Hu, Holz & Vale (2007b) proposed the idea of using the ratio of CMB convergence to galaxy lensing convergence as a way to measure the distance ratio (distance to surface of last scattering relative to the distance to the source galaxy sample used to estimate the galaxy lensing) and hence constrain the geometry, Ωk and the equation of state of dark energy. The ratio is defined as

(40)

\begin{equation}
\mathcal {R}(z_{\rm l})=\frac{\kappa (z_{\rm l},z_{\ast })}{\kappa (z_{\rm l},z_{\rm s})}=\frac{\Sigma _{\rm c}(z_{\rm l},z_{\rm s})}{\Sigma _{\rm c}(z_{\rm l},z_{\ast })}.
\end{equation}

Similar distance ratio tests have also been proposed using galaxy or galaxy cluster lensing alone, in both strong lensing (e.g. Link & Pierce 1998; Golse, Kneib & Soucail 2002) and weak lensing regimes (e.g. Jain & Taylor 2003; Bernstein & Jain 2004). Several studies have already measured the distance ratios (e.g. Taylor et al. 2012; Diego et al. 2015; Kitching et al. 2015; Caminha et al. 2016, and references therein), though they are afflicted by several systematics such as, uncertainties in modelling cluster profiles and cosmic variance in the case of multiple strong lens systems, and photometric redshift uncertainties as well as imaging systematics that cause a redshift-dependent shear calibration in the case of weak lensing. The small redshift baseline also limits the cosmological applications of these measurements using optical weak lensing alone (see discussion in Hu et al. 2007b; Weinberg et al. 2013). Using CMB lensing in cosmographic measurements is advantageous in several ways. First, the source redshift for the CMB (redshift of surface of last scattering) is well known, so one of the two redshift slices being compared has no redshift uncertainty. The long redshift baseline between CMB and galaxy lensing sources also improves the sensitivity of $\mathcal {R}$ to cosmological parameters (Hu et al. 2007b). However, using CMB lensing with galaxy lensing makes $\mathcal {R}$ become more sensitive to some of the systematics in galaxy lensing (for example, multiplicative bias), and $\mathcal {R}$ can also be used as test for the presence of such systematics.


The ESPRESSO DFS concept (Di Marcantonio et al. 2018) was conceived during its preliminary design phases with the goal of maximizing operational efficiency, flexibility, and scientific output while complying with the standard Paranal Observatory operational scheme. The main challenge derives from the requirement to operate ESPRESSO in a seamless way with any of the UT’s or with all four UT’s simultaneously. This must be possible not only with a predetermined schedule, but also “on the fly”. The flexibility in ESPRESSO’s operations has been tackled by adopting a new DFS deployment plan described in Di Marcantonio et al. (2018) that is exceptional under various aspects because it has to cope with various telescope and instrument configurations while remaining operationally simple. Figure 8 shows the main ESPRESSO DFS elements and their final deployment. Besides the software packages already described, part of the software for the control of the CT devices has been incorporated into the VLT telescope CS to allow CT operations even when ESPRESSO is offline (thus avoiding conflicts, e.g., with instruments of the VLT Interferometer operations). In addition to the standard DFS software packages, ESPRESSO is the first instrument to also provide a data analysis package that is able to extract relevant astronomical observables from the reduced data. The following DFS subsystems are specific to ESPRESSO: (1) the ETC hosted on the ESO web page9; (2) the CS with the full suite of acquisition, observation, and calibration templates that are able to control all vital parts of the instrument and the CT (Calderone et al. 2018); (3) the data reduction software (DRS) package (or “pipeline”) capable of providing “science-ready” reduced data only minutes after the end of the individual observation; (4) the data analysis software (DAS) package that produces higher-level astronomical observables with no or limited supervision; (5) the DRS and DAS are distributed to the community10.


In the era of gravitational wave and multimessenger astronomy of binary neutron stars accurate numerical modelling of neutron-star mergers and their remnants on long time-scales $\simeq 1\, \rm s$ has never been more important. The coincident detection of a gravitational-wave signal from a neutron-star merger (The LIGO Scientific Collaboration & The Virgo Collaboration 2017) and an accompanying electromagnetic counterpart in form of a short gamma-ray burst (LIGO Scientific Collaboration et al. 2017) and kilonova afterglow (Kasen et al. 2017; Drout et al. 2017) has established a firm connection with electromagnetic counterparts and highlights the need for multiphysics modelling of neutron-star mergers. A neutron-star merger consists of several stages starting from the late inspiral, where accurate numerical waveforms are needed to calibrate analytical models for waveforms, through merger (Kawaguchi et al. 2018; Nagar et al. 2018; Dietrich et al. 2019), which requires sophisticated microphysics in terms of finite-temperature equations of state (EOS) satisfying recent observational constraints (Annala et al. 2018; Most et al. 2018; Tews, Margueron & Reddy 2018; Burgio et al. 2018; Raithel, Özel & Psaltis 2018) until the post-merger phase where neutrino and magnetic viscosity can drive large amounts of mass ejection (Just et al. 2015; Siegel & Metzger 2017, 2018; Fernández et al. 2019; Fujibayashi et al. 2018), that are needed to make a connection to the kilonova afterglow produced by the decay of heavy elements in the matter outflow. The modelling of this complicated multiphysics system requires both the use of numerical relativity (Baiotti & Rezzolla 2017; Duez & Zlochower 2019) and of an accurate modelling of the fluid, the electromagnetic fields as well as the microphysics. Considerable effort has been placed on improved and highly accurate methods to solve Einstein field equations numerically (Baumgarte & Shapiro 2010; Shibata 2016) and to couple them with high-order methods for relativistic hydrodynamics (Radice, Rezzolla & Galeazzi 2014a; Bernuzzi & Dietrich 2016). At the same time, mainly driven by an effort to model core-collapse supernovae, very sophisticated numerical schemes for neutrino transport have been developed (Ruffert, Janka & Schaefer 1996; Buras et al. 2006; Shibata et al. 2011; Sumiyoshi & Yamada 2012; Foucart et al. 2015; Just et al. 2015). When considering the late stages of the evolution of the system not only is it important to account for the various relevant physics contributions, such as neutrino interactions, but it is also crucial to understand how numerical errors at finite-numerical resolution accumulate over time. This is even highlighted by the fact that current simulations of neutron-star mergers sometimes show non-convergent behaviour in the magnetic field evolution (Endrizzi et al. 2016; Ciolfi et al. 2017) even when small resolution changes are used. Notwithstanding, that with current computational efficiencies and available resources not even all relevant physical scales involving magnetic turbulence can be resolved (Kiuchi et al. 2015b, 2018), studying the late-time evolution of the remnants accretion disc is not only feasible but has been the subject of recent investigations (Siegel & Metzger 2017, 2018; Fernández et al. 2019). While all such simulations so far have used traditional second-order accurate finite-volume schemes to model the evolution of the general-relativistic magnetohydrodynamics system (GRMHD), earlier works have already indicated the benefit of using more accurate high-order methods in this context (Del Zanna et al. 2007; Tchekhovskoy, McKinney & Narayan 2007; Radice et al. 2014a), while even more recent studies have already started to consider advanced finite-element approaches (Kidder et al. 2017; Fambri et al. 2018). Taking an intermediate approach similar to Del Zanna et al. (2007), McCorquodale & Colella (2011), Chen, Tóth & Gombosi (2016), and Felker & Stone (2018), we will consider the impact of using a fourth-order accurate numerical scheme to model the merger of magnetized binary neutron stars and show the advantages gained when additionally finite-temperature effects and neutrino cooling are included.


Using Eq. (16), we derive the probability density in the parameter space (σDRW, RBLR) for a given set of parameters ⟨M⟩, fBLR, ve, and R0. By marginalising on ve and R0 we obtain the measurement of RBLR shown in Fig. 10. One could argue that we obtain a bi-modal distribution in the posterior probability for RBLR. This observation can be explained by the fact that, as shown in Sect. 4, the R-band encapsulates the Mg II and Fe II emission lines which can arise from two distinct regions of the BLR. Indeed, the Hβ (used in Mosquera & Kochanek 2011) and Mg II lines seem to arise from the same part of the BLR in various quasars (e.g., Karouzos et al. 2015; Khadka et al. 2021) and should both yield similar sizes; whereas the Fe II line is thought to arise from a larger part of the BLR (e.g., Sluse et al. 2007; Hu et al. 2015; Zhang et al. 2019; Li et al. 2021). Therefore, the combination of the two signals modelled as a single BLR emission could broaden our measurement and induce its slight bi-modality. Still, the core of the probability lies in the [0.1–1.5] RBLRMK11 range and the second mode observed for higher values of RBLR rises only for the highest values of σDRW. The marginalisation of this posterior over σDRW yields a probability distribution for RBLR and by taking its 16th, 50th, and 84th percentiles we measure

R
BLR

=
1
.

6

−
0.8

+
1.5

×

10
17

$ R_{\mathrm{BLR}} = 1.6^{+1.5}_{-0.8}\times 10^{17} $

 cm. With a relative precision of ≈80% our method is less precise than recent spectroscopical reverberation mapping measurements (e.g., Grier et al. 2019; Penton et al. 2022 have around 30% relative precision for quasars with z > 1.3) but is more precise than photometric reverberation mapping (e.g., Kaspi et al. 2021 have above 100% relative precision when using a cross-correlation function with R and B filter light curves). The value of RBLRMK11 predicted by the luminosity–size relation is in agreement with our measurement at the 1−σ level.


Modulation in steady-state has been well studied by previous works (Potgieter 2013; Potgieter et al. 2014; Zhao et al. 2014). Potgieter et al. (2014) studied the modulation of proton spectra with the PAMELA data from 2006 to 2009 July, and they concluded that the recent solar minimum was “diffusion dominated.” In the work of Potgieter et al. (2014), parameters in diffusion coefficients and drift coefficients were adapted to observations (see also Potgieter et al. 2015; Raath et al. 2016). Zhao et al. (2014) studied the modulation of the GCR energy spectra during the past three solar minima using an empirical diffusion coefficient model according to Zhang (1999). They found that decreased perpendicular diffusion in polar direction, which is in contrast to the assumption of enhanced diffusion in polar regions that was used to explain the observed Ulysses CR gradients (see, e.g., Potgieter 2000), and increased parallel diffusion might be the reason for the record high-level of GCR intensity measured at Earth. Since the diffusion coefficients describe the scattering of GCRs by random fluctuations in the IMF, turbulence quantities are needed in diffusion theory. In the solar wind, the evaluation of turbulence is well described by magnetohydrodynamic (MHD) theory (Marsch & Tu 1989; Zhou & Matthaeus 1990), and the turbulence transport throughout the heliosphere has been studied over the years (e.g., Zank & Matthaeus 1993; Zank et al. 1996, 2012, 2017; Matthaeus et al. 1999; Smith et al. 2001; Breech et al. 2008; Hunana & Zank 2010; Oughton et al. 2011; Wiengarten et al. 2016). With the turbulence transport models (TTMs), the diffusion tensor can be calculated (e.g., Zank et al. 1998; Pei et al. 2010a; Engelbrecht & Burger 2013; Zhao et al. 2017). Theoretical and numerical works have shown that drift coefficients can be reduced in the presence of turbulence (e.g., Jokipii 1993; Fisk & Schwadron 1995; Giacalone & Jokipii 1999; Candia & Roulet 2004; Stawicki 2005; Minnie et al. 2007; Tautz & Shalchi 2012); see also the first-order approach in Engelbrecht et al. (2017). The reduced drift coefficients, which are obtained from fitting the simulation results (Burger & Visser 2010; Tautz & Shalchi 2012), are also used together with the turbulence transport theory to study the modulation of GCRs (e.g., Engelbrecht & Burger 2013). Using the nearly incompressible (NI) MHD TTM developed by Zank et al. (2017), Zhao et al. (2017) also showed the effect of both weak and moderately strong turbulence on drift coefficients. Since there exists close coupling between turbulence, solar wind, and energetic particles, some work combined large-scale solar wind flow with small-scale fluctuations in a self-consistent way (see, e.g., Usmanov et al. 2011, 2014, 2016; Wiengarten et al. 2015; Shiota et al. 2017) to study the spatial variations of the diffusion coefficients (see, e.g., Chhiber et al. 2017). Furthermore, using a diffusion coefficient model according to Giacalone & Jokipii (1999), Guo & Florinski (2016) studied the modulation of GCRs by CIRs at 1 au. They combined the small-scale turbulence transport with the MHD background for the simulation of cosmic-ray transport to show short-term modulation effects.


During our monitoring period V2492 Cyg remained always undetected at our sensitivity, therefore the light curve depicted in Fig. 1 displays only upper limit values at different levels, as explained in Sect. 3. As a consequence, no fading or outbursting event can be detected, nevertheless some useful information can be derived. As mentioned above, after its discovery in 2010, V2492 underwent a long-lasting period of strong activity with intermittent burst and fading events (see Hillenbrand et al. 2013 and AAVSO2 data) and reached its maximum recorded brightness in 2017 Giannini et al. (2018). During most of this period, the source was sampled with an almost daily cadence and, for long time intervals, remained brighter than the following values: B  18, V  16, R  15, and I  14 mag. In comparison, our plate measurements are largely undersampled, presenting long periods (up to a decade) without any data. In any case (not considering the I band, which is practically uncovered, and the B band, which presents no significant upper limits), our V and R-band upper limitstentatively suggest that duringa period of about 30 yr from 1958 to 1987 an activity similar (both in duration and in brightness) to that more recently (2010–2017) monitored, did not occur. Indeed, we note that for a significant amount of time the source is brighter than the level indicated by our upper limits, thus suggesting that, in the past, the activity of V2492 Cyg was not as strong as it is now. The above scenario, if correctly described, means that an enhanced brightness variability could be an infrequent feature of V2492 Cyg. Such circumstances favour an accretion- more than an extinction-driven origin for the bursts. Indeed, the former is expected to occur with a long and irregular cadence related to the viscous motion of the matter toward the inner edge of the disk, while the latter should occur more frequently and regularly, according to the orbital motion of the obscuring matter along the line of sight.


However, one can reduce the order of the LD equation using the method proposed in Landau & Lifshitz (1975), i.e., by rewriting the self-force in terms of the external force and the four-velocity of a particle. Substituting the higher-order terms in Equation (3) with the derivatives of the Lorentz force, we get the equation in the following form:
5

This equation, usually referred to as the Landau–Lifshitz (LL) equation, has important consequences: it is of the second order, does not violate the principle of inertia, and the self-force vanishes in the absence of the external (Lorentz) force (Rohrlich 2001; Poisson 1999). The self-contained derivation of Equation (5) in terms of retarded potentials is given in Poisson et al. (2011). Equation (5) can be applied to cases with any external forces acting on a charged particle instead of the Lorentz force. In the case where

, the radiation-reaction force can be rewritten in the form
6

where

 is the specific charge of the particle,

, and the comma in the first term denotes the partial derivative with respect to the coordinate xα. Spohn (2000) concluded that using the LL equation is identical to imposing Dirac’s asymptotic condition

 on the LD equation. It was later confirmed by Rohrlich (2001) that the reduced form of the equation of motion is exact, rather than approximative, though the LL equation was proposed in Landau & Lifshitz (1975) as an approximative solution to the third-order LD equation. More details on the treatment of the radiation reaction of charged particles in flat spacetime can be found in the book by Spohn (2004). In our numerical study, we found that the LL approximation is perfectly applicable if the Schott term is small with respect to the radiation recoil term, which is the case we consider here. Below we show a representative example of charged particle motion in an external uniform magnetic field, integrating both LD and LL equations. The results of the numerical studies of LD and LL equations for the motion of a charged particle in a uniform magnetic field in flat spacetime are in accord with the analytical treatment of the radiation-reaction force performed in Spohn (2000).


BE values can also be obtained by means of computational approaches that, in some situations, can overcome the experimental limitations. Many computational works have so far focused on a few important astrochemical species like H, H2, N, O, CO, and CO2, in which BEs are calculated on periodic/cluster models of crystalline/amorphous structural states using different computational techniques (e.g., Al-Halabi & Van Dishoeck 2007; Karssemeijer et al. 2014; Karssemeijer & Cuppen 2014; Ásgeirsson et al. 2017; Senevirathne et al. 2017; Shimonishi et al. 2018; Zamirri et al. 2019a). In addition, other works have computed BEs in a larger number of species but with a very approximate model of the substrate. For example, in a recent work by Wakelam et al. (2017) BE values of more than 100 species are calculated by approximating the ASW surface with a single water molecule. The authors then fitted the most reliable BE measurements (16 cases) against the corresponding computed ones, obtaining a good correlation between the two data sets. In this way, all the errors in the computational methods and limitations due to the adoption of a single water molecule are compensated by the fitting with the experimental values, in the view of the authors. The resulting parameters are then used to scale all the remaining computed BEs to improve their accuracy. This clever procedure does, however, consider the proposed scaling universal, leaving aside the complexity of the real ice surface and the specific features of the various adsorbates. In a similar work, Das et al. (2018) have calculated the BEs of 100 species by increasing the size of a water cluster from one to six molecules, noticing that the calculated BE approaches the experimental value when the cluster size is increased. As we will show in the present work, these approaches, relying on an arbitrary and very limited number of water molecules, cannot, however, mimic a surface of icy grain. Furthermore, the strength of interaction between icy water molecules, as well as with respect to the adsorbates, depends on the hydrogen bond cooperativity, which is underestimated in small water clusters.


Next, we applied a correction for the expected difference between the magnitude of each Cepheid at the observed phase and the magnitude at the epoch of mean intensity of its light curve. These phase corrections are derived from ground-based light curves of each Cepheid in filters with wavelengths best corresponding to the WFC3 filters. Because the phase corrections are relative quantities, they do not change the zero-point of the light curves, which remain on the HST WFC3 natural system.6

6
In practice, the ground-based light curves are transformed to the HST system using color terms. While an uncertainty in color term could produce systematic errors, these are negligible. We determined empirically that a 10% error in the color terms changes the mean phase correction by ≤0.1 mmag.
 We derived and applied these phase corrections following the same methodology described in R18b. The periods and phases for F555W and F814W were determined using the V- and I-band light curves from OGLE surveys (Szymanski 2005; Udalski et al. 2008, 2015). For some Cepheids (OGL0434, OGL0501, OGL0510, OGL0512, OGL0528, OGL0545, OGL0590, OGL0712, OGL0757, OGL0966, and OGL0992), we also included V-band light curves from the ASAS survey (Pojmanski 1997) and/or ASAS-SN survey (Shappee et al. 2014; Kochanek et al. 2017) to increase the baseline coverage. We made use of the J- and H-band light curves from M15 and Persson et al. (2004) to correct the F160W random phased measurements to mean intensity. The standard deviations of these corrections are 0.29, 0.17, and 0.11 mag in F555W, F814W, and F160W, respectively, decreasing with the smaller light-curve amplitudes at redder wavelengths. Phase corrections also account for the difference between the Cepheid light-curve magnitude mean (the average of many measured magnitudes) and the magnitude at the epoch of mean intensity (the standard convention for distance measurements). This expected difference is consistent with our sample average correction of −0.048, −0.013, and −0.001 mag, in F555W, F814W, and F160W, respectively. The uncertainties in these phase corrections depend on the quality of the ground-based light curves; the average uncertainty is 0.013, 0.008, and 0.029 mag per epoch in F555W, F814W, and F160W, respectively, which dominates over the statistical photometry errors (i.e., photon statistics) in a single epoch. The differences between repeat measurements for the same target, available for a subset of 19 epochs and filters, is consistent with these uncertainties. The final mean individual uncertainty for these 70 Cepheids is 0.016, 0.012, and 0.029 mag in F555W, F814W, and F160W, respectively. The final mean photometry for each Cepheid in three colors is given in Table 2.


The situation seems to be more complicated in luminous AGNs, which can be divided into radio-quiet (RQ) and radio-loud (RL) AGNs according to their radio loudness R (R = f5 GHz/f4400 Å, where f5 GHz and f4400 Å are the radio flux at 5 GHz and optical flux at 4400 Å, respectively, Kellermann et al. 1989). The accretion process can be well described by a disk-corona model in RQAGNs (Jin et al. 2012; Lusso & Risaliti 2017; Qiao & Liu 2018), where the optical-UV flux is emitted from an optically thick, geometrically thin accretion disk and the hard X-ray flux comes from the inverse Compton scattering of optical-UV photons by the hot corona. This model can naturally fit the observational positive relationships between αOX and λO as well as Γ and λO in RQAGNs (Shemmer et al. 2006; Risaliti et al. 2009; Lusso et al. 2010; Brandt & Alexander 2015; Li 2019), where the optical to X-ray spectral index αOX is defined as αOX = 0.384 log[Lν(2500 Å)/Lν(2 keV) (e.g., Lusso et al. 2010), and λO = 8.1νLν(5100 Å)/LEdd is the Eddington ratio based on the optical luminosity at 5100 Å (Runnoe et al. 2012a), with LEdd being the Eddington luminosity. In contrast, the origin of X-ray emission is still unclear in RLAGNs. In observations, RLAGNs appear to have different properties than RQAGNs, for instance the positive relationships listed above in RQAGNs have not been found in RLAGNs (Li 2019; Zhou & Gu 2020). Furthermore, the average X-ray luminosity in RLAGNs is found to be 2–3 times higher than that in RQAGNs (Zamorani et al. 1981; Wilkes & Elvis 1987; Wu et al. 2013; Gupta et al. 2018). This seems to indicate that the X-ray emission from jets is important in RLAGNs. However, Gupta et al. (2018) recently compiled an excellent sample to investigate the differences of X-ray properties between luminous radio galaxies and their radio-quiet counterparts, where the black hole mass and Eddington ratio were well selected and the bolometric luminosity were calculated from mid-infrared emission observed by the Wide-field Infrared Survey Explorer (WISE) mission. They argue that the X-ray emission in radio-loud radio galaxies should also come from a disk-corona system because their distribution of the X-ray slope is very similar with those of radio-quiet counterparts (see Gupta et al. 2018 for details, see also Gupta et al. 2020).


Finally, in order to measure the ICL fraction once we have a background-free ICL map, we created an image of the cluster removing the CHEF models of the foreground and background galaxies. As described in Jiménez-Teja & Benítez (2012), the cluster membership is determined in a two-step process, the PEAK+GAP algorithm (Owers et al. 2011), using the spectroscopic data available for each system. This composite method first identifies the peak of the cluster in the redshift space and selects a redshift window wide enough to contain the whole distribution of velocities assigned to that peak. Implicitly, the size of this window is proportional to the velocity dispersion of the clusters: merging clusters, with a more scattered velocity distribution, will need a wider window, compared to relaxed systems. This crude selection of cluster member candidates is obviously prone to contamination by interlopers. So, we further refine it using the shifting gapper method (Fadda et al. 1996; Girardi et al. 1996; Boschin et al. 2006; Owers et al. 2011), which uses velocity and spatial information on the candidates simultaneously. The shifting gapper method spatially distributes the candidates according to their clustercentric distance in radial bins. The mean velocity of the candidates within each bin is calculated, and those candidates with velocities that are too far from the others are rejected. As unrelaxed clusters are more likely to have a broader spatial distribution, this procedure naturally allows candidates at larger distances to be identified as cluster members for these systems. These two steps are, thus, essential to guarantee that our cluster membership algorithm implicitly takes into account the dynamical state of the systems and does not bias the measurement of their total luminosity, while minimizing contamination by interlopers at the same time. We refer the reader to Jiménez-Teja & Benítez (2012) for further information on the cluster membership selection algorithm.


RCW 57A (also known as NGC 3576, G291.27–0.70, or IRAS 11097–6102) is a H ii region associated with a filament and bipolar bubble, and is located at a distance of 2.4–2.8 kpc (Persi et al. 1994; de Pree et al. 1999). We adopt 2.4 kpc, which is within uncertainties of both the kinematic and spectroscopic determinations (see Persi et al. 1994). Figure 1 depicts the overall morphology of RCW 57A. It contains optically bright nebulosity with several dark globules and luminous arcs (Persi et al. 1994). It is one of the massive star-forming regions in the southern sky, hosting a H ii region (cyan contour) embedded in a filament (white contour) from which a widely extended bipolar bubble (yellow contours) is emerging. A deeply embedded near-IR cluster, consisting of more than 130 young stellar objects (YSOs), is associated with this region (Persi et al. 1994). The observed ratios of the infrared fine-structure ionic lines (Ne ii, Ar iii, and S iv; Lacy et al. 1982) indicate that at least eight O7.5V stars are necessary to account for the ionization of the region. However, even these stars may not be sufficient to account for the Lyα ionizing photons inferred from radio data (Figuerêdo et al. 2002; Barbosa et al. 2003; Townsley 2009). Based on the newly discovered cluster of stars, using X-ray data, Townsley et al. (2014) suggested that an additional cluster of OB stars that were not known before might be deeply embedded. This cluster is located slightly southwest of the center of the near-IR cluster. The 10 μm map (cf., Frogel & Persson 1974) reveals the presence of five infrared sources (IRS; black squares in Figure 1) near the center of the H ii region. These, together with water and methanol maser sources (green crosses in Figure 1) distributed along the filament, are indicative of active ongoing star formation in RCW 57A (Frogel & Persson 1974; Caswell 2004; Purcell et al. 2009). Therefore, RCW 57A is an ideal target to investigate the morphological links among filaments, bipolar bubbles, and B-fields so as to understand the star formation history.


The characterization of the interior of observed exoplanets is one of the main goals in current exoplanetary science. With the large number of newly discovered exoplanets expected in the next 10 years by ground-based surveys such as the Wide Angle Search for Planets (WASP; Pollacco et al. 2006), the Next-Generation Transit Survey (NGTS; Wheatley et al. 2017), and the Hungarian Automated Telescope Network/Hungarian Automated Telescope Network-South (HATNet/HATSouth; Hartman et al. 2004; Bakos et al. 2013), as well as the ongoing Transiting Exoplanet Survey Satellite (TESS) space survey (Ricker et al. 2014) and the upcoming PLAnetary Transits and Oscillations (PLATO) mission (Rauer et al. 2014), a rapid characterization scheme of the interior structure of these planets will become increasingly necessary to further our understanding of planetary populations. The vast majority of the confirmed exoplanets has been identified either through transits or radial velocities surveys. Planets identified with both techniques are characterized by their mass and radius, which, combined, provide a first indication of the bulk composition through comparison with theoretical mass–radius curves (e.g., Valencia et al. 2006; Sotin et al. 2007; Zeng & Sasselov 2013). A common approach to the interior characterization of exoplanets is the use of numerical models to compute interior structures that comply with the measured mass and radius of the planet (e.g., Fortney et al. 2007; Sotin et al. 2007; Valencia et al. 2007; Wagner et al. 2011; Zeng & Sasselov 2013; Unterborn & Panero 2019). As this is an inverse problem, it requires the calculation of a large number of interior models to obtain an overview over possible interior structures (Rogers & Seager 2010a; Brugger et al. 2017; Dorn et al. 2017). If other observables are used in addition to mass and radius, the number of samples needed for an accurate inference of possible interior structures increases drastically, due to the increase in dimensionality (e.g., James et al. 2013). Thus, the inference can quickly become computationally expensive. Moreover, with only mass and radius, possible solutions tend to be highly degenerate, with multiple, qualitatively different interior compositions that can match the observations equally well (e.g., Rogers & Seager 2010a, 2010b).


The object J004415.00 required our special consideration. We notice large variations of spectra at the hydrogen series limits. We designate the limits of the Balmer, Paschen, Brackett and Pfund series in Fig. 4 for J004415.00 with vertical arrows. A jump at the Brackett series limit in the IR spectrum can be clearly seen. The Balmer and Paschen jumps can also be noticed by photometric brightness changes. These inverse jumps at the hydrogen series limits attest to the noticeable contribution of free–free (f–f) and free–bound (f–b) emissions to the spectrum. This confirms the presence of an ionized circumstellar envelope where the f–f and f–b emissions originate, which is typical for B[e]SGs (Zickgraf et al. 1985, 1986, 1989). To take the contribution of f–f and f–b radiations into account and estimate the corresponding spectra, we used the chianti package (Dere et al. 1997; Landi et al. 2013). We consider the case of isothermal pure hydrogen plasma at a temperature of Te = 10 000 K (Lamers et al. 1998). From the spectrum of the star we assume that its effective temperature is Tstar =15 000 K and match the model spectrum to the observations with the following parameters: Te = 10 000 K, EM = 1.37 × 1039 cm−5 (emission measure), Tstar = 15 000 K, Rstar = 43R⊙, AV = 1.1. In order to describe the IR excess of the SED we also add hot dust emission to the model spectrum by assuming it to be effective blackbody radiation with a temperature of about 1000 K (the best fit obtained with Tdust = 1050 K), which is typical for B[e]SG hot circumstellar dust (Lamers et al. 1998). The result of the SED fitting is shown in Fig. 4: the dashed line shows the blackbody radiation, the dotted line designates the contribution of free–free and free–bound emissions, the dash-dotted line demonstrates the dust emission contribution, the solid line indicates the total model spectrum. All spectra shown include the interstellar extinction (Fitzpatrick 1999, assuming RV = 3.1) with AV = 1.1 obtained as the best-fitting parameter. Since the object J004415.00 does not show considerable photometric variability, we incorporate some more published photometric data points for fitting (see Table 3) in addition to the BTA data. For better illustration of the matching between the model and observed spectra, the synthetic photometry of the total model continuum multiplied by the normalized spectrum is shown with filled circles. Note that since the parameters are obtained in the isothermal plasma approximation with fixed temperatures of the star and circumstellar plasma, we report the other parameters derived from them as estimates and do not assess their uncertainties. Nevertheless, our estimates of the model parameters are good enough and allow us to constrain the dust extinction and luminosity of the object.


Cluster radio relics are usually found in the outskirts of merging galaxy clusters. They exhibit elongated morphologies and high degrees of polarisation above 1 GHz (up to 70%, Ensslin et al. 1998; Bonafede et al. 2014; Loi et al. 2019; de Gasperin et al. 2022). The resolved spectral index in radio relics shows a gradient: it steepens towards the cluster centre and flattens towards the outskirts. Their size can reach up to ∼2 Mpc, and high-resolution observations have revealed filamentary structures within relics themselves (Di Gennaro et al. 2018; Rajpurohit et al. 2020, 2022a,b; de Gasperin et al. 2022). The Largest Linear Sizes (LLS) and radio powers of relics are correlated, as well as the integrated spectral index and the radio power (van Weeren et al. 2009b; Bonafede et al. 2012; de Gasperin et al. 2014). Relics trace ICM shock waves with relatively low (M   3) Mach numbers (Finoguenov et al. 2010; Akamatsu et al. 2013; Shimwell et al. 2015; Botteon et al. 2016). The acceleration of electrons is believed to proceed via diffusive shock acceleration (DSA) in the ICM (Ensslin et al. 1998; Roettiger et al. 1999), in which particles scatter back and forth across the shock front gaining energy at every crossing. Nevertheless, this mechanism has been shown to be rather inefficient in accelerating electrons from the thermal pool (Vazza & Brüggen 2014; Vazza et al. 2016; Botteon et al. 2020a; Brüggen & Vazza 2020; see Brunetti & Jones 2014 for a review). Recently, it has been suggested that seed electrons could originate from the tails and lobes (driven by AGN outflows) of cluster radio galaxies (Bonafede et al. 2014; van Weeren et al. 2017; Stuardi et al. 2019), which alleviates the requirements of high acceleration efficiencies at cluster shocks (e.g., Markevitch et al. 2005; Kang et al. 2012, 2017; Botteon et al. 2016; Eckert et al. 2016). In some cases, double relics have been detected on opposite sides of the cluster centre (e.g., Rottgering et al. 1997; van Weeren et al. 2010, 2012b; Bonafede et al. 2012; de Gasperin et al. 2015a). In these clusters it is possible to constrain the merger history, providing important information about the formation processes of relics.


For comparisons with the light curve YORP constraints, the YORP effect acting on Cuyo could be predicted by computing the total recoil forces and torques from reflected and thermally emitted photons from the asteroid surface using the ATPM. These calculations were made for both a smooth and rough surface, and were averaged over both the asteroid rotation and elliptical orbit (see Rozitis & Green 2012, 2013, for methodology). As demonstrated in Rozitis & Green (2012), the inclusion of rough-surface thermal-infrared beaming effects in the YORP predictions tends to dampen the YORP rotational acceleration on average but can add uncertainties of up to several tens of per cent if the roughness was varied across the surface. Since the light curve inversion produced convex shape models only, then shadowing and self-heating effects inside global-scale concavities (see Rozitis & Green 2013) were not possible to model. However, a study of non-convex shape models for fast two to four hour rotators in Rozitis & Green (2013) indicated that such asteroids have rather minimal levels of global-scale concavities, and the ~ 2.7 h rotation period of Cuyo implies that its shape could be similar. Furthermore, the Tangential-YORP effect, that is, a predicted rotational acceleration caused by temperature asymmetries within exposed rocks and boulders on the surface of an asteroid (Golubov & Krugly 2012), was also not included in the ATPM predictions. However, the very low thermal inertia value measured for Cuyo implies the absence of rocks and boulders on its surface of the quantity and size that are necessary to induce a significant Tangential-YORP component. As Cuyo is likely to be an S-type rubble-pile asteroid, a bulk density equivalent to that measured for the S-type rubble-pile asteroid (25143) Itokawa (Abe et al. 2006) of 2 g cm−3 was assumed for the YORP computations. Using the thermo-physical properties derived earlier, the ATPM predicts YORP rotational acceleration of (−6.39 ± 0.96) × 10−10 rad day−2 for the nominal shape model. The uncertainty given here corresponds to the standard deviation of results when the degree of surface roughness israndomly varied across the surface of Cuyo (see Lowry et al. 2014, for details of the Monte Carlo methodology used). These values lie well within the light curve rotational acceleration constraints determined previously.


The understanding of proton acceleration at the Sun in large solar energetic particle (SEP) events has oscillated between flare and shock pictures (Cliver 2009b; Reames 2015). The earliest picture following the discovery of ground-level events (GLEs; major SEP events requiring >500 MeV protons) by Forbush (1946) was that protons were accelerated in flares, the clear choice in the absence of other observations. Subsequently, Wild et al. (1963) conjectured, mainly on the basis of radio observations, that large SEP events required coronal shock waves as manifested by type II solar radio bursts. Smaller electron-dominated SEP events were linked to metric type III bursts. Early observational support for this view on the SEP side was provided by Lin (1970). Through the work of Švestka & Fritzová-Švestková (1974), Kahler et al. (1978, 1984), Cliver et al. (1982, 1983a, 1983b), Cane & Stone (1984), Klecker et al. (1984), Mason et al. (1984, 1986), Meyer (1985), Reames et al. (1985, 1994, 1996), Cane et al. (1986, 1988), Luhn et al. (1987), Reames (1990, 1999), Kahler (1992, 1994), Gosling (1993), and others, involving various comparisons of SEP events with flare electromagnetic emissions and coronal mass ejections (CMEs), as well as considerations of SEP composition, charge states, and the longitude distribution of SEP-associated flares, the two-class picture of SEP acceleration presciently proposed by Wild et al. (1963) became established. The new consensus view was almost immediately challenged by observations of the first large (“gradual”; Reames 1993) proton events observed by the Advanced Composition Explorer (ACE). Mazur et al. (1999), Cohen et al. (1999), Mason et al. (1999a), and Mason et al. (1999b) reported that large SEP events, including GLEs, recorded by ACE and SAMPEX in 1997 and 1998 had elemental composition and charge states at >10 MeV/nuc that were similar to those found in small (“impulsive”) SEP events (e.g., Mason et al. 1986; Luhn et al. 1987) at lower energies. Subsequently, Cane et al. (2002, 2003, 2006) presented evidence based on low-frequency radio observations, SEP composition data, and flare location to argue for the presence of a flare-accelerated high-energy (>25 MeV) proton component in large SEP events to augment that produced by coronal/interplanetary shock waves driven by CMEs. The relative importance of flare and shock components was left as an open question.


The core of a neutron star is composed primarily of neutrons, with ∼5%–10% of the mass in protons; for the electrically neutral medium, the number density of electrons is equal to that of the protons. At the supranuclear densities of the outer core, the Fermi energy for protons and neutrons is well above the typical temperature of a mature neutron star, and both the neutrons and protons are expected to condense into Bardeen–Cooper–Schrieffer superfluids, with 3PF2 and 1S0 Cooper pairing, respectively (Migdal 1959; Baym et al. 1969). To support rotation, the neutron superfluid forms an array of quantized vortices, filaments of microscopic cross section, each carrying one quantum of circulation. The superconductivity of the protons is predicted to be type II, and the magnetic field is supported by an array of quantized flux tubes, each carrying one quantum of magnetic flux. Fermi-liquid interactions between the two condensates results in a nondissipative coupling between the mass currents of the two species (Andreev & Bashkin 1975; Chamel & Haensel 2006), so the neutron vortices are magnetized by entrained proton currents (Alpar et al. 1984a). Electron scattering from magnetized vortices and flux tubes produces dissipative and nondissipative forces on the vortices and flux tubes. The magnetic interaction at junctions between magnetized neutron vortices and flux tubes is energetic enough to produce pinning, wherein the neutron vortices pin to the dense array of flux tubes in the outer core (Srinivasan et al. 1990; Jones 1991; Chau et al. 1992; Ruderman et al. 1998; Link 2012b), similar to the predicted pinning of the vortices to the nuclear lattice of the crust (Anderson & Itoh 1975; Alpar 1977; Epstein & Baym 1988; Donati & Pizzochero 2006; Avogadro et al. 2007; Link 2009). Thermal fluctuations stochastically excite vortex motion, causing the neutron vortices to slip with respect to the flux tubes (Ding et al. 1993; Sidery & Alpar 2009; Link 2014).


We consider a radio galaxy of SMBH mass M = 109
M
9
M
⊙ with a mass accretion rate of

Ṁ=ṁLEdd/c2≃1.4×1022M9ṁ−4gcm−2

, where c is the speed of light and L
Edd is the Eddington luminosity. The gravitational radius of the BH is r

g
 = GM/c
2 ≃ 1.5 × 1014
M
9 cm. We consider that the accretion flow is in the MAD state, and then the magnetic field strength around the SMBH is estimated to be

Bmad=ṀcΦmad2/(4π2rg2)≃1.1×103M9−1/2ṁ−41/2Φmad,1.7G

 (e.g., Yuan & Narayan 2014), where Φmad ≈ 50Φmad,1.7 is the saturated magnetic flux (Tchekhovskoy et al. 2011; Narayan et al. 2012; McKinney et al. 2012; White et al. 2019). The high-resolution GRMHD simulation with a BH spin parameter a = 0.9375 suggests that magnetic reconnection occurs at a distance of r
rec ∼ 2r

g
 (Ripperda et al. 2022). The value of r
rec could depend on a or other parameters, but we fix r
rec = 2r

g
 throughout this paper for simplicity. We estimate the reconnecting magnetic field strength to be (see Appendix A)
1

Brec≈2Bmadrrecrg−2≃3.9×102M9−1/2ṁ−41/2Φrec,1.2G,

where

Φrec=2Φmad(rrec/rg)−2

 is the effective magnetic flux at the reconnection region. The magnetosphere will be formed around the SMBH. The minimum number density of the magnetosphere that can maintain the electric current for the BZ process is (Goldreich & Julian 1969; Levinson & Cerutti 2018)
2

nGJ=BrecΩF2πec≈Brec8πerg≃2.2×10−4M9−3/2ṁ−41/2Φrec,1.2cm−3,

where Ω
F
 ≈ ac/(4r

g
) is the field line angular velocity (Tchekhovskoy et al. 2010; Nathanail & Contopoulos 2014; Ogihara et al. 2021; Camilloni et al. 2022) and we assume the BH spin parameter as a ∼ 1. For the magnetosphere, which consists of e
+
e
− pair plasma with the density n
GJ, the magnetization parameter is
3

σB,GJ=Brec24πnGJmec2≈6.8×1013M91/2ṁ−41/2Φrec,1.2.

This value should be regarded as an upper limit, because the number density of the magnetosphere can be higher than n
GJ. Various mechanisms of particle injection into the BH magnetosphere have been proposed (see Appendix B), which can lead to multiplicity of κ
± ≡ n/n
GJ ∼ 1 − 103. This results in the magnetization parameter of σ

B
 ≳ 1010.