers, Preston & Shectman 1992; Christlieb et al. 2002, 2008; Beers & Christlieb 2005; Frebel et al. 2006; Schörck et al. 2009), wide-band photometric surveys (Schlaufman & Casey 2014), and blind spectroscopic surveys, such as the Sloan Digital Sky Survey (SDSS) SEGUE and BOSS surveys (Yanny et al. 2009; Eisenstein et al. 2011; Dawson et al. 2013), and from the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST; Cui et al. 2012). According to the SAGA data base (see Suda et al. 2017, and references therein), there are ∼500 stars with [Fe/H]  −3.0, though fewer than half have detailed chemical abundances. Recently, narrow-band photometric surveys have shown higher success rates for finding metal-poor stars, particularly SkyMapper (Keller et al. 2007; DaCosta et al. 2019) and the Pristine survey (Starkenburg et al. 2017b; Youakim et al. 2017; Aguado et al. 2019a). Pristine photometry with follow-up Keck II/DEIMOS spectroscopy has also been used to increase sample sizes and improve the chemodynamical studies of faint satellites (Draco II and Sgr II, Longeard et al. 2018, 2019). At the same time, Simon (2018) has shown that Gaia DR2 proper motion cleaning may also be a promising way to find new metal-poor members of ultra-faint dwarf galaxies.


Thermonuclear (type-I) X-ray bursts are intermittently observed from many neutron star low-mass X-ray binaries (LMXBs; Strohmayer & Bildsten (2006) and references therein). Such a burst originates from an unstable thermonuclear burning of the accreted matter accumulated on the neutron star surface (Joss 1977; Lamb & Lamb 1978; Strohmayer & Bildsten 2006). For most bursts, the observed X-ray intensity rises in ≈0.5–5 s, decays in ∼10–100 s as the neutron star surface cools down after the nuclear burning, and the typical recurrence time is a few hours to days (Galloway et al. 2008). The burst spectrum is traditionally described with a blackbody model, and the best-fit burst blackbody normalization, which can be identified as the burst emission area, usually matches well with the expected surface area of a neutron star (Hoffman et al. 1977; Swank et al. 1977). These motivated an effort to measure the neutron star radius using the burst continuum spectrum, where the normalization of the burst blackbody is expected to be proportional to the square of the stellar radius (e.g., van Paradijs 1978; Goldman 1979; van Paradijs 1979; van Paradijs & Lewin 1986). Note that such a radius measurement is extremely important to probe the superdense and degenerate core matter of neutron stars, which is a fundamental problem of physics (e.g., Lattimer & Prakash 2007; Bhattacharyya et al. 2017). However, a reliable radius measurement using this method has so far not been possible due to a number of systematic uncertainties, which include (1) burst emission from and the visibility of an unknown fraction of the neutron star surface and (2) plausible deviation of the burst spectrum from a blackbody, etc. (Bhattacharyya 2010; Bhattacharyya et al. 2010; Kajava et al. 2017a). Nevertheless, the use of continuum burst spectrum remains a promising method to measure the neutron star radius for the following reasons: (1) neutron star LMXBs provide many complementary methods to measure neutron star parameters, the joint application of which has a potential to significantly reduce the systematics (Bhattacharyya 2010) and (2) it was generally believed that the much more intense burst emission could be reliably distinguished from the persistent (i.e., non-burst) emission during the burst.


Finally, our observations are consistent with the bilobate shape of the nucleus of comet 8P/Tuttle. As noted in Sect. 1, this shape is likely common among comets because it was found for four out of the six comets for which we have spatially resolved images. This is also the case of the trans-Neptunian object 2014 MU69 (Ultima Thule) observed by the New Horizon spacecraft (Stern et al. 2019). This binary configuration has some implications for the formation and evolution of 8P/Tuttle. A contact binary could result from (i) the accretion at low velocity of two primordial objects (Massironi et al. 2015; Davidsson et al. 2016), (ii) the disruption of a monolithic object due to excessive spin-up resulting from non-gravitational forces or YORP5 effect followed by a reaccretion (Boehnhardt 2004; Ćuk 2007; Hirabayashi et al. 2016), or (iii) the catastrophic disruption of a monolithic object by a collision followed by a re-accretion (Jutzi & Benz 2017; Schwartz et al. 2018). On the one hand, with a low thermal inertia compared with NEAs, the YORP effect is low for comets, in particular for NIC, which have an elongated orbit and spend most of their time far from the Sun, and it may not be sufficient to increase the spin rate of the nucleus to the point where centrifugal exceed gravitational forces. On the other hand, comet 8P/Tuttle has been on a very stable orbit for centuries, and it is likely an evolved comet, as suggested by its low activity, so that it could have been much more active in the past. For cometary nuclei, the primary cause for spin-up is torques caused by outgassing, therefore it is possible that 8P/Tuttle formed as a monolithic body and became a contact binary after its injection into the inner Solar System as a result of excessive spin-up resulting from non-gravitational forces. This scenario has been proposed for comet 67P/Churyumov-Gerasimenko by Hirabayashi et al. (2016). Alternatively, if the binary nature of comet 8P/Tuttle is the result of a primordial accretion or a catastrophic collision in the early Solar Sytem, it could have persisted until now. Similar examples are offered by some binary asteroids that can be stable over the age of the Solar System (Chauvineau et al. 1991), or as proposed by Davidsson et al. (2016) for comet 67P/Churyumov-Gerasimenko. For comet 8P/Tuttle, it is however not possible to distinguish the solution of a binary nucleus that formed in the first billion years of our Solar System (e.g., Matonti et al. 2019) from a more recent origin following its injection into the inner Solar System (e.g., Hirabayashi et al. 2016).


Although the magnetic (i.e., one-photon) pair production is also taken into account, most electron–positron pairs are found to be produced via photon–photon (i.e., two-photon) collisions, which take place via two paths. One path is through the collisions of two MeV photons, both of which were emitted from the equatorial ADAF. Another path is through the collisions of TeV and eV photons; the former photons were emitted by the gap-accelerated leptons via inverse Compton process, while the latter were emitted from the ADAF via the synchrotron process. There is, indeed, a third path, in which the gap-emitted GeV curvature photons collide with the ADAF-emitted keV inverse Compton photons; however, this path is negligible, particularly when

. If the pairs are produced via TeV–eV collisions (i.e., via the second path) outside the gap outer boundary, they have outward ultrarelativistic momenta to easily “climb up the hill” of the potential k0 (Takahashi et al. 1990; see also Figure 2 of HP16) and propagate to large distances without turning back. However, if the pairs are produced via MeV–MeV collisions (i.e., via the first path), they are produced with subrelativistic outward momenta; thus, they eventually return to fall onto the horizon owing to the strong gravitational pull inside the separation surface (Figure 2 of HP16). When the returned pairs arrive at the gap outer boundary, only positrons can penetrate into the gap because of E∥  0. Accordingly, electrons accumulate at the boundary, whose surface charge leads to the jump of the normal derivative of E∥. Thus, although the stationary gap solutions show that the γ-ray spectrum little depends on the injected current density (Section 5.5), the gap solution inevitably becomes time dependent owing to the increasing discontinuity of

 with an accumulated surface charge (in this case, electrons) at the outer boundary. If the injected current is much small compared to the GJ current, the time dependence will be mild. However, if the injected current becomes a good fraction of the GJ current, the assumption of the stationarity becomes invalid, as pointed out by Levinson & Segev (2017). In this sense, a caution should be made in the applicability of the stationary solutions presented in this paper, when the injected current is non-negligible compared to the current created within the gap.


Using the RADEX3 non local thermodynamic equilibrium (LTE) modeling program (van der Tak et al. 2007) with collisional rate coefficients from Wiesenfeld & Faure (2013), we modeled the relation between the gas kinetic temperature and the measured average of para-H2CO 0.5 × [(322–221 + 321–220)/303–202] ratios, adopting a 2.73 K background temperature, an average observational linewidth of 4.0 km s−1, and column densities N(para-H2CO) = 2.7 × 1012 and 3.7 × 1012 cm−2 for N113 and N159W, respectively. The results are shown in Fig. 5. The values of the para-H2CO column density were obtained with APEX data (beam size ~30″; Tang et al. 2017b), which cover similar regions. Different column densities of para-H2CO only weakly affect derived kinetic temperatures (see Fig. 3 in Tang et al. 2017b or Fig. 4 in Tang et al. 2018a; this was also shown in Fig. 13 and discussed in Sect. 4.3.1 of Mangum & Wootten 1993) as long as all lines are optically thin. Considering that the relation between the gas temperature and the para-H2CO line ratio may vary at different spatial densities (see Fig. 2 in Tang et al. 2017b), we modeled it at spatial densities 104, 105, and 106 cm−3 in Fig. 5. It appears that Tkin at n(H2) = 105 cm−3 is consistently lower than values at 104 and 106 cm−3 by ≲23% and ≲34%, respectively, for Tkin ≲ 100 K. Local thermodynamic equilibrium (LTE) is a good approximation for the H2CO level populations under optically thin and high-density conditions (Mangum & Wootten 1993; Tang et al. 2017a,b, 2018b). Following the method applied by Tang et al. (2017b) in their Eq. (2), we plot the relation between the LTE kinetic temperature, TLTE, and the para-H2CO (3–2) line ratio in Fig. 5. Apparently, TLTE agrees well with Tnon-LTE at volume densities n(H2) ~ 105 cm−3 as long as Tkin ≲ 100 K. Previous observations show that para-H2CO (3–2) is sensitive to gas temperature at density 105 cm−3 (Ginsburg et al. 2016; Immer et al. 2016; Tang et al. 2017b). The spatial density measured with para-H2CO (303–202) and C18O (2–1) in N113 and N159W is n(H2) ~ 105 cm−3 on a size of ~30″ (Tang et al. 2017b). Therefore, here we adopt 105 cm−3 as an averaged spatial gas density in the N113 and N159W regions.


In regarding AGNs, the Te method tends to underestimate the oxygen abundance by an average value of about 0.6 dex in comparison to estimations based on strong-line methods and it produces subsolar O/H values for most of these objects (Dors et al. 2015; Dors, Freitas-Lemes & Âmores 2020). An alternative method to derive the metallicity or abundances in the nuclear regions of spiral galaxies is the extrapolation of the radial oxygen abundance. Along decades, results based on this indirect method have indicated Z near or slightly above the solar value in nuclear regions (Vila-Costas & Edmunds 1992; Zaritsky, Kennicutt & Huchra 1994; van Zee et al. 1998; Pilyugin, Vílchez & Contini 2004; Gusev et al. 2012; Dors et al. 2015; Zinchenko et al. 2019), in consonance with predictions of chemical evolution models (e.g. Mólla & Díaz 2005) and with the use of strong-line methods (e.g. Groves, Dopita & Sutherland 2004; Groves, Heckman & Kauffmann 2006; Feltre, Charlot & Gutkin 2016; Pérez-Montero et al. 2019; Thomas, Kewley & Dopita 2019; Dors et al. 2020). Therefore, Temethod does not seem to work for AGNs. The origin of the discrepancy between Z values calculated via Te method and via strong-line methods, the so-called Teproblem, could be attributed, in part, to the presence of heating/ionization by gas shock in the narrow-line region (NLR) of AGNs. In fact, Contini (2017) carried out detailed modelling of AGN optical emission lines by using the SUMA code (Contini & Aldrovandi 1983) and suggested the presence of gas shock with low velocity ($v \: \lesssim \: 400 \: \rm km \:s^{-1}$) in a sample of Seyfert 2 nuclei. This result is supported by recent spatially resolved observational studies of Seyfert 2 nuclei, in which the presence of gas outflows with velocity of the order of 100–300 $\rm km \: s^{-1}$ have been found (e.g. Riffel, Storchi-Bergmann & Riffel 2017; Riffel, Hekatelyne & Freitas 2018). Moreover, the Te problem can also be originated due to the use of an unappropriate calculation of the ionization correction factor (ICF) for oxygen in AGNs (Pérez-Montero et al. 2019; Dors et al. 2020).


The results presented in this paper are based on data from IllustrisTNG,1the next-generation suite of state-of-the-art magnetohydrodynamical cosmological simulations of galaxy formation (Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018; Pillepich et al. 2018b; Springel et al. 2018). Building on the success of its predecessor Illustris (Genel et al. 2014; Vogelsberger et al. 2014a,b; Nelson et al. 2015; Sijacki et al. 2015), IllustrisTNG follows the same fundamental approach but includes improved aspects and novel features in its galaxy formation model and expands its scope to several simulated volumes and improved resolution. The models for galaxy formation include physical processes such as gas heating by a spatially uniform and time-dependent UV background, primordial and metal-line gas cooling, a subgrid model for star formation, and the unresolved structure of the interstellar medium (Springel & Hernquist 2003), as well as models for the evolution and chemical enrichment of stellar populations, which track nine elements (H, He, C, N, O, Ne, Mg, Si, and Fe) in addition to europium and include yields from supernovae Ia, II, and AGB stars (Vogelsberger et al. 2013; Torrey et al. 2014). Furthermore, IllustrisTNG incorporates improved feedback implementations for galactic winds caused by supernovae as well as accretion and feedback from black holes. In particular, depending on accretion, black hole feedback occurs in two modes: low accretion rates result in purely kinetic feedback while high accretion rates invoke thermal feedback (Weinberger et al. 2017). Galactic winds are injected isotropically and the wind particles’ initial speed scales with the one-dimensional dark matter velocity dispersion (Pillepich et al. 2018a). Magnetic fields are amplified self-consistently from a primordial seed field and follow ideal magnetohydrodynamics (Pakmor & Springel 2013). The TNG simulations were run using the moving mesh code arepo (Springel 2010). Here, concepts from adaptive mesh refinement and smooth particle hydrodynamics are combined to create an unstructured, moving Voronoi tessellation. IllustrisTNG follows the ΛCDM framework, adopting cosmological parameters according to recent constraints from Planck data: matter density $\Omega _\rm {m} = 0.3089$, baryonic density $\Omega _\rm {b} = 0.0486$, cosmological constant $\Omega _\Lambda = 0.6911$, Hubble constant h = 0.6774, normalization σ8 = 0.8159, and spectral index $n_\rm {s} = 0.9667$ (Planck Collaboration I 2016).