As previously mentioned, the small amplitude of the RV modulation in the NIR as measured by GIANO contemporaneously with REM photometry is intriguing. Assuming that the depth of the spectral lines relative to their adjacent continuum is constant and considering a spot with a contrast Cs at latitude ϕ with a filling factor fs, we expect an RV modulation approximately of Csfsvsinicosϕ (cf. Saar et al. 1997; Desort et al. 2007) that is ≈ 0.75−1.0 km s−1 for a spot at ϕ = 60°, which is remarkably higher than what has been observed. A cool spot at a higher latitude would reduce the amplitude of the NIR wide-band flux modulations; a quenching of the convective shifts or the Zeeman effect also do not appear to be viable explanations because they increase the effect of a cool spot on the RV at NIR wavelengths (Reiners et al. 2013). Nevertheless, the variation of the relative depths of the spectral lines in the NIR cannot be neglected and it is the dominant effect in the cool spot responsible for the large photometric modulation in the infrared. The relative line depths are strong functions of the continuum opacity and of the degree of element ionization both remarkably varying in a cool spot area with respect to the unperturbed photosphere. In general, these effects produce a remarkable increase of the relative depths of the spectral lines in the cool spot. This compensates for the decrease of the continuum intensity in the spot, reducing the distortions of the spectral line profiles and yielding an RV variation in the NIR smaller than expected from the wide-band photometric variation in the case of constant relative line depths. In any case, a quantitative analysis is not warranted by our data, since a larger number of observations would be required. This scenario suggests a need to better investigate this kind of target, since they might go through specific activity phases during which the VIS and NIR RV amplitudes are similar, possibly resulting in false positives. Looking at the curve phase shifts might give crucial information in these cases (see e.g. the recent result by Hatzes et al. 2018 for the K-giant γ Draconis).


Due to their high core temperatures at birth, neutron stars cool pre-dominantly by neutrino emission at ages ≲ 106 yr (Potekhin, Pons & Page 2015). The most rapid changes of surface temperature occur early, first when the temperature of the outer layers achieves equilibrium with the rapidly cooling core at an age of ≲ 100 yr (Lattimer et al. 1994; Gnedin, Yakovlev & Potekhin 2001; see also Nomoto & Tsuruta 1987) and then when the temperature drops below the critical temperature for core neutrons to become superfluid, which activates the efficient neutrino emission process of Cooper pair formation and breaking (Gusakov et al. 2004; Page et al. 2004). The rapid cooling of the CCO in Cassiopeia A (at a ten-year rate of ≈2.2 ± 0.2 or 2.8 ± 0.3 per cent, depending on whether NH varies between observations) indicates the latter starts to take place at an age of ∼200 yr (Page et al. 2011; Shternin et al. 2011). Neutron star cooling models predict that by an age of several hundred years, the cooling rate will be 1 per cent per decade. From the 1σ temperature uncertainties of our fit results with model parameters linked between observations (see Tables 4 and 7), we estimate upper limits on the ten-year cooling rates of 6 per cent for XMMU J172054.5−372652 and 17 per cent for CXOU J160103.1−513353. We measure a possible increase in temperature of ∼4 ± 2 per cent (accompanied by a decrease in emission area; see Table 5 and 6) for 1WGA J1713.4−3949. We also perform fits of the spectra of XMMU J172054.5−372652 and CXOU J160103.1−513353 which allow the temperature to be different between each observation, and the results are shown in Table 9 and Fig. 8 (analogous results for 1WGA J1713.4−3949 are shown in Fig. 3). We point out that we are concerned in Fig. 8 with relative changes in temperature and not in absolute temperature differences between CCOs since absolute temperatures depend on a variety of factors that are intrinsic to each CCO and may be different among CCOs in our sample, e.g. mass (and hence neutrino cooling rate) and radius (and hence gravitational redshift) and envelope composition and thickness. Nevertheless it is noteworthy that the temperatures of all three older CCOs appear to be higher than those of Cassiopeia A. Unlike for the 340 yr old CCO in Cassiopeia A, we do not see that temperatures of the 600 yr old XMMU J172054.5−372652 and 1000 yr old CXOU J160103.1−513353 are changing, at least within measurement uncertainties.


Several molecules show a large discrepancy between the abundances derived from observations and calculated by chemical equilibrium, although it is not as severe as for the molecules discussed above. We refer to PN in O-rich stars and H2S in C-rich stars, which are indicated by hatched rectangles in Fig. 2. For PN in O-rich AGB atmospheres, the disagreement between the observed abundances, (1–2) × 10−8 (Ziurys et al. 2018), and the calculated maximum chemical equilibrium abundance is almost three orders of magnitude. However, uncertainties on the observational and theoretical sides mean that the true level of disagreement is unclear. For example, while Ziurys et al. (2018) derived a PN abundance of 10−8 relative to H2 in IK Tau, De Beck et al. (2013) and Velilla Prieto et al. (2017) derived higher abundances, (3–7) × 10−7, in this source. When we give preference to these latter abundances, the level of disagreement would be even higher. On the other hand, the formation enthalpy of PN is rather uncertain (see Lodders 1999), which directly translates into the calculated chemical equilibrium abundance. In this study we adopted the thermochemical data for PN from Lodders (1999), who gives preference to a formation enthalpy at 298.15 K of 171.5 kJ mol−1, while other compilations such as JANAF use lower values that would result in higher chemical equilibrium abundances for PN. This would reduce the level of disagreement. In the case of H2S in C-rich AGB stars, the calculated maximum chemical equilibrium abundance is 7 × 10−11, while the value derived from observations is ~50 times higher. In this case, the observed abundance is based on the detection of only one line in only one source (see Agúndez et al. 2012), and thus it has to be viewed with some caution. In summary, the main failures of chemical equilibrium to account for the observed abundances of parent molecules in circumstellar envelopes are NH3, HCN, CS, SO2, and possibly PN in M-type stars, H2O and NH3 in S-type stars, and the hydrides H2O, NH3, SiH4, PH3, and perhaps H2S as well in C-type stars. The large discrepancies between the abundances derived from observations and those calculated with chemical equilibrium necessarily imply that nonequilibrium chemical processes must be at work in AGB atmospheres. Any invoked nonequilibrium scenario must account for all these anomalously overabundant molecules, but must also reproduce the remaining molecular abundances that are reasonably well explained by chemical equilibrium. No scenario currently provides a fully satisfactory agreement with observations, although two mechanisms that can drive the chemical composition out of equilibrium have been proposed.


The LLAGN interpretation of LINERs was initially motivated by their significant X-ray emission (Ferland & Netzer 1983; Halpern & Steiner 1983). Although LLAGNs are found via radio and X-ray observations in the majority of LINERs (Dudik et al. 2005, 2009; Nagar et al. 2005; Filho et al. 2006; Flohic et al. 2006; González-Martín et al. 2009), they are not powerful enough to photoionize the gas in their vicinity on ∼100 pc (i.e., a few arcseconds in nearby galaxies) scales on which the characteristic emission lines are detected (Flohic et al. 2006; Eracleous et al. 2010a, and references therein). Imaging studies of LINERs have found extended line-emitting regions and complex circumnuclear dust morphologies that might obscure and further prevent the LLAGNs from fully ionizing the surrounding gas (Barth et al. 1999; Pogge et al. 2000; Simões Lopes et al. 2007; González Delgado et al. 2008; González-Martín et al. 2009; Masegosa et al. 2011). Wolf-Rayet stars (i.e.,“warmers”; Terlevich & Melnick 1985) could successfully mimic the X-ray emission produced by a LLAGN, as well as provide the hard ionizing photons necessary to explain the relative intensities of the observed optical emission lines. If Wolf-Rayet stars were the primary source of ionizing photons for LINER-like emission lines, then most LINERs would be in the immediate post-starburst phase, which is unlikely given their high occurrence rate (Ho et al. 1997b) and stellar populations (Cid Fernandes et al. 2004; González Delgado et al. 2004). Compact starbursts containing hot O stars offer an alternative explanation for the relative intensities of LINER emission lines (Filippenko & Terlevich 1992; Shields 1992), but have difficulty explaining the broad Balmer emission wings often seen in LINER spectra (Filippenko 1996), since this would require long-lived supernova remnants. Moreover, the census of stellar populations in LINERs by González Delgado et al. (2004) and Cid Fernandes et al. (2004) does not show a high incidence of compact, nuclear starbursts. pAGB stars and planetary nebulae (Binette et al. 1994; Taniguchi et al. 2000; Yan & Blanton 2012; Belfiore et al. 2016) are more plausible stellar-based models, but are applicable only to a subset of LINERs due to their inability to explain large Hα equivalent widths (Ho et al. 2003). Shock models can adequately describe the off-nuclear optical and ultraviolet (UV) emission-line spectra of some LINERs, such as M87, obtained with the Hubble Space Telescope (HST; see Dopita et al. 1996, 1997; Sabra et al. 2003). Meanwhile the UV spectra of some LINER nuclei, such as NGC 4579, do not have emission line ratios that are well described by shock excitation, and yet show high ionization lines that would require a hard extreme UV source, such as the continuum from an active galactic nucleus (AGN), or fast shocks (Barth et al. 1996; Dopita et al. 2015). Successful shock models could have a wide range of shock velocities (Filippenko 1996), but the gas must be continuously shocked to maintain LINER-like ratios. The shocks could potentially be driven by radio jets, which are fairly common in LINERs and whose kinetic power is considerably higher than the electromagnetic luminosity of the LLAGNs (Filho et al. 2002; Nagar et al. 2005; Maoz 2007). Alternatively, the shocks could result from supernovae or winds from either young or evolved stars.


T Tauri stars in general are known to flare (e.g., Gahm 1990; Guenther & Ball 1999). A potentially better analog of the type of variable Hα emission expected from chromospheric emission and flaring on PTFO 8-8695 is the WTTS V410 Tau, with v sin i = 77.7 km s−1 (e.g., Carroll et al. 2012) compared to the measured v sin i = 80.6 ± 8.1 km s−1 for PTFO 8-8695 (van Eyken et al. 2012). The Hα emission equivalent width (3 Å with a typical value ∼1–2 Å ) on V410 Tau (e.g., Hatzes 1995; Fernández et al. 2004; Mekkaden et al. 2005) is weaker than seen on PTFO 8-8695, although V410 Tau has an earlier spectral type that raises the continuum level without necessarily affecting the strength of the chromospheric emission. V410 Tau has been observed to flare in a number of studies. Outside of flares, the Hα line of V410 Tau is fairly symmetric, relatively narrow, and is similar in shape to the chromospheric Hα profiles for PTFO 8-8695 seen in Figures 3, 5, and 6 (Hatzes 1995; Fernández et al. 2004; Skelly et al. 2010). The Hα line of V410 Tau can grow much stronger and broader during a flare, and also show asymmetries; however, the observed asymmetries seen during flares do not show excess emission with apparent peaks shifted out to greater than ±200 km s−1 (Hatzes 1995; Rice et al. 2011) as seen here in PTFO 8-8695. The typical pattern in a flare is for the line to very rapidly (timescale of a few minutes) strengthen and broaden with only a slight asymmetry developing. The strength and width of the line then decay exponentially with a timescale of ∼1 hr for strong flares (e.g., Fernández et al. 2004). This is not the temporal behavior observed in PTF08-8695. There is at least one additional piece of evidence against the flaring interpretation for the excess Hα emission seen in PTFO 8-8695. Whenever V410 Tau shows flare emission in Hα, significant He i 5876 Å emission also appears. This He i line is covered in the echelle formats of both our McDonald and Kitt Peak data. We have searched both data sets for evidence of this emission, including co-adding the spectra when the Hα emission appears stationary (UT 9:44 to 11:17 for McDonald; UT 6:45 to 8:25 for Kitt Peak) to increase the signal-to noise. No evidence of He i emission is seen. Lastly, if the observed excess Hα emission seen in Figures 2 and 7 were the result of a stellar flare, it would be a remarkable coincidence that the flare-induced asymmetry just happened to appear at and move with the same velocity position in the line profile as that expected for the planetary companion. In particular, the motion shown in Figures 2 and 4 where the excess emission first appears strongly on one side of the line profile and then moves to the other side has not to our knowledge been observed in the Hα emission of flare stars. Flares have been observed on PTFO 8-8695 (van Eyken et al. 2012; Ciardi et al. 2015), and while flares on this star likely will produce changes in the strength and shape of the Hα emission line, we believe all the points described above argue strongly against a purely stellar origin.


The Hα imaging for the galaxies discussed in this paper was generated from two different sources: NGC 3628 was observed on May 8, 1991 using the ESO New Technology Telescope (NTT, red arm of the ESO Multi-Mode Instrument (EMMI)) for 900 s in Hα and 300 s in R as part of ESO program 047.01-003. The detector was a Ford 20482 single CCD (ESO CCD #24). Both images were taken with subarcsecond seeing. The data and all relevant calibration files taken during the run and a few days before and after the observing run were retrieved from the ESO archive and re-reduced by us using IRAF in the usual manner. L.A. Cosmic (van Dokkum 2001) was used to clear the image of cosmic rays to produce the final Hα and final R image. The continuum subtracted image was then produced by aligning Hα and R band, homogenizing the PSF, and subtracting the appropriately scaled R image from the Hα image (e.g., Skillman et al. 1997). To determine the scaling factor, we measured the apparent fluxes for several stars in the field on both the Hα and R images. Scaling, subtraction, and correction to reach an optimal correction of the continuum light of the galaxy was performed with our own IRAF scripts. The NGC 4522 Hα data were taken directly from the work of Koopmann et al. (2001) and the Galaxy On Line Database Milano Network (GOLDMine, Gavazzi et al. 2003). The images were astrometrically calibrated to the Digitized Sky Survey (DSS) system. Flux calibration of the continuum subtracted Hα images was performed by transferring the total Sloan Digital Sky Survey (SDSS) r′ band flux of each galaxy to the its continuum image. With the derived scaling factor (see above), the flux scale can then be directly transferred to the continuum corrected Hα image. A conversion from magnitudes to flux was performed using the fact that SDSS is calibrated in AB magnitudes, so that the zero-point flux density of each filter is 3631 Jy (with 1 Jy = 1 Jansky = 10-26 W Hz-1 m-2 = 10-23 erg s-1 Hz-1 cm-2)1.


Galaxy clusters are the traces of the formation of the largest structures in the Universe and so reliable tools to investigate structures formation and evolution. In principle, this is possible only if and when we have full knowledge of the properties of these objects. The total mass (i.e. the total amount of the dark matter (DM), the intracluster medium (ICM), and the stellar components) is an invaluable quantity when exploring the abundances of clusters along the redshift: a standard way to infer cosmological parameters such as the mean matter density Ωm and the amplitude of matter perturbations σ8(Planck Collaboration XIII 2016). Furthermore, under the assumption of a simple self-similar model (Kaiser 1986; Voit 2005), we could derive the total mass of the clusters from a few observables in optical, X-ray, or millimetre band (Giodini et al. 2013). This approach results in a few scaling relations valuable when we are interested to obtain averaged results based on some statistics. However, it is prone to the assumed simplified approximations: hydrostatic equilibrium and isothermal and spherical distribution for DM and ICM (Bryan & Norman 1998). It is well known that the hydrostatic equilibrium in haloes is not always satisfied, due to non-thermal pressure contributions from internal motions and turbulence (see e.g. Fang, Humphrey & Buote 2009; Lau, Kravtsov & Nagai 2009; Laganá, de Souza & Keller 2010; Rasia et al. 2012; Nelson, Lau & Nagai 2014; Yu, Nelson & Nagai 2015; Biffi et al. 2016; Eckert et al. 2019; Angelinelli et al. 2020; Ansarifard et al. 2020; Gianfagna et al. 2020; Green et al. 2020), pointing out the impact that the dynamical state of those large gravitational bounded objects should have. Several attempts have been made to infer clusters dynamical state, using both observational data and simulations, by analysing the images of the emission in optical (see e.g. Ribeiro, Lopes & Rembold 2013; Wen & Han 2013) and in the X-ray band (see e.g. Rasia, Meneghetti & Ettori 2013; Lovisari et al. 2017; Nurgaliev et al. 2017; Bartalucci et al. 2019; Cao, Barnes & Vogelsberger 2020; Yuan & Han 2020) or of the diffusion of the cosmic microwave background (CMB) photons by thermal Sunyaev–Zel’dovich (tSZ) effect in the millimetre band (Cialone et al. 2018; De Luca et al. 2020, hereafter DL20), or a combination of some of them (see e.g. Mann & Ebeling 2012; Molnar, Ueda & Umetsu 2020; Ricci et al. 2020; The CHEX-MATE Collaboration 2020; Zenteno et al. 2020). Among the possibilities, we have to mention the studies of the clusters morphology in X-ray and tSZ maps. Several indicators are commonly used, such as asymmetry parameter (Schade et al. 1995), light concentration (Santos et al. 2008), third-order power ratio (Buote & Tsai 1995; Weißmann et al. 2013), centroid shift (Mohr, Fabricant & Geller 1993; O’Hara et al. 2006), strip parameter, Gaussian fit parameter (Cialone et al. 2018), and so on. They exploit the maps with different apertures and efficiencies and are applied individually or combined together, even with different weights (see e.g. Böhringer et al. 2010; Nurgaliev et al. 2013; Rasia et al. 2013; Weißmann et al. 2013; Mantz et al. 2015; Cui et al. 2016; Lovisari et al. 2017; Cialone et al. 2018; Cao et al. 2020; DL20; Yuan & Han 2020). A complementary approach is by applying thresholds on specific thermodynamic variables. Among the others, the central electron gas density and the core entropy are fairly reliable (Hudson et al. 2010). The azimuthal scatter in radial profiles of gas density, temperature, entropy, or surface brightness (Vazza et al. 2011) is also used as a proxy of the ICM inhomogeneities and correlated to the clusters dynamical state (see e.g. Roncarelli et al. 2013; Ansarifard et al. 2020). Alternatively, the projected sky separations between key positions in the images are resulting in reliable estimators of the dynamical state. Interestingly, the offsets between the bright central galaxy (BCG) and the peaks and/or the centroids of X-ray or tSZ maps are an indication of how much the relaxation condition is satisfied, with different efficiency (see e.g. Jones & Forman 1984; Katayama et al. 2003; Lin & Mohr 2004; Sanderson, Edge & Smith 2009; Mann & Ebeling 2012; Rossetti et al. 2016; Lopes et al. 2018; DL20; Ricci et al. 2020; Zenteno et al. 2020). To be mentioned also other approaches based on wavelets analysis (Pierre & Starck 1998), on the Minkowski functionals (Beisbart, Valdarnini & Buchert 2001), or on machine learning (see e.g. Cohn & Battaglia 2019; Green et al. 2019; Gupta & Reichardt 2020).


Understanding the influence of environment is contingent on being able to identify and quantify galaxy environments. Common environmental measures include the projected number density of galaxies out to the Nth nearest neighbour, the halo mass of a host group or cluster, or the projected separation from the centre of a group or cluster. Star formation and morphology of galaxies correlate well with these environment proxies, with galaxies in high densities regions (or alternatively, high halo mass or small group/cluster-centric radius) being preferentially red, passive, and early type (Dressler 1980; Goto et al. 2003; Poggianti et al. 2008; Kimm et al. 2009; Li, Yee & Ellingson 2009; Wetzel, Tinker & Conroy 2012; Wilman & Erwin 2012; Fasano et al. 2015; Haines et al. 2015). An alternative way to parametrize the environment of a host group or cluster is to classify the degree to which a system is dynamically relaxed. A relaxed, dynamically old group or cluster should be characterized by a central galaxy which is the brightest (most massive) member by a significant margin (e.g. Khosroshahi, Ponman & Jones 2007; Dariush et al. 2010; Smith et al. 2010) and is located near the minimum of the potential well (e.g. George et al. 2012; Zitrin et al. 2012, however also see Skibba et al. 2011), satellite galaxies which are distributed in velocity space according to a Gaussian profile (e.g. Yahil & Vidal 1977; Bird & Beers 1993; Hou et al. 2009; Martínez & Zandivarez 2012), and diffuse X-ray emission which is symmetric about the group/cluster centre (e.g. Rasia, Meneghetti & Ettori 2013; Weißmann et al. 2013; Parekh et al. 2015). The dynamical state of clusters is related to the age of the halo and the time since infall for member galaxies, which simulations have shown is an important quantity in determining the degree to which galaxy properties are affected by environment (e.g. Wetzel et al. 2013; Oman & Hudson 2016; Joshi, Wadsley & Parker 2017). Unrelaxed groups and clusters are systems which formed more recently or which have recently experienced a significant merger event, and in either case it would be expected that the time-since-infall on to the current halo for member galaxies will be relatively short. Therefore galaxies in unrelaxed groups may have properties which have been less influenced by environment compared to galaxies in more relaxed systems.


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.


We detect a deep (τsil  ∼  2.3) absorption feature due to silicate grains at around 10 μm. We compared the optical depth of the silicate feature in LEDA 1712304 with those in other AGNs in a wide range of IR luminosities (1010 L⊙   LIR   1013 L⊙). The spectra of the AGNs to be compared are taken from those of the IR galaxies observed by Spitzer/IRS (Stierwalt et al. 2013; Imanishi et al. 2007; Imanishi 2009; Roussel et al. 2006) with the threshold that the equivalent width of the PAH 6.2 μm feature is smaller than 0.27 μm (Stierwalt et al. 2013). In addition, we also take AGNs with low IR luminosities (LIR   1011 L⊙) from Wu et al. (2010). Figure 3 shows the relation between the IR luminosity and the optical depth of the silicate feature for LEDA 1712304 and the AGNs. We estimated the optical depths of the AGNs of Stierwalt et al. (2013), Wu et al. (2010), and Roussel et al. (2006) by ourselves in the same manner as was performed for LEDA 1712304 with the method defined by Imanishi et al. (2007), the spectra of which were obtained from the NASA/IPAC IR Science Archive (IRSA). On the other hand, we adopted the values given in each reference paper for the other AGNs. The blue dotted lines in Fig. 3 show the differences between our estimates and those by Stierwalt et al. (2013), which confirms that the differences between the different methods are not large enough to change a global relation. Figure 3 shows that galaxies with low IR luminosities (LIR   1011 L⊙) show significantly shallow silicate absorption features, as already pointed out by Stierwalt et al. (2013). Imanishi (2009) suggested that the number of heavily obscured AGNs that have deep silicate absorption features (τsil >  2) increases with the IR luminosities of the host galaxies. Therefore, LEDA 1712304 may be a rare galaxy from the aspect of having both deep absorption feature τsil ∼ 2.3 and low IR luminosity (5 ± 1)×1010 L⊙. Such galaxies have hardly been observed; an exception is NGC 1377 (Roussel et al. 2006), as can be seen in Fig. 3. NGC 1377 is a lenticular galaxy (de Vaucouleurs et al. 1991), the stellar mass of which is 109.3 ± 0.1 M⊙ (Skibba et al. 2011). The IR spectrum of NGC 1377 shows a featureless continuum except the silicate feature due to circumnuclear dust (Imanishi 2006; Roussel et al. 2006).


Our case studies focus on several regions of the parameter space of explosive transients that may be related to specific source categories. From Sect. 3, different types of transient emissions from highly magnetized pulsars (also magnetars) can be affected by secondary acceleration. As mentioned previously, magnetars have been identified in many studies as promising candidates for the acceleration of cosmic rays and the production of secondary high-energy neutrinos, for instance Blasi et al. (2000), Fang et al. (2012, 2013), Lemoine et al. (2015), Kotera et al. (2015). The case of newborn magnetars with millisecond periods illustrates a non-relativistic source class, whereas the case of magnetar giant flares involves relativistic outflows. Moreover, tidal disruption events, low-luminosity gamma-ray bursts and blazar flares are examples of relativistic outflows, whose properties partially overlap in the parameter space of explosive transients. In these overlapping regions, they can be similarly affected by secondary acceleration. Therefore, we chose to describe the case of jetted tidal disruptions, while keeping in mind that this case study can be used as a benchmark example for low-luminosity gamma-ray bursts and blazar flares. We note that beyond standard scenarios involving gamma-ray bursts (e.g., Waxman & Bahcall 1997; Murase & Nagataki 2006; Murase et al. 2008; Mészáros 2015) and active galactic nuclei (e.g., Bednarek & Protheroe 1999; Atoyan & Dermer 2001; Halzen & Hooper 2005; Dermer et al. 2014; Petropoulou et al. 2016; Murase et al. 2018; Gao et al. 2019), jetted tidal disruptions have also been proposed as candidate sources for the production of high-energy cosmic rays and neutrinos (Wang et al. 2011; Senno et al. 2016; Dai & Fang 2017; Lunardini & Winter 2017; Wang & Liu 2016; Zhang et al. 2017; Biehl et al. 2018; Guépin et al. 2018). These case studies are associated with different types of photon fields that we simply model by hard or soft broken power laws and we can thus assess their impact on the high-energy neutrino spectrum. From Sect. 3, we can see that all these source categories are affected by strong secondary synchrotron losses and should be affected differently by secondary acceleration.


We estimated the optical depths of the AGNs of Stierwalt et al. (2013), Wu et al. (2010), and Roussel et al. (2006) by ourselves in the same manner as was performed for LEDA 1712304 with the method defined by


The interaction of H2 and HD with atomic hydrogen is among the most widely investigated and important processes in elementary chemical reactions. The H + H2, H + D2, and H + HD reactions serve as benchmarks for experimental and theoretical investigations of bimolecular processes (Marinero, Rettner & Zare 1984; Zhang & Miller 1989; D’Mello, Manolopoulos & Wyatt 1991; Fernández-Alonso & Zare 2002; Harich et al. 2002; Aoiz, Bañares & Herrero 2005; Yang 2007; Gao et al. 2015; Karandashev et al. 2017; Yuan et al. 2018a,b, 2020; Goswami et al. 2020) and continue to attract much attention in the quest for unraveling quantum effects such as the geometric phase (GP) in chemical reactions (Kendrick, Hazra & Balakrishnan 2015; Hazra, Kendrick & Balakrishnan 2016; Croft et al. 2017; Kendrick 2018; Yuan et al. 2018a,b; Kendrick 2019). These elementary reactions are also of considerable interest in early universe chemistry models in determining H2 and HD column densities and the relative abundance of H/D in the interstellar medium (Flower 1999, 2000; Flower & Roueff 1999; Neufeld et al. 2006; Wrathmall, Gusdorf & Flower 2007; Gay et al. 2011; Nolte et al. 2011; Desrousseaux et al. 2018; Walker, Porter & Stancil 2018; Neufeld et al. 2019; Zhou et al. 2020). The H + HD ↔ D + H2 chemical reaction is especially important in this context as it cycles the heavier isotope between molecular form (HD) and purely atomic form. The HD molecule by virtue of its small dipole moment also serves as a tracer of H2 through its j = 1 → 0 rotational transition at 112 μm (Neufeld et al. 2006; Desrousseaux et al. 2018). Observations (Howat et al. 2002; Yuan et al. 2012) using the Infrared Spectrograph on the Spitzer Space Telescope have reported HD emissions from excited rovibrational level v = 1,  j = 5, as well as the pure rotational R(3) and R(4) lines, but relevant reaction rate coefficients are still limited in terms of initial HD rovibrational levels and gas temperature.


Now with the recent availability of high quality full 6D phase-space information for large numbers of sources, much effort has been made to decrease the uncertainties in the Milky Way mass estimate. Recent works using a tracer mass estimator with 6D phase-space information include Sohn et al. (2018, globular clusters), Watkins et al. (2019, globular clusters), and Fritz et al. (2020, satellites). The most recent work using the spherical Jeans equation by Zhai et al. (2018) is very similar to our current investigation in method and data (LAMOST K giants) although only line-of-sight velocities were included, whereas we additionally make use of proper motions from Gaia to obtain the stellar tangential velocities. Using Bayesian analysis to fit a distribution function to full 6D phase-space data (globular clusters, satellites, and halo stars) has been a recent popular choice among many works (Eadie & Jurić 2019; Posti & Helmi 2019; Vasiliev 2019; Deason et al. 2021; Correa Magnus & Vasiliev 2022; Shen et al. 2022; Slizewski et al. 2022; Wang, Hammer & Yang 2022) and a similar distribution function analysis using 5D phase-space data from Gaia (Hattori, Valluri & Vasiliev 2021). In addition to fitting the observational data with a distribution function, several works have incorporated into the fitting a comparison of the observed data with Milky Way-type galaxies from cosmological simulations (Callingham et al. 2019; Li et al. 2020). Newly discovered high velocity stars with full 6D phase-space information have been used to estimate the mass of the Milky Way (Hattori et al. 2018; Monari et al. 2018; Deason et al. 2019; Grand et al. 2019; Koppelman & Helmi 2021; Necib & Lin 2022). Vasiliev, Belokurov & Erkal (2021) and Craig et al. (2021) have estimated the Milky Way mass by fitting models for the Sagittarius and Magellanic Steams, respectively. Several recent studies have estimated the Milky Way mass using measurements of the rotation curve (de Salas et al. 2019; Eilers et al. 2019; Ablimit et al. 2020; Cautun et al. 2020; Karukes et al. 2020; Jiao et al. 2021). Other works have used 6D satellite phenomenology, characterizing simulated Milky Way-type satellite populations and comparing to the observations of satellites in the Milky Way, to estimate the mass of the Milky Way (Patel et al. 2018; Villanueva-Domingo et al. 2021; Rodriguez Wimberly et al. 2022). Zaritsky et al. (2020) apply the timing argument to distant Milky Way halo stars to derive a lower limit to the Milky Way mass.


Solar filaments, or prominences as they are called when observed above the solar limb, can be observed in a stable state for many days or weeks. Sometimes, they suddenly start to ascend as a whole (full eruptions) (Joshi & Srivastava 2011; Holman & Foord 2015) or within limited sections of their length (partial eruptions) (Gibson & Fan 2006; Kliem et al. 2014). The ascending of a filament can go on high into the corona (successful eruptions) and gives rise to a coronal mass ejection (CME) or can stop at some greater height in the corona (confined or failed eruptions) (Ji et al. 2003; Török & Kliem 2005; Alexander, Liu & Gilbert 2006; Kuridze et al. 2013; Kushwaha et al. 2015). Occasionally two-step eruptions are observed. A filament after the first jump decelerates and stops at a greater height as in failed eruptions, but after a rather short period of time it starts to rise again and develops into the successful eruption with a CME formation. Byrne et al. (2014) observed on 2011 March 8 at the solar limb the erupting loop system that stayed in a metastable intermediate position for an hour and then proceeded and formed the core of a CME. Gosain et al. (2016) analysed observations of the eruption of a long quiescent filament on 2011 October 22 observed from three viewpoints by space observatories. A two-ribbon flare and the onset of a CME appeared 15 h after the filament disappearance on the disc. The filament was not observed at the high metastable position but some coronal structures that can be attributed to a corresponding flux rope were recognized. A clear example of the two-step filament eruption on 2015 March 14–15 was reported by Wang et al. (2016) and Chandra et al. (2017). In this event, a part of a large filament separated from the main body of the filament at the height of ≈30 Mm and rose upwards to the height of ≈80 Mm, where it stayed for 12 h clearly visible in chromospheric and coronal spectral lines. Finally, it erupted and produced a halo CME.


In configuration 1S, the field close to the separatrix was sheared, producing steady interchange reconnection modulated by quasi-periodic reconnection bursts. We can roughly estimate the free energy release rate of the steady component from the energy injected before the onset of reconnection in the first 200 time units of the simulation. By t = 200, around 2 units of free magnetic energy are injected into the closed field; see Figure 16(a). Accounting for the ramp up of the driver and scaling the values, this corresponds to an energy injection rate of ≈5.6 × 1023 erg s−1 at the maximum driving speed. During the quasi-steady phase, this injection is balanced by losses to numerical diffusion and equates to roughly the free energy available for heating the plasma. Even after accounting for the unrealistically fast driving speed (see below), this energy release rate compares well with the observed values of 1023–1024 erg s−1 for bright points (Golub et al. 1974; Priest et al. 1994). The energy released by the bursts was a small fraction of the stored free magnetic energy—≈0.5 × Es = 4.9 × 1025 erg occurring with a period of ≈240 × ts = 8 minutes—while the outflow speeds reached typical values of ≈0.05 × Vs ≈ 60 km s−1 along the outer spine. The energy released in each burst corresponds to ≈18% of the energy released over the same period by the steady component. Many bright points exhibit quasi-periodic intensity increases, with periods ranging from a few minutes to a couple of hours (Kariyappa & Varghese 2008; Tian et al. 2008; Zhang et al. 2012). Our results demonstrate that some of this periodicity can be explained by the natural modulation of the interchange reconnection that occurs as minority-polarity elements are moved by surface motions. The predicted outflow speeds, and certainly the periods of the reconnection cycles, are likely too fast because the driving speed (12.5 km s−1) employed in our simulations is too high. However, configuration 1F demonstrated that the cycle period is mainly set by the displacement of the minority polarity. We speculate that, at more typical photospheric speeds (≈1.5 km s−1; e.g., Brandt et al. 1988), the reconnection cycle period would increase by a factor of 12.5/1.5 × 8 minutes ≈67 minutes, corresponding to the longest observed oscillations in brightness. Without a full treatment of the thermodynamics, however, it is not clear whether the repetitive, low-intensity reconnection jets in this case would be observable.


The leading FRB source model invokes magnetars as the power source to produce repeating bursts. There are two versions of this model. One version invokes rapidly spinning young magnetars that are produced in extreme stellar transients such as GRBs and SLSNe. The main motivation is that the host galaxy of FRB 121102 resembles those of LGRBs and SLSNe (Metzger et al. 2017; Nicholl et al. 2017; Wadiasingh & Timokhin 2019). The fact that the hosts of all other FRBs do not resemble that of FRB 121102 disfavors the simplest version of this proposal. A possible fix of this proposal is to introduce rapidly spinning magnetars born from binary neutron star (BNS) mergers (Margalit et al. 2019; Wang et al. 2020). In order to make this scenario work, one needs to require that rapidly spinning magnetars made from BNS mergers should be much more abundant than those made from LGRBs and SLSNe. Comparing the event rate densities of BNS mergers, LGRBs, and SLSNe (e.g., Sun et al. 2015; Abbott et al. 2017; Nicholl et al. 2017), this may be possible if a significant fraction of BNS mergers leave behind stable neutron stars (e.g., Gao et al. 2016). However, if this fraction is very low, as required if GW170817 leaves behind a black hole (Margalit et al. 2019), the fast magnetar model may fail to explain the small fraction of LGRB/SLSN-like hosts in FRB samples. The second version of the magnetar model invokes emission (e.g., giant flares) from slowly rotating magnetars like the ones observed in the Galaxy (e.g., Popov & Postnov 2010; Katz 2014; Kulkarni et al. 2014). The births of these magnetars do not require extreme explosions such as GRBs and SLSNe (e.g., Beniamini et al. 2019). If this is the case, the host galaxy distribution may be more analogous to that of SNe II. All FRBs but FRB 121102 are consistent with this scenario (Figure 4). In order to interpret FRB 121102, the more extreme channel of forming rapid magnetars is still needed. So we conclude that the magnetar model would work only if both fast magnetars produced in extreme explosions and slow magnetars produced in regular channels (Beniamini et al. 2019) can produce FRBs. In any case, since the birth rate of these magnetars is very high (Beniamini et al. 2019), an additional factor is needed to select a small fraction of magnetars to produce FRBs (e.g., Ioka & Zhang 2020).


Having found evidence that galaxies show morphological signatures of a recent galaxy merger over time-scales on the order of 300–500 Myr, we now consider the typical BH merger time-scales and the impact that may have on our results. Within the Illustris simulation (and indeed many similar simulations), a pair of BHs merge as soon as their separation is less than the particle’s smoothing length, rather than incorporating a coalescence time for the binary. Recently, several works have attempted to estimate the expected coalescence time for binary BHs by post-processing cosmological simulations, finding time-scales on the order of 100s of Myr to Gyr for the binary coalescence time (e.g. Blecha et al. 2016; Rantala et al. 2017; Kelley, Blecha & Hernquist 2017a; Mannerkoski et al. 2019; Sayeb et al. 2021). Additionally, the time for a satellite BH to reach the centre of a galaxy and form a binary with the central BH can also be on the order of 100s of Myr to Gyr, based on the dynamical friction time-scale for infall to the galactic centre (e.g. Volonteri et al. 2020). The galaxy structure, e.g. the existence or lack of a dense stellar core, can affect the time satellite BHs spend at large radii (Tremmel et al. 2018a,b; Barausse et al. 2020), and directly incorporating dynamical friction into cosmological volumes suggests that the orbital decay time-scale may be both substantial and redshift dependent (Bartlett et al. 2021). The Illustris simulation uses a re-centring scheme whereby BHs are re-positioned towards the local potential minimum; this prevents numerical wandering of BHs, but also means the the full infall time to reach the galaxy centre may be notably underestimated. Furthermore, both simulations (e.g. Bellovary et al. 2019) and observations (e.g. Reines et al. 2020) suggest that BHs in dwarf galaxies may frequently be located offset from the galaxy centre, which could further delay any mergers involving low-mass BHs seeded into Illustris (which are initially placed at the galaxy centre). Overall, this suggests that the Illustris simulation likely overestimates the speed with which BHs merge following the merging of their host galaxies, and properly accounting for this has the potential to impact the expected GW detection rate, shift the peak detection time to lower redshift, and prevent GW hosts from being visibly disturbed. Although a complete investigation into accurately estimating the time delays remains beyond the scope of this paper, we address this, by imposing a delay between when the BH particles merge in the simulation (which is closer to when the BH binary may form) and when the final coalescence and GW emission occur.


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

j

ENA

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

Δ
P
×
l
=

4
π

3

n

H

m

H

v

j

ENA

(
E
)

σ
(
E
)

Δ
E

c

f

4

c

f

=

(
v
+

u

R

)

2

v

4

(

v

2

+
4

u

R

2

+
2

u

R

v
)
.

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


Several well-studied TeV blazars show rich spectral behavior in X-rays, which may represent the general behavior of the synchrotron peak of all AGN jets. The X-ray spectra are usually curved (Massaro et al. 2004) and can only locally be fitted by a power law. The spectral variation with flux can be complex (Zhang et al. 2002; Cui 2004). Generally, the spectrum hardens when the flux increases (e.g., Gliozzi et al. 2006; Xue et al. 2006; Tramacere et al. 2009), but photon indices can saturate at higher fluxes (Xue & Cui 2005; Giebels et al. 2007). The synchrotron peak usually moves to higher frequencies with increasing flux during outbursts (e.g., Pian et al. 1998), but no correlation between the break energy and the flux exists when a broken power law is adopted to fit the X-ray spectra (Xue & Cui 2005; Giebels et al. 2007; Garson et al. 2010). A cooling break in the spectrum of emitting particles cannot explain these features (Wierzcholska & Wagner 2016), and some special particle acceleration processes may be involved (Madejski & Sikora 2016). There are also energy-dependent lags between the variations of different energy bands. In some flares, soft bands lag behind hard bands (e.g., Zhang et al. 2002), while lags in the opposite direction can also happen (e.g., Ravasio et al. 2004; Sato et al. 2008). Hysteresis in the HR (hardness ratio)–flux diagram is often used as a diagnostic of lags. Clockwise loops (e.g., Acciari et al. 2009; Kapanadze et al. 2016) in the HR–flux plane are a sign of soft lags while counterclockwise loops (e.g., Tramacere et al. 2009) are a sign of hard lags. The same source can exhibit both clockwise and counterclockwise loops; the observed patterns are further complicated by the superposition of flares at different timescales (Cui 2004). The above knowledge of TeV blazars in the X-ray regime comes from studies focusing on timescales of hours to weeks. We will extend this kind of analysis to much smaller timescales in this paper.


Several nucleosynthesis processes have been proposed as production sites of these light neutron-capture elements, including r-process in neutron star mergers (Wanajo et al. 2014; Watson et al. 2019), in magneto-rotational supernovae (Winteler et al. 2012), or in collapsars (Siegel et al. 2019), s-process in low- to intermediate-mass stars (Karakas & Lattanzio 2014), weak s-process in rapidly rotating massive stars (Frischknecht et al. 2012; Choplin et al. 2018), and weak r-process in electron-capture supernovae (Wanajo et al. 2011). It is not yet clear which process is the dominant source of the elements in the early Universe (see discussions by, e.g., Côté et al. 2019; Prantzos et al. 2018; Kobayashi et al. 2020). Since we here discuss the low-metallicity end of the sample, the production of neutron-capture elements would not be dominated by low- to intermediate-mass stars (e.g., de los Reyes et al. 2022). One possible explanation for the low light neutron-capture element abundances of the Helmi streams is that, as a result of the low stellar mass of the galaxy, the progenitor did not experience rare r-process nucleosynthesis events, such as neutron star mergers, electron capture supernovae, and magneto-rotational supernovae. In this case, a small amount of light neutron-capture elements could be produced by rapidly rotating massive stars (Hirai et al. 2019; Tarumi et al. 2021). Another explanation is that the progenitor dwarf galaxy had a small number of rotating massive stars. The small number of rotating massive stars might be a result of the top-light initial mass function in dwarf galaxies (Weidner & Kroupa 2005), or different distribution of initial rotation velocity of stars. The observational indication by Gull et al. (2021) that metal-poor stars of the Helmi streams show r-process abundance pattern in neutron-capture elements heavier than Ba might favor the second possibility. However, it is necessary to investigate the abundance pattern of light neutron-capture elements in order to understand the cause of the low light neutron-capture element abundance of the Helmi streams. A larger sample of low-metallicity Helmi stream stars with neutron-capture element abundances would also be welcomed. They would enable us to constrain the property of the nucleosynthesis processes, such as their event rates, by studying how neutron-capture elements were enriched as a function of metallicity (e.g., Tsujimoto et al. 2017).


Hierarchical structure formation scenarios (e.g. Fall & Efstathiou 1980; van den Bosch et al. 2002; Agertz, Teyssier & Moore 2011) predict that massive galaxies acquire much of their stellar mass through a combination of continuous cold gas accretion and mergers with smaller objects (e.g. Press & Schechter 1974; Moster, Naab & White 2013; Kaviraj et al. 2015; Rodriguez-Gomez et al. 2016; Martin et al. 2018b; Davison et al. 2020; Martin et al. 2021). As a consequence, mergers are also expected to play a significant role in driving the evolution of galaxy properties, for example, by triggering (Schweizer 1982; Mihos & Hernquist 1996; Duc et al. 1997; Elbaz & Cesarsky 2003; Kaviraj et al. 2011; Lofthouse et al. 2017; Martin et al. 2017) or quenching (Schawinski et al. 2014; Barro et al. 2017; Kawinwanichakij et al. 2017; Pontzen et al. 2017) star formation in the host galaxy or by driving its morphological evolution (e.g. Toomre 1977; Conselice, Yang & Bluck 2009; Dekel, Sari & Ceverino 2009; Taranu, Dubinski & Yee 2013; Naab et al. 2014; Fiacconi, Feldmann & Mayer 2015; Graham, Dullo & Savorgnan 2015; Deeley et al. 2017; Gómez et al. 2017; Welker et al. 2017; Martin et al. 2018a; Jackson et al. 2019). Signatures of past mergers take the form of faint extended tidal features such as tails (e.g. Pfleiderer 1963; Toomre & Toomre 1972; Peirani et al. 2010; Kaviraj 2014; Kaviraj, Martin & Silk 2019), or plumes (e.g. Lauer 1988) – which are typically produced by major mergers – and streams (e.g. Johnston, Sigurdsson & Hernquist 1999; Shipp et al. 2018; Martinez-Delgado et al. 2021) or shells (e.g. Malin & Carter 1983; Quinn 1984) – which mainly arise from minor interactions – as well as in the structure of the surrounding diffuse light (e.g. Choi, Guhathakurta & Johnston 2002; Graham 2002; Johnston, Choi & Guhathakurta 2002; Seigar, Graham & Jerjen 2007; Kaviraj et al. 2012; Monachesi et al. 2016, 2019; Iodice et al. 2019; Montes 2019). These features, which arise from many different types of encounter, hold a fossil record of the host galaxy’s past interactions and mergers which can be used to reconstruct its assembly history and dynamical history (Johnston et al. 2008; Martínez-Delgado et al. 2009; Belokurov et al. 2017; Montes et al. 2020; Ren et al. 2020; Spavone et al. 2020; Vera-Casanova et al. 2021). However, the majority of tidal features are expected to have surface brightnesses fainter than 30 mag arcsec−2 in the r-band (Johnston et al. 2008). Although pushing towards these kinds of limiting surface brightnesses remains extremely challenging, it is nevertheless desirable to do so, being necessary to uncover a more detailed history of local Universe. This is not only vital for our understanding of hierarchical galaxy assembly (e.g. Johnston, Sackett & Bullock 2001; Wang et al. 2012), but also serves as a novel galactic scale probe of more fundamental physics such as theories of gravity (e.g. Gentile et al. 2007; Renaud, Famaey & Kroupa 2016) and dark matter (Dubinski, Mihos & Hernquist 1996; Kesden & Kamionkowski 2006; Dumas et al. 2015; van Dokkum et al. 2018; Montes et al. 2020). In particular, tidal structure is a powerful tracer of the underlying galactic halo potential (e.g. Dubinski, Mihos & Hernquist 1999; Varghese, Ibata & Lewis 2011; Bovy et al. 2016; Ibata et al. 2020; Malhan, Valluri & Freese 2021).


The discovery of ultraluminous pulsars (ULPs or PULXs; Bachetti et al. 2014; Fürst et al. 2016; Israel et al. 2017a,b; Carpano et al. 2018) has revolutionised the field of ultraluminous X-ray sources (ULXs; see the review of Kaaret, Feng & Roberts 2017). Whilst ULXs were long considered to be possible candidates for hosting intermediate-mass black holes (IMBHs), it was immediately apparent that the explanation for the extreme observed luminosities (>1039 erg s−1) in at least some ULXs was accretion in excess of the classical Eddington limit on to common-place primary objects – in this case neutron stars. However, whilst the mass regime of the compact object in ULXs has been at least partly resolved (we note that candidate IMBHs still remain, e.g. Farrell et al. 2009), the relative number of black hole to neutron star primaries in ULXs (see King, Lasota & Kluźniak 2017; Middleton & King 2017) and the nature of the accretion flow in ULPs remain outstanding puzzles. At the centre of the debate is the strength of the surface dipole field and any multipolar component. Should the dipole field strength be similar to that of Galactic HMXBs (1012 G – e.g. Bellm et al. 2014; Fürst et al. 2014; Tendulkar et al. 2014; Yamamoto et al. 2014) then it is quite plausible that the flow will be supercritical ($\dot{m}/\dot{m}_{\rm Edd} \gt $ 1 where $\dot{m}_{\rm Edd}$ is the Eddington accretion rate) at radii greater than the magnetospheric truncation radius (rM). In this case, the supercritical portion of the disc will have a large – close to unity – vertical scale height and winds will be launched from the surface (see Shakura & Sunyaev 1973; Poutanen et al. 2007 and the simulations of Ohsuga et al. 2009; Jiang, Stone & Davis 2014; Sa̧dowski et al. 2014). Within rM, the flow will take the form of an accretion curtain (Mushtukov et al. 2017, 2019) and shock-heated column as material falls on to the magnetic poles. Due to collimation by the disc and outflows beyond rM, it is expected that the intrinsic luminosity is then partially geometrically beamed (see King 2009). Conversely, should the dipole field strength be very high (typically > 1013 G) then it is quite probable that the disc will truncate before becoming locally supercritical. The geometry in this case is then expected to take the form of a geometrically thin disc down to rM, an accretion curtain and shock-heated column. Rather than a supercritical disc and geometrical beaming, super-Eddington luminosities can then be explained by a magnetic pressure supported accretion column (Basko & Sunyaev 1976) and high field strength, the latter allowing for a substantially increased luminosity from a reduction in the electron scattering cross-section (e.g. Herold 1979; Paczynski 1992; Thompson & Duncan 1995; Mushtukov et al. 2015).


Although it is a simple concept, obtaining galaxy sizes is not an easy task and is subject to a number of assumptions. The most common way to derive galaxy sizes is by performing light-profile fitting assuming a given shape of the surface brightness profile using a χ2 minimization (e.g. Simard et al. 1999; Peng et al. 2002; Ravindranath et al. 2004; Daddi et al. 2005; Ravindranath et al. 2006; Trujillo et al. 2006; Akiyama et al. 2008; Franx et al. 2008; Tasca et al. 2009; Cassata et al. 2010, 2013; Williams et al. 2010; Mosleh et al. 2011; Huang et al. 2013; Ono et al. 2013; Stott et al. 2013; Morishita et al. 2014; van der Wel et al. 2014; Straatman et al. 2015; Shibuya et al. 2015). Another method assumes circular or elliptical apertures around a predefined galactic center and computes the size enclosing a given percentage of the total galaxy flux (e.g. Ferguson et al. 2004; Bouwens et al. 2004; Hathi et al. 2008; Oesch et al. 2010; Ichikawa et al. 2012; Curtis-Lake et al. 2016). A third approach, involving counting the number of pixels belonging to the galaxy to derive its size, was also explored in Law et al. (2007). Studies of galaxy sizes at z> 2 became possible with the deep imaging obtained with HST. The first reports on size evolution found that galaxy sizes as observed in the UV rest-frame were becoming smaller at the highest redshifts (Bouwens et al. 2003, 2004; Ferguson et al. 2004). We have now access to the size evolution up to z ~ 10 from the deepest HST imaging data (e.g., Hathi et al. 2008; Jiang et al. 2013; Ono et al. 2013; Kawamata et al. 2015; Holwerda et al. 2015; Shibuya et al. 2015). With the multiwavelength and near-infrared coverage of CANDELS (Grogin et al. 2011; Koekemoer et al. 2011) optical rest-frame measurements are reported up to z ~ 3 for a large collection of galaxies in diverse populations (e.g. Bruce et al. 2012; van der Wel et al. 2014; Morishita et al. 2014). At z ~ 2 the size of star-forming galaxies (SFGs) is, to first order, independent of the observed rest-frame bands (Shibuya et al. 2015). It is generally accepted that galaxy sizes tend to decrease with increasing redshift (e.g. Bouwens et al. 2003, 2004; Ferguson et al. 2004; Mosleh et al. 2012) and that galaxy sizes depend on stellar mass (e.g. Franx et al. 2008; van der Wel et al. 2014; Morishita et al. 2014) and luminosity (e.g. Grazian et al. 2012; Huang et al. 2013). However, some results point to a scenario consistent with no size evolution as seen in UV rest-frame from HST data (Law et al. 2007; Curtis-Lake et al. 2016) and, at a fixed stellar mass, from optical rest-frame ground-based data (Ichikawa et al. 2012; Stott et al. 2013).


DIG contributes with a fraction of 20% to 90% of the total Hα flux in galaxy disks, with a mean fraction around 50%–60% (Hoopes & Walterbos 2003; Oey et al. 2007; Sanders et al. 2017; Tomičić et al. 2017; Poetrodjojo et al. 2019; Della Bruna et al. 2020; Tomičić et al. 2021). This large contribution may cause star formation rates (SFRs) to be overestimated as Hα flux from DIG may be wrongly associated with star formation. There is a debate about the extent to which DIG affects measurements of gas-phase metallicity and its radial slope (Searle 1971; Vila-Costas & Edmunds 1992; Sánchez et al. 2014; Belfiore et al. 2017b; Sanders et al. 2017; Sánchez-Menguiano et al. 2018; Zhang et al. 2017; Vale Asari et al.2019; Kumari et al. 2019; Poetrodjojo et al. 2019) as some observations indicate lower metallicity (up to 1 dex) in DIG compared to nearby H ii regions. DIG may also exhibit different values of line ratios and ionizing parameter log(q), further affecting observations and analysis of ISM characteristics as well as adding scatter in the distribution of galaxy properties measured from unresolved observations (Martin 1997; Flores-Fajardo et al. 2011; Dopita et al. 2014; Zhang et al. 2017; Poetrodjojo et al. 2018; Mingozzi et al. 2020). Furthermore, the detection of gas that shows different line ratios and ionization parameters located at large distances from H ii regions—larger than the thickness of a typical galactic disk ( ≈ 1 kpc)—would indicate that sources other than star-forming (SF) regions are ionizing such gas (for example HOLMES, shocks, or mixing of different gas layers; Flores-Fajardo et al. 2011; Zhang et al. 2017; Poetrodjojo et al. 2018; Poggianti et al. 2019a). Different galactic characteristics (like mass, SFR, age, etc.) and external physical processes, such as galaxy interactions and gas stripping caused by ram pressure (Gunn et al. 1972; Toomre & Toomre 1972), may affect the ionization parameter and various line ratios (Maier et al. 2006; Nagao et al. 2006; Flores-Fajardo et al. 2011; Zhang et al. 2017; Sánchez 2020).


The line mass (mass per unit length) of G1.75-0.08 is Mline = 1011 ± 146 M⊙ pc−1. The dynamical state of the filament can be addressed by comparing its line mass with the virial or critical line mass (e.g. Fiege & Pudritz 2000, Eq. (12) therein). To calculate the latter quantity, we used the total (thermal+non-thermal) velocity dispersion, where the observed spectral line width (FWHM) was taken to be the FWHM of the HCN(1 – 0) line detected towards clump B in G1.75-0.08 from Miettinen (2014), that is, 13.50 ± 0.38 km s−1. We note that this is a very broad line width (and it is even broader (by a factor of 1.73) in clump A; Sect. 3.5), which could be attributed to multiple factors. From an observational point of view, the hyperfine structure of HCN was not resolved in the MALT90 spectra, which can lead to an overestimation of the line width although it was derived through fitting the hyperfine structure of the transition (Miettinen 2014). Moreover, the angular resolution of the Mopra telescope observations employed by Miettinen (2014) is 38″ (HPBW), which corresponds to 1.5 pc at the cloud distance, and hence the beam might have captured emission from the turbulent outer parts of the cloud. For example, if G1.75-0.08 follows the line width–size relation in the central molecular zone, or CMZ, which for HCN is found to be σ ∝ R0.62 (Shetty et al. 2012; Table 2 therein), the aforementioned HCN(1 – 0) line width would be expected to be only ~2.5 km s−1 on the ~0.1 pc scale, which is a typical inner width (FWHM) of filamentary molecular clouds (e.g. Arzoumanian et al. 2019; Priestley & Whitworth 2022, and references therein). We note that Henshaw et al. (2016a) derived a velocity dispersion of 11 km s−1 (~26 km s−1 FWHM for a Gaussian profile) for another Galactic centre region IRDC, namely G0.253+0.016 or the Brick from spectral line observations with Mopra, which is comparable to the observational results for G1.75-0.08 with the same telescope (Miettinen 2014). However, based on much higher angular resolution (1″.7) observations with the Atacama Large Millimetre/submillimetre Array (ALMA), Henshaw et al. (2019) derived an average velocity dispersion of 4.4 km s−1 in the Brick, which demonstrates that higher resolution spectral line observations towards G1.75-0.08 are also required. The effect of the angular resolution of the observations on the derived spectral line widths was also demonstrated by Hacar et al. (2018) in the case of the Orion integral filament (see e.g. Fig. 6 therein). From a physical point of view, there are several effects that can lead to line broadening. First, the HCN lines detected towards the G1.75-0.08 clumps were not optically thin, and hence the optical thickness effects might contribute to the broadening of the lines (e.g. Hacar et al. 2016). On the other hand, even the optically thin transitions detected towards the clumps had line widths that are comparable to those of HCN(1 – 0) (Miettinen 2014, Table 3 therein). Second, G1.75-0.08 might be associated with high-velocity gradients along the filament (e.g. Federrath et al. 2016; Gong et al. 2018) that would be blended in the MALT90 spectra and hence lead to overestimated line widths. Third, star formation driven outflows and shocks could lead to broad line profiles. Fourth, G1.75-0.08 is located close to the Galactic centre (RGC ≃ 270 pc), where the interstellar medium is highly turbulent (e.g. Salas et al. 2021 and references therein). At least part of this turbulent gas could contribute to our single-dish-observed spectral line widths. Obviously, further spectral line observations are needed to study the gas kinematics of G1.75-0.08 in more detail.


Recently, machine learning (ML) has been applied to derive various physical parameters of galaxies (e.g., Masters et al. 2015; Krakowski et al. 2016; D’Isanto & Polsterer 2018; Bonjean et al. 2019; Davidzon et al. 2019; Hemmati et al. 2019; Chang et al. 2021) and improves on linear combinations through nonlinear activations (e.g., Ackermann et al. 2018; Walmsley et al. 2019; Ferreira et al. 2020; Bickley et al. 2021; Bickley et al. 2022; Ferreira et al. 2022). In particular, classification by ML (e.g., Banerji et al. 2010; Huertas-Company et al. 2015; Domínguez Sánchez et al. 2018; Bottrell et al. 2019; Pearson et al. 2019; Barchi et al. 2020; Chang et al. 2021) can avoid time-consuming visual inspections and will be helpful for the visual classification of galaxy−galaxy interactions from the forthcoming large surveys. For instance, Pearson et al. (2019) developed a convolutional neural network (CNN) architecture with observational SDSS and simulated EAGLE images to identify galaxy mergers. They showed that the networks achieve better performance in observational data than in simulations. Ferreira et al. (2020) achieve 0.90 accuracy to classify major mergers and measure galaxy mergers in all five CANDELS fields using CNN trained with simulated galaxies from the IllustrisTNG simulation and separate star-forming galaxies from post-mergers in a following work (Ferreira et al. 2022). Bickley et al. (2022) deployed a CNN and evaluated mock observations of simulated galaxies from the IllustrisTNG simulations to identify post-mergers. Bottrell et al. (2022) examine both the morphological and kinematic features of merger remnants from the TNG100 and show that the stellar kinematic data have few contributions. Moreover, it has been discussed whether ancillary information such as kinematics and spectroscopic information in addition to the images may provide an additional basis for classification (e.g., Nevin et al. 2019; Pan et al. 2019; Bottrell et al. 2022; McElroy et al. 2022). Therefore, it is important to identify specific features for classification with ML from both photometric and spectroscopic observables.


The FORCAST images of HD 168625 are shown in Figure 4. The nebula is clearly resolved, with a partially complete ring structure that has two peaks almost symmetric around the star. We concur with Meixner et al. (1999) and O’Hara et al. (2003) in their interpretation of these two peaks as limb-brightened peaks of a torus of dust with a radius of ∼10″. The appearance is consistent with previously obtained images at 8.8, 12.5, and 20.6 μm from Meixner et al. (1999) and PACS 70 μm images (Groenewegen et al. 2011). We stress that our SOFIA/FORCAST images do not detect the outer polar rings seen in Spitzer IRAC images (Smith 2007), suggesting that the rings must be cold and below the sensitivity limits of SOFIA/FORCAST. The emission detected with the ring morphology in the IRAC band 4 image was probably polycyclic aromatic hydrocarbon (PAH) emission or atomic line emission, not thermal emission from warm dust. Figure 5 shows the temperature map that was derived from stacking the λFλ SOFIA/FORCAST 7.7–37.1 μm images and performing a least-squares fit of the dust temperature, Td, using the best-fit modified blackbody of the SED (i.e., Bλ(Td) · λ0.33) at each pixel location. The images were centered relative to one another by comparing the locations of the limb brightness peaks, and the 7.7–33.6 μm images were convolved with a 2D Gaussian kernel with an FWHM of 35 to match the resolution of the 34.8 and 37.1 μm images. Our temperature map shows a large gradient in dust temperatures with inner torus temperatures of ∼180 K and outer temperatures of ∼80 K, which is in agreement with the estimate of 170 ± 40 K obtained from our least-squares fit to the IR excess but is slightly higher than the equilibrium temperature estimates made by Pasquali et al. (2002; 113 K), Robberto & Herbst (1998; 135 K), and O’Hara et al. (2003; 130 K). The inaccuracies of this temperature map are due in large part to the fact that the method used to create it assumes that emission is purely thermal and that the dust shell is in thermal equilibrium. As noted previously, much of the 8.8–12.5 μm flux arises from transient, nonequilibrium emission from PAH grains. Therefore, using images at these wavelengths to derive quantitative conclusions from the temperature map has some limitations; however, we can interpret the maps qualitatively as discussed in Section 4.


We adopted the model developed by Ďapek et al. (2005), in which 1D thermal conduction below each of the surface facets is solved numerically with the nonlinear Robin boundary condition at the surface, and the assumption of an isothermal core at a sufficient depth is made. A temperature-dependence of the thermal conductivity following Eq. (2) was used. For the sake of simplicity, the specific heat capacity c was assumed constant, c = 560 J kg−1 K−1, and the regolith grain density obtained for C-type meteorites was used, ρ = 3.11 g cm−3 (both from Gundlach & Blum 2013). We ran solutions for four values of the packing factor ϕ in the range between 0.3 and 0.6. Each time, the parameters of the thermal conductivity were adjusted to satisfy the constraints from thermal observations described in Sect. 3.3 (see Table 2). The time domain of one revolution about the Sun was divided into steps of 60 s, short enough when compared to the ≃3.6 h rotation period, and the space grid describing the depth below each of the surface increased exponentially, as described in Ďapek et al. (2005). We ensured that at each depth, the von Neumann stability condition was satisfied. Typically, ten iterative steps of the algorithm provide the temperature with an accuracy of one degree or better in the whole space and time domain of the solution. The shape and spin state of Phaethon was taken from the modeling in Sect. 3.1. Similarly, the volume-equivalent size of 5.1 km from Sect. 3.2 was used as an implicit value. The last parameter required to compute the thermal recoil acceleration (the Yarkovsky effect) is the bulk density of Phaethon. Our nominal models use 1 g cm−3 for the clarity, but we treated this value as a free parameter in the orbit determination process (similarly to what was done for asteroid Bennu in Chesley et al. 2014). Scaling to different densities is easily implemented by using the inverse-proportional dependence of the thermal acceleration on the bulk density. In our analysis we neglected the enhancement of the Yarkovsky effect that is due to surface roughness (Rozitis & Green 2012). This effect could cause an increase in our bulk density estimate of less than 10%, which is well within the formal uncertainty.


Cavagnolo et al. (2010) suggested that the jet kinetic power is able to inflate the X-ray cavities or bubbles in different systems, including giant elliptical galaxies and cD galaxies (Type cD galaxy, a subtype of type-D giant elliptical galaxy), and proposed to evaluate the kinetic power Pkin = Pcav. However, this method is only limited to a small number of sources at present. It is known that the luminosity of extended region of radio jet, which is believed to be less Doppler-boosted, is related to jet kinetic power (Rawlings & Saunders 1991; Willott et al. 1999; Cavagnolo et al. 2010; Meyer et al. 2011), $P_{\rm rad} = \eta \, L_{\rm 5GHz}^{\rm ext}{}^{\kappa }$. Though the factor κ and η are given in discrepancy in literature due to the different sizes and source types of sample (Cavagnolo et al. 2010; Meyer et al. 2011), the ${\rm log}\, L^{\rm ext}_{\rm 5GHz}$ scales with the ${\rm log}\, P_{\rm rad}$ in the logarithmic space. We collect the total radio flux density from literature (Taylor et al. 1996 at 5 GHz; Piner & Edwards 2014 at 8.4 GHz; and Lister et al. 2018 at 15 GHz), and we convert the data at other frequencies to 5 GHz by assuming that
(14)$$\begin{eqnarray*}
S_{\rm 5GHz}^{\rm core} = S_{\rm \nu }^{\rm core} \, \, {\rm and} \, \, S_{\rm 5GHz}^{\rm ext} = S_{\rm \nu }^{\rm ext} \left(\frac{\nu }{\rm 5 \, GHz} \right)^{\alpha _{\rm ext}},
\end{eqnarray*}$$where the total radio flux is the sum of the flux of core and the flux of the extended region, Stot = Score + Sext, the αext = 0.75 and αcore = 0 (Fan et al. 2011; Pei et al. 2016, 2019, 2020). Together with the radio-core dominance parameter at 5 GHz
(15)$$\begin{eqnarray*}
R = \left(\frac{S^{\rm core}}{S^{\rm ext}} \right) (1+z)^{\alpha _{\rm core}-\alpha _{\rm ext}},
\end{eqnarray*}$$that we collect from Pei et al. (2020), we obtain $S_{\rm 5GHz}^{\rm ext}$ and calculate ${\rm log}\, L^{\rm ext}_{\rm 5GHz}$. The correlations of ${\rm log}\, P_{\rm rad}$ and ${\rm log}\, L_{\rm 5GHz}^{\rm ext}$ against ${\rm log}\, \beta _{\rm app}^{\rm max}$ are illustrated in Fig. 6 and linear regression results are listed in Table 2. Positive correlations of ${\rm log}\, P_{\rm rad}\, versus \, {\rm log}\, \beta _{\rm app}^{\rm max}$ and ${\rm log}\, L_{\rm 5GHz}^{\rm ext}\, versus \, {\rm log}\, \beta _{\rm app}^{\rm max}$ are found for blazars. The positive correlation of ${\rm log}\, P_{\rm rad}\, versus \, {\rm log}\, \beta _{\rm app}^{\rm max}$ holds for both FSRQs and BL Lacs when we consider them independently, while the positive correlation of ${\rm log}\, L_{\rm 5GHz}^{\rm ext}\, versus \, {\rm log}\, \beta _{\rm app}^{\rm max}$ only hold for BL Lacs. It is found that the motion of jet knots is significantly correlated with jet radiation power for both FSRQs and BL Lacs, however, the motion of jet knots is correlated with the kinetic power only for BL Lacs.


Filippenko & Chornock (2001) first presented the dynamical estimate of mass of the source to be around 7.4 ± 1.1 M⊙. Recently, Radhika & Nandi (2014) claimed that the mass of XTE J1859+226 is perhaps in between 6.58 and 8.84 M⊙ which is similar to the prediction of Shaposhnikov & Titarchuk (2009), although the lower mass limit is estimated as 5.4 M⊙ by Corral-Santana et al. (2011). However, we consider the typical mass of the source as 7 M⊙. The distance of this source is around d ∼ 11 kpc (Filippenko & Chornock 2001). Steiner et al. (2013) measured the spin as ak ∼ 0.4; however, Motta et al. (2014b) recently reported that the spin of the source is ak ∼ 0.34. Since the spin predictions are quite close, we use ak ∼ 0.4 for this analysis. We estimate the fluxes Fx (see Table 1) of LHS and HIMS of the 1999 outburst of the source (Radhika & Nandi 2014). The corresponding disc luminosities are calculated as $L_{\rm disc}^{{\rm LHS}}=8.26 \times 10^{37}\ {\rm erg\ s^{-1}}$ and $L_{\rm disc}^{{\rm HIMS}}=1.85 \times 10^{38}\ {\rm erg\ s^{-1}}$, respectively. Now, it is reasonable to assume the accretion efficiency for rotating BH as η = 0.3 which corresponds to the accretion rate of the inflowing matter as ${\dot{M}}_{{\rm acc}}^{{\rm LHS}} = 0.304 {\dot{M}}_{{\rm Edd}}$ in LHS and ${\dot{M}}_{{\rm acc}}^{{\rm HIMS}} = 0.680 {\dot{M}}_{{\rm Edd}}$ in HIMS. For LHS, we use $R_{\dot{m}}=9.83$ per cent following our theoretical estimate where xs = 64.6rg for ak = 0.4, ${\mathcal {E}}=0.001\,98$ and λ = 3.18. Incorporating these inputs in equation (15), we obtain the jet kinetic power as $L^{{\rm LHS}}_{{\rm jet}} = 2.52\times 10^{37}\ {\rm erg\ s^{-1}}$. The maximum mass outflow rate for HIMS corresponding to ak = 0.4 is obtained from Fig. 9 as $R^{\rm max}_{\dot{m}}=17.5$ per cent for ${\mathcal {E}}=0.005\,47$ and λ = 3.1, where the shock transition occurs at 21.9rg. Using these values in equation (15), we obtain the maximum jet kinetic power as $L^{{\rm HIMS}}_{{\rm jet}} = 1.08\times 10^{38}\ {\rm erg\ s^{-1}}$ which we regard to be associated with the HIMS of this source.


Cluster mergers can stir the intra-cluster medium (ICM) and lead to complex distributions of density and temperatures. The X-ray surface brightness traces regions of high electron densities ($\propto n_e^{2}$) and the SZ is sensitive to the pressure (∝neT) along the line of sight. An offset in the peaks of these signals can be used as an indicator of the density and temperature distribution in the disturbed ICM. There are examples of merging clusters that show presence of X-ray–SZ offsets, such as Abell 2146 (AMI Consortium et al. 2011) and Bullet cluster (Malu et al. 2010). Simulations have shown that the offset is sensitive to initial relative velocity of the merging clusters and the mass ratio (e.g. Molnar, Hearn & Stadel 2012; Zhang, Yu & Lu 2014). The cluster PLCK G200.9−28.2  discussed in this work has its X-ray peak and the Planck detection peak offset by 3.4 arcmin, which is the extreme in the Planck  sample (PC12). The Planck  SZ positions have mean and median errors of 1.5 and 1.3 arcmin, respectively (Planck Collaboration IV 2013). The X-ray peak is located at the northern sub-cluster [Fig. 1(a) and Fig. 6(a)] and the Planck  SZ position is separated from it by 3.4 arcmin (700 kpc) in the direction of the radio relic. Due to the presence of a shock at the relic, the region is expected to be overpressured and thus may result in shifting the peak of the SZ-signal. The offset in the direction of the relic indicates possible physical origin for the offset in addition to the position reconstruction uncertainty of Planck. Based on the results of simulations, the offset can be explained as a result of two comparable mass sub-clusters with mass ratio between 1 and 3 (Zhang et al. 2014). Deep optical observations tracing the galaxy distribution in this cluster will be useful to measure the mass ratios of the sub-cluster masses. Due to the large uncertainty in the Planck  position we cannot analyse the offsets for a statistical sample of merging clusters. However, the offset in the X-ray and SZ positions opens an additional probe for understanding the properties of merging galaxy clusters.


For the density of neutral hydrogen in the inner heliosheath a constant nH = 0.1 cm−3 is assumed


Using ANTARES data from the end of 2007–2017, a search for upward-going muon neutrinos and antineutrinos in spatial and temporal coincidence with 784 GRBs has been performed. The numerical model NeuCosmA was used to estimate the expected neutrino flux from each burst individually, in the context of one-zone internal shock model. A novel aspect of the search here presented is the inclusion in the data analysis chain of the uncertainty that possible unknown parameters, related to the characteristic activity of the central engine, can introduce in the neutrino flux evaluation. This is crucial in order to correctly interpret the validity of model-dependent results, in terms of upper limits set by non-detections of neutrinos in coincidence with GRBs (Adrián-Martínez et al. 2013; Aartsen et al. 2017). These parameters have been identified in the bulk Lorentz factor, variability time-scale, and source redshift, all of which are affecting the so-called dissipation radius, where shell collisions are realized. Among these parameters, the former was shown to impact the most GRB-neutrino flux predictions. At the same time, it is also possible to marginalize the uncertainty related to it by assuming a correlation with the source isotropic gamma-ray luminosity (which is in turn a physical observable). This was realized by relying upon the observational correlation found by Lü et al. (2012). As a result of such procedure, the minimum variability time-scale was found to contribute more than redshift to the uncertainty on the neutrino flux predictions from GRBs. Indeed, when letting tv free to vary, the estimated uncertainty on the neutrino flux expected from the model is observed to span up to several orders of magnitude. As a consequence, the expected ν-fluxes are provided with an uncertainty band of ±2σ. Analogously to previous ANTARES searches (Adrián-Martínez et al. 2013, 2017b; Celli et al. 2017), MC simulations of the signal predicted by NeuCosmA were performed, while the respective background was estimated directly from off-source data collected by ANTARES. Only track-like events reconstructed within 10° in radius from the expected GRB position were selected and in temporal correlation with the prompt gamma-ray emission.

Adrián-Martínez et al. 2013
Adrián-Martínez et al. 2013


In the 50 Myr after a star particle is formed, it can undergo supernova (SN) explosions. These are randomly drawn from a delay-time distribution (Kimm et al. 2015). We employ the mechanical feedback model described in Kimm et al. (2015, 2017) and Rosdahl et al. (2018) and the amount of momentum injected into the gas depends on the phase of the SN that is resolved by the simulation as to capture the final momentum of the snowplow phase. The equivalent of 1051 ergs is injected into the gas for each SN. The maximum momentum that we inject is boosted according to Geen et al. (2015) to account for unresolved H ii regions (Kimm et al. 2017). For each massive star that explodes, 20 per cent of the mass is recycled back into the gas. This gas is metal enriched assuming a metallicity of 0.075. Following Rosdahl et al. (2018), we have calibrated the SN feedback in order to reproduce the high-redshift stellar mass–halo mass relation from abundance matching (Behroozi, Wechsler & Conroy 2013). For our simulation, this requires assuming that the mean SN progenitor mass is 5 M⊙ which leads to 4× more SN on average compared to a standard Kroupa IMF (Kroupa 2001). While not ideal, this results in galaxies that fall nicely on the stellar mass–halo mass relation (see fig. 1 of Katz et al. 2018) and produces a UV luminosity function consistent with observations for a similar set of simulations at approximately the same resolution (Rosdahl et al. 2018). While we cannot be certain that even our calibrated simulations have the correct stellar mass–halo mass relation as we are using a high-redshift extrapolation and there is intrinsically a lot of scatter, we have made an effort to calibrate on one of the best available predictions as any significant offset from the stellar mass–halo mass relation may lead to large systematic offsets in the SFR-line luminosity relations. In summary, our star formation and stellar feedback models are based on the work of Rosdahl et al. (2018) which were chosen to reproduce both a reasonable reionization history and UV luminosity function.


Aided by the tight localization constraints of the three-detector network and the proximity of the GW source, multiple independent surveys across the EM spectrum were launched in search of a counterpart beyond the sGRB (Abbott et al. 2017c). Such a counterpart, SSS17a (later IAU-designated AT 2017gfo), was first discovered in the optical less than 11 hours after merger, associated with the galaxy NGC 4993 (Coulter et al. 2017a, 2017b), a nearby early-type E/S0 galaxy (Lauberts 1982). Five other teams made independent detections of the same optical transient and host galaxy all within about one hour and reported their results within about five hours of one another (Allam et al. 2017; Arcavi et al. 2017a, 2017b; Lipunov 2017b; Tanvir & Levan 2017; Yang et al. 2017; Soares-Santos et al. 2017; Lipunov et al. 2017a). The same source was followed up and consistently localized at other wavelengths (e.g., Corsi et al. 2017; Deller et al. 2017a, 2017b, 2017c; Goldstein et al. 2017; Haggard et al. 2017a, 2017b; Mooley et al. 2017; Savchenko et al. 2017; Alexander et al. 2017; Haggard et al. 2017c; Goldstein et al. 2017; Savchenko et al. 2017). The source was reported to be offset from the center of the galaxy by a projected distance of about 10″ (e.g., Coulter et al. 2017a, 2017b; Haggard et al. 2017a, 2017b; Kasliwal et al. 2017; Yang et al. 2017; Yu et al. 2017). NGC 4993 has a Tully–Fisher distance of ∼40 Mpc (Freedman et al. 2001; NASA/IPAC Extragalactic Database164

164
The NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
), which is consistent with the luminosity distance measurement from gravitational waves (

 Mpc). Using the Tully–Fisher distance, the ∼10″ offset corresponds to a physical offset of ≃2.0 kpc. This value is consistent with offset measurements of sGRBs in other galaxies, though below the median value of ∼3–4 kpc (Fong et al. 2010; Fong & Berger 2013; Berger 2014).


The observation of massive neutron stars Demorest et al. (2010), Antoniadis et al. (2013) indicates that the EoS of nuclear matter must be very stiff in the regime of high densities and low temperatures. The degree of stiffness in the nuclear matter EoS is directly related to the repulsive interaction among particles at high densities, as well as to the particle content in the core of the stars. In particular, it has been extensively discussed in the literature whether exotic degrees of freedom might populate the core of neutron stars. On the one hand, it is more energetically favorable for the system to populate new degrees of freedom, such as hyperons (Dexheimer & Schramm 2008; Ishizuka et al. 2008; Bednarek et al. 2012; Fukukawa et al. 2015; Gomes et al. 2015; Maslov et al. 2015; Oertel et al. 2015; Lonardoni et al. 2015, 2016); Biswal et al. 2016; Burgio & Zappalà 2016; Chatterjee & Vidana 2016; Mishra et al. 2016; Vidaña 2016; Yamamoto et al. 2016; Tolos et al. 2017); Torres et al. 2017), delta isobars (Fong et al. 2010;Schurhoff et al. 2010; Drago et al. 2014; 2016; Cai et al. 2015; Zhu et al. 2016), and meson condensates (Ellis et al. 1995; Menezes et al. 2005; Takahashi 2007; Ohnishi et al. 2009; Alford et al. 2010; Fernandez et al. 2010; Mesquita et al. 2010; Mishra et al. 2010; Lim et al. 2014; Muto et al. 2015), in order to lower its Fermi energy (starting at about two times the saturation density). On the other hand, the EoS softening due to the appearance of exotica might turn some nuclear models incompatible with observational data, in particular with the recently measured massive neutron stars. One possible way to overcome this puzzle is the introduction of an extra repulsion in the YY interaction Schaffner & Mishustin (1996), Bombaci (2016), allowing models with hyperons to be able to reproduce massive stars (Dexheimer & Schramm 2008; Bednarek et al. 2012; Weissenborn et al. 2012; Banik et al. 2014; Bhowmick et al. 2014; Gusakov et al. 2014; Lopes & Menezes 2014; van Dalen et al. 2014; Yamamoto et al. 2014; Gomes et al. 2015). Another possible solution is the introduction of a deconfinement phase transition at high densities Bombaci (2016), with a stiff EoS for quark matter, usually associated with quark vector interactions (see Klähn et al. 2013 and references therein).


The primary impact of the 1859 storm was on telegraphy (e.g. Boteler 2006). Today the principal ‘space weather’ threat is to the electric power grid (Baker et al. 2008; Hapgood, 2011, 2012; Oughton et al. 2016; Dyer et al. 2018). Because of this threat, several studies have been carried out to estimate how frequently such extreme space weather events may occur (e.g. Tsubouchi & Omura 2007; Riley 2012; Curto, Castell & Del Moral 2016; Riley & Love 2017). Such studies are dependent on the observations of a handful of storms that have approached or rivalled the Carrington geomagnetic storm in observed/inferred intensity and/or auroral extent. These include great storms in February 1872 (Chapman 1957a,b; Silverman 2008; Hayakawa et al. 2018c); September 1909 (Silverman 1995; Willis, Stephenson & Fang 2007; Love et al. 2019); May 1921 (Silverman & Cliver 2001; Kappenman 2006; Cliver & Dietrich 2013). The only such storm observed during the space era occurred in March 1989 (Allen et al. 1989; Silverman 2006a; Pulkkinen et al. 2012; Cid et al. 2014). More recently, in July 2012, a major backside eruption on the Sun was observed both remotely and in situ by the STEREO spacecraft (Kaiser et al. 2008; Russell et al. 2013; Liu et al. 2014; Riley et al. 2016). The interplanetary coronal mass ejection (CME) propagated to 1 AU in ∼20 h. Baker et al. (2013) calculated that had the eruption occurred on the frontside of the Sun – with optimal seasonal and local timing to maximize solar wind – magnetosphere coupling (worst case scenario (see e.g. Temerin & Li 2002) ─ it might have produced a storm greater than that inferred for the Carrington event. In addition to these storms, auroral evidence has recently been provided for two pre-1859 storms that may have ranked with the Carrington event: February 1730 (Hayakawa et al. 2018a), and, particularly, September 1770 (Willis et al. 1996; Nakazawa, Okada & Shiokawa 2004; Ebihara et al. 2017; Hayakawa et al. 2017e).


For consistency, we adopt the translation of this to the absolute velocities of cluster galaxies normalized by their respective galaxy cluster velocity dispersions into the range $0.3 \lt |\Delta \mathrm{V}|/\sigma _{r_{200}} \lt 0.5$ as deduced by Pimbblet (2011). Thus, if the mode of the standardised velocities for a sub-population has its foci at around $0.3 \lt |\Delta \mathrm{V}|/\sigma _{r_{200}} \lt 0.5$ for values around the virial radius, which we assume to be Rvirial ∼ r200, said sub-population would be classified as infalling. In contrast, a sub-population of backsplash cluster galaxies would be expected to peak significantly at $|\Delta \mathrm{V}|/\sigma _{r_{200}}\sim 0$ for values at or beyond our definition of the virial radius, with their fraction reaching zero at some upper limit (e.g. Mamon et al. 2004; Pimbblet 2011; Bahé et al. 2013; Haggar et al. 2020). Therefore, with respect to Fig. 5, we see that the column of our non-merging sub-populations across both bins of radius do not show any significant difference in the distributions of velocities with the exception of those that lie ≤r200, which show the non-AGN sub-population to occupy a mode within the range that nominally represents infallers, most likely for cluster galaxies 0.5 ≤ r200  1.0 (Gill et al. 2005). Additionally, the AGN sub-population slightly deviates from the non-AGN velocity distribution with a mode centred at $|\Delta \mathrm{\it V}|/\sigma _{r_{200}}\sim 0.8$, which could indicate stronger infalling. In contrast, the column of our merging AGN sub-populations shows the strongest deviations from the distribution of non-AGN, especially with the >r200 bin showing a significant centrally dominated AGN sub-population, where such a central dominance in relative velocity corresponds to a sub-population that were predominantly backsplash cluster galaxies. However, the dependence of this being the true nature of the sub-population relies upon more precise definitions of the radii since there is a natural upper limit a bound cluster galaxy can extend outward to with respect to its galaxy cluster’s potential, known as the splashback radius (More et al. 2015, 2016). In addition, Haggar et al. (2020) show that the fraction of backsplash galaxies diminishes by 2r200 and 2.5r200 for massive (∼×1015M⊙) merging and non-merging cluster systems, respectively, thus demonstrating that merging cluster environments experience a greater decrease in the fraction of harbouring backsplash galaxies as one continues to extend beyond r200. Indeed, the sub-populations of the merging cluster galaxies present in the ≤r200 bin show more variations in their general distributions with the modes of both the AGN and non-AGN sub-populations lying around $0.3 \lt |\Delta \mathrm{V}|/\sigma _{r_{200}} \lt 0.5$, which eludes to mostly infalling sub-populations rather than those associated with backsplash. Finally, if one considers the equivalent peak of the AGN density histogram at $\Delta \mathrm{V}|/\sigma _{r_{200}}\sim 1.7$ it could be possible there is a mix of recently accreted cluster galaxies and those that are relaxing on to a common potential. Although it should be noted that not much information can be confidently derived from the AGN sub-populations within the bins that possess small samples size (N ≲ 100), especially with the merging AGN-hosting cluster galaxies at ≤r200 that only has N = 15.


Irrespective of its origin, the [C II] emission is linked to the presence of stellar far-ultraviolet (FUV) photons (E 13.6 eV). As FUV photons are tied to the presence of massive O and B stars that have short lifetimes, the [C II] 158 μm line is also astar formation rate (SFR) indicator. Indeed, ISO, Herschel and SOFIA observations have demonstrated the good correlation between the [C II] luminosity and the SFR in the Milky Way and in regions of massive star formation in other galaxies (e.g., Kramer et al. 2013, 2020; Pineda et al. 2014, 2018; Herrera-Camus et al. 2015, 2018; De Looze et al. 2011). With ALMA and NOEMA, ground-based observations of the [C II] 158 μm line in high redshift galaxies have come into reach and such data are routinely used to infer SFRs (e.g., Walter et al. 2012; Venemans et al. 2012; Knudsen et al. 2016; Bischetti et al. 2018; Khusanova et al. 2021) based upon validations of this relationship in the nearby Universe (Herrera-Camus et al. 2018; De Looze et al. 2011). However, it is well-understood that the intensity of the [C II] line depends on the local physical conditions (Hollenbach & Tielens 1999). Observationally, the presence of the so-called [C II]-deficit – a decreased ratio of [C II] 158 μm luminosity to FIR dust continuum with an increasing dust color temperature and also with FIR luminosity – is well established (Malhotra et al. 2001; Díaz-Santos et al. 2013; Magdis et al. 2014; Smith et al. 2017). This deficit is particularly pronounced in (local) ultraluminous infrared galaxies (ULIRGs), very dusty galaxies characterized by vigorous embedded star formation (e.g., Luhman et al. 2003; Abel et al. 2009; Graciá-Carpio et al. 2011). This deficit, however, does not necessarily hold in the early Universe at high redshift (e.g., Stacey et al. 2010; Brisbin et al. 2015; Capak et al. 2015). Some studies have indicated that not only [C II] emission is deficient in some sources, but other FIR cooling lines ([O I], [O III], [N II]), as well (e.g., Graciá-Carpio et al. 2011; Herrera-Camus et al. 2018). These deficits must be linked to the global ISM properties and star-formation characteristics in these galaxies.


Classifying galaxies into different star formation regimes at high redshift is facilitated by the fact that star formation rate (SFR) and stellar mass (M*) of star-forming galaxies (SFGs) are strongly correlated out to at least

 (Daddi et al. 2007; Noeske et al. 2007; Pannella et al. 2009, 2015; Elbaz et al. 2011; Whitaker et al. 2012, 2014; Lee et al. 2015; Salmon et al. 2015; Schreiber et al. 2015; Tomczak et al. 2016). This correlation is commonly called the “main sequence of star formation” (MS). A common interpretation of the MS is that the location of galaxies relative to the MS follows a different time evolution of SFR (Renzini 2009; Daddi et al. 2010; Rodighiero et al. 2011; Sargent et al. 2012; Renzini & Peng 2015). The tight MS with near unity slope reflects that the majority of SFGs follow a steadily increasing star formation history governed by a set of gradual physical processes like gas exhaustion (Noeske et al. 2007). A small fraction of galaxies exhibit quasi-exponential mass and SFR growth, either through major mergers or through strong bursts of star formation in the densest regions (Elbaz et al. 2011; Sargent et al. 2012). While typical galaxies therefore spend most of their time on the MS prior to additional quenching processes, these starburst galaxies are located above the MS and play a relatively minor role in the star formation history of the universe (Rodighiero et al. 2011). Galaxies located below the MS include quiescent galaxies (QGs), with spheroidal-like structures and little star formation activity, as well as fading SFGs with diminishing star formation activity. The transient galaxies, such as those in the green valley, can dominate the lower region of the MS. At

, green valley galaxies are known to be off the MS (Schawinski et al. 2014), and they have intermediate morphologies combining disk-dominated and bulge-dominated systems (Salim et al. 2009; Mendez et al. 2011; Pandya et al. 2017).