Reconnection rate in a laminar flow can be estimated, or defined, in terms of normal diffusion of the magnetic field by magnetic diffusivity η on large scales or, in other words, in terms of the (root-mean-square, henceforth rms) average distance

 the field spreads relative to a fixed point. The related random walk of magnetic field lines was discussed by Jokipii (1966; see also Snodin et al. 2013, 2016; Servidio et al. 2014). This is of course the Taylor or normal diffusion (of particles or magnetic field) in which the rms distance between the diffusing material and a fixed point increases as

 with time; see, e.g., Eyink et al. (2013) and Jafari et al. (2019). For a diffusing magnetic field,

. In the absence of turbulence, in a reconnection zone of width δ and length Δ (parallel to the local magnetic field), using the Alfvén timescale

, and using mass conservation

, we recover the reconnection speed
1

This is, of course, the well-known Sweet–Parker reconnection rate (Parker 1957; Sweet 1958). Reconnection, and/or other instabilities such as tearing modes (Furth et al. 1963), will in general generate turbulence (Eastwood et al. 2009; Jafari & Vishniac 2018a), with the implication that the laminar Sweet–Parker model is far from realistic in turbulent systems such as most astrophysical fluids. In the turbulence inertial range, i.e., at scales larger than dissipative scale but smaller than the larger scales where Taylor (normal) diffusion of the magnetic field occurs, diffusing particles will undergo super-linear Richardson diffusion;

 which is a two-particle diffusion, i.e., d is the rms separation between any pair of particles undergoing diffusion in the inertial range. If we consider magnetic diffusion in the turbulence inertial range, we have to consider Richardson diffusion of the field, in terms of the rms distance the field spreads during the time t; see Figure 1. The eddy turnover time, in the inertial range, is of order

 with d being the length scale perpendicular to the mean magnetic field. Here,

 denotes the energy transfer rate, with turbulent velocity VT and parallel energy injection length scale

. This corresponds to the Richardson diffusion;

. The super-linear nature of Richardson diffusion broadens the reconnection zone and thereby enhances the reconnection rate. To see this, using mass conservation

, and substituting the Alfvén time

, one arrives at the fast reconnection speed (Lazarian & Vishniac 1999; Jafari et al. 2018; Lazarian et al. 2019, 2020);
2


Rather than AGN feedback, it is possible that the effects we are seeing are from a different process coeval or prior to the onset of AGN accretion. Several works have pointed out that AGN activity coincides with a recent starburst, with the AGN having significant accretion events at least ∼200 Myr after the starburst has occurred (Davies et al. 2007; Wild et al. 2007; Wild, Heckman & Charlot 2010; Yesuf et al. 2014) giving the neutral material time to propagate out to the impact parameters probed by COS-AGN (Heckman et al. 2017). With a sample of QSO sightlines probing the CGM around 17 low-redshift starburst and post-starburst galaxies, Heckman et al. (2017) have observed a similar signature of enhanced EWs of Ly α, Si iii, and C iv (the latter of which is not measured in our control sample) relative to a control-matched sample (matched in stellar mass and impact parameter). In the range of impact parameters and stellar masses probed by COS-AGN, the strength of our enhanced EW signature is consistent with the values probed by Heckman et al. (2017). However, the results of Heckman et al. (2017) show strong offsets in the kinematics of the gas from the host galaxy (≈100 km s−1; see fig. 5 from Heckman et al. 2017), whereas the COS-AGN sightlines do not (bottom panel of Fig. 6). Assuming that the AGN activity was triggered by the starburst, a minimum delay time of 200 Myr could allow for any starburst-driven winds to dissipate and kinematic offsets to no longer be present at the impact parameters of the COS-AGN sample. Although this starburst picture provides a possible explanation of our observations, we caution that starbursts are not the only astrophysical event linked to AGN accretion activity. For example, mergers that trigger the AGN (Ellison et al. 2011, 2013; Satyapal et al. 2014; Silverman et al. 2014; Goulding et al. 2018) could potentially affect the surrounding CGM gas. Past and future work focusing on the CGM of galaxy mergers can further test this result (Johnson et al. 2014; Hani et al. 2017; Bordoloi et al. in preparation).


The radial distribution of S/H ratios and the corresponding gradient are shown in panel (b) of Fig. 12. We obtain a slope of −0.035 ± 0.006 dex kpc−1 (very similar to the one we obtain with the ICF of ADIS20, as can be seen in Table 8), which is consistent with the one of −0.041 ± 0.014 dex kpc−1 estimated by Rudolph et al. (2006) using FIR lines and also very similar to the slope of our O/H gradient. We report a dispersion around the S/H gradient of 0.10 dex, somewhat larger than the individual observational uncertainties. Recently, Fernández-Martín et al. (2017) reported a slope of −0.108 ± 0.006 dex kpc−1 using optical spectra for H  ii regions located at RG between 5 and 17 kpc. That value of the slope is considerably much steeper than our determination and other previous estimates from the literature (e.g. Shaver et al. 1983; Simpson et al. 1995; Afflerbach, Churchwell & Werner 1997; Rudolph et al. 2006). Esteban & García-Rojas (2018) observed some H ii regions with a very low ionization degree – O2 +/O  0.03 – but measurable [S iii] 6312 or 9069 Å lines. For such nebulae is possible to assume that S/H ≈ S+/H+ + S2 +/H+, since the contribution of S3 +/H+ in those objects is expected to be negligible. The objects with such properties are IC 5146, Sh 2-235, Sh 2-257, and Sh 2-271, whose total abundances of S/H range from 6.70 to 7.01 but, unfortunately, cover a rather narrow range of RG – between 9.3 and 11.7 kpc – and no confident gradient can be estimated with so small baseline. Inspecting Tables 3 and 4 we can see that there is a sizable group of low-ionization degree H ii regions that lack of determination of their S2 +/H+ ratios. This is because the rather faint auroral [S iii] 6312 Å line could not be detected in those objects. We plan to obtain additional optical spectra covering the bright nebular [S iii] 9069, 9532 Å lines of that group of nebulae for trying to increase the number of objects with S/H ratios determined without ICF and estimate a more precise gradient for this element.


It is well known that magnetic fields stabilize the KH instability from the perspective of theoretical and idealized linear calculations such as those presented in Chandrasekhar (1961), which imply that the velocity shear must be super-Alfvénic to lead to the generation of the KH instability. However, it is by no means clear that more complex and typical environments such as the solar corona resemble such idealized conditions. The argument for suppression of the KH instability assumes that the magnetic fields and the flow across a boundary are highly aligned. If the magnetic field is more azimuthal, the restoring tension is reduced and the flow can be more susceptible to KH instability. In the extreme situation of a magnetic field orthogonal to two tangential streams, the sheared flow is always unstable to the KH instability, just as in the hydrodynamic case, even for subsonic flows, and the magnetic field basically plays no role. If such nontangential magnetic field conditions occur in the low solar corona, as might be expected, various forms of interchange reconnection can occur along the boundaries of nominally fast and slow wind where loops and open field collide, leading to current sheet formation and magnetic fields that cross from one side of what was a tangential flow to the other. For instance, Schwadron & McComas (2021) argue that nontangential magnetic fields crossing shearing flows can be the origin of switchbacks. So the existence of switchbacks may, in their interpretation, be a manifestation of nontangential magnetic fields associated with tangential flows as well. In these regions, very complicated structures with a weak and probably quite disordered magnetic field can arise. The simple idealized KH instability of Chandrasekhar (1961) is certainly unlikely to occur, and the KH instability may resemble its gasdynamic form instead. Hence, despite previous studies that investigated the conditions for the onset of KH instability in the solar wind and in coronal plumes (e.g., Parhi et al. 1999; Velli et al. 2011) and concluded that the KH instability may arise only in super-Alfvénic regions, at distances larger than 10 R
⊙ (Velli et al. 2011 found that the KH instability could become important at 0.2–0.3 au), the KH instability has been widely imaged in the sub-Alfvénic low solar corona, at distances well below 10 R
⊙, in strong magnetic field environments associated with active regions (Yuan et al. 2019), at the flanks of coronal mass ejections (Foullon et al. 2011; Ofman & Thompson 2011; Foullon et al. 2013; Möstl et al. 2013; Nykyri & Foullon 2013), along solar prominence/corona discontinuity layers (Berger et al. 2010; Ryutova et al. 2010; Hillier & Polito 2018; Yang et al. 2018), in solar jets (Kuridze et al. 2016; Li et al. 2018), associated with streamer wave phenomena (Feng et al. 2013), and in white-light eclipse observations (Druckmüller et al. 2014). This is because the realistic solar corona is quite unlike a nice cartoon showing well-defined large-scale magnetic field lines; rather, at least locally, it is characterized by a very complex magnetic topology. The onset of the KH instability depends on the orientation of the magnetic field relative to the tangential flows. It follows that even the sub-Alfvénic velocity shear along the fast/slow boundary in the solar corona can lead to KH instability growth, provided that, as expected, the streamer belt region does not have a nicely ordered magnetic field and instead possesses locally a very complicated structure with a nontangential magnetic field configuration. Although theoretically predicted to play an important role in the plasma dynamics between high- and low-speed coronal streams flowing alongside each other (Ismayilli et al. 2018), the KH instability has not yet been detected at the edges of coronal holes adjacent to equatorial streamers, where shear due to the outflow of fluids with different velocities can initiate KH vortices. This lack of evidence motivates the present work, which indeed aims at providing, for the first time, possible observational evidence for manifestations of the KH instability in the solar corona in the interaction region between fast and slow solar wind.


Now, we must consider a specific distribution of electrons. Ideally, with a well-constructed background-subtracted image, only recently injected coronal material should be visible in excess total brightness; hence, ideally, ne should be identically zero outside the CME. However, reality is not so kind as to clearly delineate between CME and non-CME material. The explosive eruption and ejection of coronal material may rearrange previously quiescent material. If such material is pushed into a line of sight that passes through the CME, then, due to the optically thin nature of the corona, it will be impossible to distinguish newly ejected material from newly arranged material. A further issue that must be confronted when choosing a functional form for ne is the lack of observation or direct measurement on the internal mass distribution of a CME, as well as imprecise knowledge on the morphology of the CME. For example, is a CME balloon-shaped with a circular cross section (Millward et al. 2013) or croissant-shaped with an elliptical cross section (Thernisien et al. 2006, 2009)? Are there one or more cavities in the CME, and if so, where are the cavities located, how wide are they relative to the CME, and how low is the cavity density relative to the edge density? Is the mass distributed symmetrically relative to the central axis of the CME? Does the mass distribution change with time, either by pileup at the CME leading edge or by continuous mass inflow from the lower atmosphere (Bein et al. 2013; DeForest et al. 2013a)? Nevertheless, in spite of such epistemic uncertainty on the internal mass distribution, if the shape of the CME is known—either directly through polarimetry (de Koning & Pizzo 2011) or by assuming a shape (Thernisien et al. 2006; Millward et al. 2013)—and hence the start and end points of the line-of-sight integral are known, one might choose a particularly simple distribution, namely,

 (Feng et al. 2013b). On the other hand, if both the CME mass distribution and morphology are poorly known, as was the case in the pre-STEREO era, then one might choose an even simpler distribution, that is, a point source,
12

where δ is the Dirac delta function and n0 is a constant. To enable direct comparison of our three-view mass determination with the two-view mass determination of CV09, we employ the point-source distribution.


Using the whole sample (\hbox{$\bar{z}=0.40$}z̅ = 0.40), we find a decreasing faint end for both datasets with consistent values between HST (α =  − 0.76 ± 0.07) and Subaru (α =  − 0.78 ± 0.06). Separating between low-redshift (\hbox{$\bar{z}=0.29$}z̅ = 0.29) and high-redshift (\hbox{$\bar{z}=0.51$}z̅ = 0.51) samples, we find an evolution of the faint end slope of 1.7σ with HST and 2.6σ with Subaru. There is thus a mild decrease of the faint end slope (less negative α) with increasing redshift over the range (0.187 z 0.686). This evolution is in good agreement with recent papers in the literature: in particular Zenteno et al. (2016) found a decrease of the RS faint end at 2.1σ for a wider range of redshifts (0.1 z 1.13), but with ~ 80% of their clusters being in the same redshift range as ours. De Propris et al. (2013) claim that the evolution in the faint end slope has a significant contribution from surface brightness selection effects. They used HST data of differing depths on a single cluster (MS 1358.4+6254) to show that surface brightness selection effects become important above the formal magnitude limit of their data and that they affect the RS GLF at magnitudes z ≥ 24.5 for 2.7 ks HST exposures (see their Fig. 18). The faint RS for their cluster has F814W − z = 0.25, implying that the SB selection effects in their sample become important at F814W> 24.75. On the other hand, our CLASH data are significantly deeper than theirs (4.1 ks) and we limit our GLFs at F814W 24.5. Therefore, the real SB selection effects noticed in De Propris et al. (2013) should not be playing a role in our space-based results. In addition, De Propris et al. (2013) claim that previous estimates of the evolution in the RS GLF (e.g.,  De Lucia et al. 2007; Rudnick et al. 2009) were also due to SB effects. Both of those works were based on the same ground-based data with a formal magnitude limit of I = 24 or 24.5 (for the low- and high-redshift clusters, respectively) and the evolution in the GLF was seen over the faintest 2 mag. We cannot directly address the role of SB effects in the EDisCS results without detailed simulations on those data (see below for such simulations for our clusters) but the similarity between our HST and Subaru GLFs imply that the EDisCS evolution in the GLF is not dominated by SB effects.


Various surveys of SNRs in our Galaxy and nearby galaxies have been carried out at radio, X-ray, Infrared (IR), and optical wavelengths. The first extragalactic SNR candidates were identified in the LMC by Mathewson & Healey (1964) and later confirmed with a combination of radio and optical techniques by Westerlund & Mathewson (1966). To date, a total of 60 SNRs have been confirmed in the LMC with an additional 14 suggested candidates (Maggi et al. 2016; Bozzetto et al. 2017; Maitra et al. 2019). However, sensitivity and resolution limitations severely reduce the effectiveness of the past and present generations of radio and X-ray searches for SNRs in galaxies beyond the Small and Large Magellanic Clouds (MCs) (Goss et al. 1980; Long et al. 1981; Cowan & Branch 1985; Matonick et al. 1997; Matonick & Fesen 1997; Millar, White & Filipovic 2012; Galvin & Filipovic 2014; Sasaki et al. 2018; Lin et al. 2020; Sasaki 2020). As a result, optical studies have produced the largest number (∼1200) of new extra-Magellanic SNR candidates. Optical extragalactic searches for SNRs are mainly done by using an emission line ratio criterion of the form [S ii]/H α > 0.4–0.5 (Mathewson & Clarke 1973; Dodorico, Dopita & Benvenuti 1980; Fesen 1984; Blair & Long 1997; Matonick & Fesen 1997; Dopita et al. 2010b; Lee & Lee 2014; Vučetić et al. 2019b, a, 2018; Lin et al. 2020). This criterion separates shock-ionization from photoionization in SNRs from H ii regions and Planetary Nebulae (PNe) (Frew & Parker 2010). SNR radiative shocks collisionally excite sulphur ions in the extended recombination region resulting in S+, hence the larger contribution of [S ii] accounting for an increase of the [S ii] to H α ratio. In typical H ii regions, sulphur exists predominantly in the form of S++, yielding low [S ii] to H α emission ratios. Ratios from narrow-band imaging are usually verified spectroscopically, since [N ii] lines at 6548 and 6584 Å can contaminate the H α images at an unknown and variable level. Spectroscopic observations of such emission nebulae also can provide other evidence of shock heating, such as strong [O i] λ6300 emission, elevated [N ii] to H α with respect to H ii regions, or high [O iii] electron temperatures, verifying the candidate as being an SNR (Blair, Kirshner & Chevalier 1981, 1982; Long et al. 1990; Smith et al. 1993; Blair & Long 1997). Although somewhat biased as an isolated criterion, this method is proven and a good way of identifying ordinary radiatively cooling SNRs in nearby galaxies. We note that young, Balmer-dominated SNRs (Chevalier, Kirshner & Raymond 1980) would be missed by this criterion.


These two cases correspond to the upper and lower boundaries of the tilt term. They are usually written as

(73)

\begin{equation}
\frac{{\mathrm{\partial} \sigma _{Rz}^2\left( {R,0} \right)}}{{\mathrm{\partial} z}} = \lambda (R)\frac{{\sigma _{RR}^2\left( {R,0} \right) - \sigma _{zz}^2\left( {R,0} \right)}}{R},
\end{equation}

whereλ(R) ∈ [0, 1]. The factor λ(R) can be derived either analytically from orbit integration or is assumed λ = 0 for simplicity (e.g. van der Kruit & Freeman 1986; Lewis & Freeman 1989; Sackett & Sparke 1990). Numerical simulations (e.g. Carlberg & Innanen 1987; Bienaymé 2000) are performed to calculate explicitly the moments for a given gravitational potential. The result of the above studies is that, at the Sun's position λ ≃ 0.5. In our model for the Galactic kinematics, we prefer to adopt the analytical formulation of λ(R) given by Amendt & Cuddeford (1991):

(74)

\begin{equation}
\lambda (R) = {\left. {\frac{{{R^2}{\mathrm{\partial} _{R,z,z}}\Phi }}{{3{\mathrm{\partial} _R}\Phi + R{\mathrm{\partial} _{R,R}}\Phi - 4R{\mathrm{\partial} _{z,z}}\Phi }}} \right|_{\left( {R,z = 0} \right)}}.
\end{equation}

The expression (74) is null for a potential separable in cylindrical coordinates because the term $\frac{{\mathrm{\partial} {\Phi _{{\rm {tot}}}}}}{{\mathrm{\partial} R\mathrm{\partial} {z^2}}} = 0$. In spherical coordinates λ = 1, the relation (73) will be used in the following to describe the tilt of the velocity ellipsoid, obtaining for the DM halo

(75)

\begin{equation}
{\lambda _{{\rm DM}}}(R) = - \frac{{{R^2}}}{{{R^2}\left( {{q_\Phi }^2 - 2} \right) + 2{h_{r,{\rm DM}}}^2\left( {{q_\Phi }^2 - 1} \right)}},
\end{equation}

and similarly, a unitary constant value for the bulge and stellar halo components is estimated. Finally, for the important contribution of the disc we simplify equation (73) as

(76)

\begin{equation}
{\lambda _D}(R) = - \int _0^\infty {\frac{{k{R^2}{J_1}(kR)h_z^{ - 1}{\rm d}k}}{{R\left( {k - \frac{4}{{{h_z}}}} \right){J_0}(kR) + 2{J_1}(kR)}}}
\end{equation}

that has to be included in equation (73) with a sum over all the discs components.


We have used 3.0–75.0 keV NuSTAR data to probe any cyclotron line feature. To describe the continuum of 4U 1700–37, we have applied the NPEX model [cons*TBpcf*(powerlaw*npex+gaus+gaus)], following the previous work of Jaisawal & Naik (2015a). The NPEX model has been created by adding two cutoffpl models with their cutoff energies tied to each other and keeping the photon index of one to be frozen at –2.0. For the best fit, the χ2/d.o.f is found to be 577.64/475. The fit shows some residuals in the overall spectrum. We added a Gaussian absorption model around 39 keV (following the previous work of Jaisawal & Naik 2015a), but the best fit gives the line energy as $15.44^{+0.56}_{-0.53}$ keV with χ2/d.o.f = 487.32/472. The width and the depth of the line are found to be $5.47^{+0.90}_{-0.78}$ keV and $1.29^{+0.51}_{-0.39}$, respectively. The chance probability of the line has been computed using the ftest task in xspec. The F-test with this absorption line gives an F value  = 29.2 and a chance probability of 2.61 × 10−17(Table 3). If we add another Gaussian absorption line at 38.9 keV (Energy value frozen) the best-fitting χ2/d.o.f is found to be 486.8/470. This indicates that the second absorption line is not required for the fit. If we use only one Gaussian absorption line and freeze the line energy at 38.9 keV then the width and the depth of the line are found to be $4.54_{-0.87}^{+0.90}$ keV and $2.87_{-1.05}^{+1.24}$, respectively with a χ2/d.o.f  = 549.2/473. The ftest gives a chance probability of the 38.9 keV line to be 6.4 × 10−6. So, with NPEX model we find two valid model combinations of the data. One, the presence of a Gaussian absorption line at ∼15 keV, two, the presence of a Gaussian absorption line at 38.9 keV. But, the presence of both lines together is not supported by the data. The 10.0–70.0 keV flux of the source is found to be (2.26 ± 0.01) × 10−9 erg cm-2s-1, much lower than the value (5.6 ± 0.3) × 10−9 erg cm-2s-1, previously reported from SUZAKU data (Jaisawal & Naik 2015a).


Since pulsation can be detected from the ULX pulsars, their Alfv$\rm \acute{e}$n radius should be larger than the neutron star radius RA ≥ R. This means that the neutron star dipole magnetic field cannot be arbitrarily small. This places a lower limit on the neutron star dipole magnetic field (as a function of mass accretion rate):
(16)
\begin{eqnarray*}
B_{\rm p} \gt B_{\rm p,min}= 2.8\times 10^8 \skew4\dot{M}_{\rm 18}^{1/2} \, \rm G.
\end{eqnarray*}
During the calculations, a typical neutron star radius of $10\, \rm km$ is assumed.8 This idea is similar to that of accreting normal neutron stars ( Bildsten et al. 1997; Zhang & Kojima 2006). Accreting neutron stars in high-mass X-ray binaries are often observed as X-ray pulsars. While, the pulsation of accreting neutron stars in low-mass X-ray binaries is often not detected. This may because neutron stars in low-mass X-ray binaries have a lower dipole magnetic field. This also means that if some accreting magnetars have a low dipole magnetic field, then they may not been observed as pulsating sources. Finding pulsations is only one way to confirm the neutron star nature of ULX sources. Dall’Osso et al. (2015)’s lower limits on the mass accretion rate is about $5\times 10^9 \, \rm G$, corresponding to an accretion rate $\skew4\dot{M} \sim 38 \times 10^{18} \, \rm g \, s^{-1}$ (inset in their fig. 2). According to equation (16), the corresponding lower limit at that accretion rate is about $1.7 \times 10^9 \, \rm G$. A factor of 3 difference is caused by the coefficient of 0.5 in the definition of the magnetospheric radius. The lower limits on magnetic field here (equation 16) is a function of the corresponding mass accretion rate. Although the accretion torque information is not required in obtaining equation (16), Dall’Osso et al. (2015) chose a specific accretion torque and combined it with equation (16). Therefore, a specific numerical value for the magnetic field lower limit can be obtained there.


Left panel: observed-frame H − [3.6] color plotted vs. the observed [3.6] magnitude for our sample of BBGs, color-coded by their photometric redshift and scaled in size as a function of their stellar mass (legend shown in right panel). The CANDELS color-selected sample is plotted in gray with the size also scaled according to the masses. The 0.3σ, 1σ, and 2σ distributions of the mass-limited sample are shown by the light blue density regions. The black triangles represent the four massive galaxies at z > 4.5 found by Huang et al. (2011), black filled circles show the extremely red sources from Caputi et al. (2012), and black diamonds correspond to the H-band dropouts reported by Wang et al. (2016). Lines (dashed) of constant H values are also shown. The darker background indicates the regions of lower completeness for the H band (Guo et al. 2013). Individual error bars are not plotted for clarity, but the average values for our sample of BBGs are shown in the top right corner of each panel. The H-band upper limits (H − [3.6] lower limits) are also shown. Right panel: rest-frame U − V vs. V − J color–color plot, where BBGs are color-coded by SFR and scaled by stellar mass. The SFR lower limits are shown in dark gray. Sources from the CANDELS color-selected sample scaled by mass are also shown. The 0.3σ, 1σ, and 2σ distributions of the mass-limited sample are shown by the light blue areas. The MIPS-detected galaxies are surrounded by a circle, while the X-ray detected galaxies are highlighted with an asterisk inside the symbol. The Whitaker et al. (2011) upper boundary (black wedge) separates quiescent galaxies (top left) from SFGs (bottom). The black diagonal line denotes an additional criterion proposed in our work (perpendicular to the attenuation vector) to separate bSFGs from dSFGs. The plot also includes a 1 mag attenuation vector (which assumes a Calzetti et al. 2000 law). The H-band upper limits (U − V lower limits) are also shown.


Fast radio bursts (FRBs) are cosmological radio transients with millisecond durations. Since the first FRB (FRB 010724, the Lorimer burst) was discovered in 2007 (Lorimer et al. 2007), hundreds of FRB sources have been detected, dozens of which are repeaters (e.g., the CHIME/FRB Collaboration et al. 2021). Recently, a Galactic FRB, FRB 200428, was detected to be associated with SGR J1935+2154 (Bochenek et al. 2020; CHIME/FRB Collaboration et al. 2020; Mereghetti et al. 2020; Li et al. 2021a; Ridnaia et al. 2021; Tavani et al. 2021), which suggests that at least some FRBs originate from magnetars born from the core collapse of massive stars (e.g., Popov & Postnov 2013; Katz 2016; Murase et al. 2016; Beloborodov 2017; Kumar et al. 2017; Yang & Zhang 2018, 2021; Metzger et al. 2019; Lu et al. 2020; Margalit et al. 2020; Wadiasingh et al. 2020; Wang et al. 2022; Zhang 2022). However, FRB 20200120E was found to be in a globular cluster of a nearby galaxy, M81 (Bhardwaj et al. 2021; Kirsten et al. 2022). This is in tension with the scenario that invokes active magnetars with ages ≲10 kyr formed in core-collapse supernovae (Kremer et al. 2021; Lu et al. 2022) and suggests that FRBs might originate from magnetars formed in compact binary mergers (Margalit et al. 2019; Wang et al. 2020; Zhong et al. 2020; Zhao et al. 2021). Therefore, the physical origin of FRBs is still not well constrained from the data (e.g., Cordes & Chatterjee 2019; Petroff et al. 2019; Zhang 2020; Xiao et al. 2021). The growing FRB detections start to shed light on the diversity among the phenomena. The repeaters presented in the first CHIME FRB catalog have relatively larger widths and narrower bandwidths compared with one-off FRBs (Pleunis et al. 2021). The behaviors of fluence with respect to peak flux exhibit statistically significant differences between bursts with long and short durations (Li et al. 2021c). Multiple origins for the FRB population seem increasingly likely.


In active galactic nuclei (AGNs), the gaseous accretion disc around the SMBH may facilitate binary formation and mergers of stellar-mass compact objects (McKernan et al. 2014; Bellovary et al. 2016; Bartos et al. 2017; Stone, Metzger & Haiman 2017; Tagawa, Haiman & Kocsis 2020a). In this scenario, BHs form in situ in the vicinity of a GN and sink to the inner region due to mass segregation or they are delivered to these regions by infalling globular clusters (Morris 1993; Miralda-Escudé & Gould 2000; Freitag, Amaro-Seoane & Kalogera 2006; Hopman & Alexander 2006; O’Leary et al. 2009; Antonini 2014), then get captured in the disc by hydrodynamic drag as they cross the disc (e.g. Goldreich, Lithwick & Sari 2002; Bartos et al. 2017; Yang et al. 2019b; Tagawa et al. 2020a). Alternatively, some BHs may have formed in the disc itself (Levin 2007; Stone et al. 2017). Once in the disc, BHs get transported to the inner regions by exchanging angular momentum with the surrounding gas (Goldreich & Tremaine 1979). In certain regions, the BHs open an annular gap in the accretion disc and accumulate in a narrow range of radii, the so-called migration traps (Bellovary et al. 2016; Secunda et al. 2019, 2020, 2021). Bellovary et al. (2016) argue that migration traps may be expected to be close to the SMBH from ∼20 to ∼300 Schwarzschild radii (rS = 2GMSMBH/c2) from the central SMBH of mass MSMBH.6 However, they may exist in slim discs near the innermost stable circular orbit (ISCO; Peng & Chen 2021) or near the boundary of a gap region if a gap opens due to a heavy stellar-mass BH or an intermediate-mass BH (McKernan et al. 2014). Dynamical encounters frequently happen in migration traps leading to the formation and subsequent merger of binary black holes (BBHs) on short time-scales (Secunda et al. 2019, 2020; Yang et al. 2019a), where the binary separation is efficiently reduced by gas dynamical friction (Escala et al. 2004; Kim & Kim 2007; Baruteau, Cuadra & Lin 2011) to the point where GW emission drives the binaries together. Alternatively, BBHs may also form and merge in the disc outside migration traps (Tagawa et al. 2020a). Because of the deep potential barrier of the SMBH, the merger remnant BH remains near the migration trap and may undergo subsequent mergers with additional BHs, which leads to high BH masses, characteristic spin properties, and possibly non-zero eccentricity identifiable via GW observations (Yang et al. 2019a; Secunda et al. 2020; Tagawa et al. 2020b, 2021a,b; Samsing et al. 2022).


Feature VY may not be a dusty clump in the same sense as the other features since it has a significant flux contribution from the star. In our model, VY is modeled as dusty medium of a Gaussian density distribution centered on VY CMa and uniformly surrounding the star, as in an idealized spherical outflow. Alternatively, however, it could be a clump located in front of or behind the star and seen along the same line of sight. In our implementation, we clear the central space of dust within a radius of 90 AU (equivalent to a diameter of

0

.
″

15

$ 0{{\overset{\prime\prime}{.}}}15 $

) where solids would be too warm to exist heated by the cool but very luminous star. The peak surface brightness simulated with a beam of 152 mas are 34 and 140 mJy beam−1 in Bands 6 and 7, respectively. Of that, 13.0 and 30.1 mJy beam−1 comes from the blackbody radiation of the model star. O’Gorman et al. (2015) noted that stellar fluxes are underestimated in a blackbody model at millimeter and submillimeter wavelengths owing to the unaccounted presence of an extended radiophotosphere. We extrapolated fluxes expected from their radiophotosphere model getting 12 mJy in Band 6 and 44 mJy in Band 7. Given the small difference with our assumed blackbody fluxes and uncertainties in the radiophotosphere model of O’Gorman et al. (2015), we did not correct our model for this effect. We required 0.014 M⊙ of dust to explain the observed fluxes which is rather large compared to most other clumps (except C). The stellar contribution partially explains the very low spectral index of 1.7 toward VY because the stellar spectrum is expected to have α ≈ 2 (Lipscy et al. 2005). At the modeled parameters of VY, the medium must be very thick at visual light and obscure the stellar photosphere from a direct view for a terrestrial observer, as visual observations indeed seem to indicate. The stellar photosphere and its light variations are seen mainly through light scattered in the surrounding medium with a high degree of inhomogeneity (Humphreys et al. 2005).


Samples of dust particles from comet 81P/Wild 2 were returned to Earth by the Stardust mission in 2006. They were collected in aerogel with entrance velocity of 6 km s−1 and some of them made craters in the aluminium foils separating the aerogel tiles. Analyses of 81P/Wild 2 samples trapped in aerogel and of residues in the craters in the Al foils have shown that this comet contains mineral components similar to those found in primitive meteorites, including fragments of refractory minerals found in Ca–Al-rich inclusions (CAIs) (Zolensky et al. 2006; Simon et al. 2008; Schmitz et al. 2009), and chondrule fragments (Leroux et al. 2008a; Nakamura et al. 2008). However, during the capture process, the impacting 81P/Wild 2 dust particles were dispersed along the impact tracks and mixed with the aerogel (Leroux et al. 2008b; Stodolna et al. 2012). The mineralogy of terminal particles (at the end of the tracks) is dominated by olivine and pyroxene minerals, the number of pyroxene grains compared to that of olivine being higher (∼1) than that currently observed in carbonaceous chondrites, where olivine grains dominate the silicate mineralogy (number of pyroxenes/olivines 0.1) (Zolensky et al. 2006; Tomeoka et al. 2008). Apart from these single minerals present at the end of the impact tracks, fine-grained particles mixed with melted aerogel have partially survived the impact and are present along the tracks, together with significant amounts of crystalline silica (Leroux 2012; Roskosz & Leroux 2015). The oxygen isotopic composition of the minerals exhibits 18O/16O and 17O/16O ratios within the range observed in carbonaceous chondrites (Nakashima et al. 2012; Ogliore et al. 2015). No evidence for 26Mg excess was found in the 81P/Wild 2 minerals, suggesting that short-lived 26Al radionuclide was not incorporated at the time of their formation, implying a formation a few million years after the formation of the meteoritic CAIs (Ogliore et al. 2012; Nakashima et al. 2015). The abundance of isotopically anomalous presolar grains in 81P/Wild 2 is estimated to be less than 1000 ppm (Floss et al. 2013).

Zolensky et al. 2006
Zolensky et al. 2006


Intensive and extensive efforts in numerical simulations have revealed so far that no successful explosion is obtained in spherical symmetry (e.g., Liebendörfer et al. 2001, 2005; Rampp & Janka 2002; Sumiyoshi et al. 2005), and that multidimensional effects are crucially important (Burrows et al. 2006; Bruenn et al. 2009; Marek & Janka 2009; Suwa et al. 2010; Müller et al. 2012; Takiwaki et al. 2012; Couch 2013; Couch & Ott 2013; Hanke et al. 2013; Murphy et al. 2013; Lentz et al. 2015; Melson et al. 2015; Nakamura et al. 2015; Bruenn et al. 2016; Roberts et al. 2016; O’Connor & Couch 2018). Among them are rotation (Fryer & Heger 2000; Kotake et al. 2003; Thompson et al. 2005; Marek & Janka 2009; Iwakami et al. 2014a; Nakamura et al. 2014; Takiwaki et al. 2016; Summa et al. 2018), a magnetic field (Akiyama et al. 2003; Kotake et al. 2004; Yamada & Sawai 2004; Sawai et al. 2005; Obergaulinger et al. 2006, 2014, 2018; Burrows et al. 2007; Takiwaki et al. 2009; Sawai & Yamada 2014, 2016; Mösta et al. 2015), non-spherical structures of the progenitor (Couch & Ott 2013; Takahashi & Yamada 2014; Couch et al. 2015; Takahashi et al. 2016), turbulence (Murphy & Burrows 2008; Murphy & Meakin 2011; Murphy et al. 2013; Couch & Ott 2015; Mabanta & Murphy 2018), (magneto)hydrodynamical instabilities (Blondin et al. 2003; Scheck et al. 2006; Blondin & Mezzacappa 2007; Iwakami et al. 2008; Guilet et al. 2010; Wongwathanarat et al. 2010; Fernández et al. 2014; Takiwaki et al. 2014; Fernández 2015), general relativistic gravity (Dimmelmeier et al. 2002; Shibata & Sekiguchi 2004, 2005; Kuroda et al. 2012, 2016; Müller et al. 2012; Ott et al. 2012), and neutrino transport (Nagakura et al. 2014, 2017, 2018; Dolence et al. 2015; Pan et al. 2016). It is true that large-scale dynamical simulations have played a crucial role in recent progresses in our understanding of these ingredients, but we believe that a more phenomenological approach that employs toy models still plays an indispensable and complementary role to understand each effect more deeply.


The many unexpected surprises of comet 67P/Churyumov-Gerasimenko (hereafter 67P) revealed by the historic Rosetta mission highlight the importance of observing the evolution of comets throughout their orbits. One of the surprises was the drastic heterogeneity in both the major and minor volatile species in the coma that was observed early on in the mission (Hässig et al. 2015; Luspay-Kuti et al. 2015, hereafter ALK15). When Rosetta first arrived at comet 67P in August 2014, the Rosetta Orbiter Mass Spectrometer for Ion and Neutral Analysis/Double Focusing Mass Spectrometer (ROSINA/DFMS; Balsiger et al. 2007) detected large diurnal variations in the intensity profiles of various species in the coma from distances to the comet as far as 250 km. At this time, 67P was still at a distance of about 3 AU and inbound from the Sun. The intensity variations in the major and minor volatile species were found to be periodic, and were dependent on both the observing sub-spacecraft latitude and longitude (Hässig et al. 2015; Luspay-Kuti et al. (2015)). As reported in Hässig et al. (2015), the intensity of H2O in the coma dominated the overall signal, with maxima in the H2O signal every ~6 h, about twice during a rotation. Interestingly, however, CO2 and CO displayed a separate additional maximum when the H2O signal was near its minimum. This independent maximum in CO2 and CO only occurred at negative observing latitudes that are associated with a particular “view” of Rosetta at 67P, with the larger lobe blocking out the neck and head. At this time, 67P had not yet reached its first equinox (10 May 2015), and the poorly illuminated southern hemisphere was experiencing winter. In addition, the largest H2O activity was localized at the well-illuminated neck region, as also seen by the Microwave Instrument on the Rostta Orbiter (MIRO; Gulkis et al. 2015; Biver et al. 2015; Lee et al. 2015) and by the Visible InfraRed Thermal Imaging Spectrometer (VIRTIS; Bockelée-Morvan et al. 2015; Migliorini et al. 2016). VIRTIS also measured weak H2O production in regions with low solar illumination, while CO2 was outgassing from both illuminated and non-illuminated regions pre-inbound equinox (Bockelée-Morvan et al. 2015; Migliorini et al. 2016; Fink et al. 2016). The observed outgassing pattern of the major cometary species suggested that CO and CO2 may be sublimating from a depth below the diurnal skin depth.


Lynch et al. (2010) and the review by Rouillard (2011) (see Fig. 1) paint a rather positive picture for our ability to connect RS observations and IS measurements of certain interplanetary propagating (IP) structures, particularly under solar minimum conditions. The reality, however, is more complicated. Despite the availability of continuous imaging and tracking of IP disturbances from the STEREO heliospheric imagers, CME time-of-arrivals and especially speeds at 1 AU can have errors upwards of 13 h and 200 km s−1, respectively, even for de-projected trajectories (Colaninno et al. 2013). Reconstructions of the CME shape from RS observations rarely agree with in situ ones (e.g., Nieves-Chinchilla et al. 2013; Wood et al. 2017). Some of the discrepancies can be attributed to limitations of the triangulation techniques (whether applied on J-maps or not) arising from the optically thin nature of the white light emission (Howard et al. 2012). Much of the remaining discrepancies, though, should arise from interaction between the structures and the ambient solar wind and/or from internal evolution that can lead to deflections (e.g., Isavnin et al. 2013, 2014), rotations (Nieves-Chinchilla et al. 2012) or distortions (Nieves-Chinchilla et al. 2013). We note, however, that these effects are inferred rather than observed directly in the data. In terms of the 3D global morphology, there is a current debate about distortion or deformation of the internal magnetic field configuration associated to the CMEs. The elongated dark cavity shape associated with the CME flux rope, called “pancaking”, provides an evidence of a highly distorted global structure, probably due to the solar wind interaction (Odstrcil & Pizzo 1999; Riley & Crooker 2004; Owens 2006; Savani et al. 2010; DeForest et al. 2013; Owens et al. 2017). However, another interpretation is that it could be an effect of the projection of a 3D structure in the plane of the sky, creating the appearance of distortion (Vourlidas et al. 2011; Nieves-Chinchilla et al. 2013). In contrast, from the in situ perspective, the magnetic field strength asymmetries observed can be interpreted as a consequence of the local effect of flux rope expansion (Farrugia et al. 1993; Osherovich et al. 1993; Démoulin & Dasso 2009) or erosion (Dasso et al. 2007; Ruffenach et al. 2012), but it could also be a result of the distortion (Hidalgo et al. 2002; Berdichevsky 2013; Nieves-Chinchilla et al. 2018a). Longitudinal deflections during inner heliospheric transit are particularly hard to quantify because heliospheric imaging is taken from and restricted along the ecliptic plane. This is the reason, for example, why the “garden-hose spiral” nature of solar wind streams has never been imaged directly but only inferred by de-projection techniques based on J-maps (Rouillard et al. 2008; Sheeley et al. 2008). While major progress was achieved with STEREO data, establishing the exact longitudinal extent of streamer blowouts (Vourlidas & Webb 2018), whether CMEs deflect longitudinally or merge with each other, where CIRs form or how shocks evolve require observations away from the ecliptic (Gibson et al. 2018). This is an area where Solar Orbiter imaging, particularly from Solar OrbiterHI (Howard et al. 2020) will be trailblazing. However to fully exploit this data we need to adapt our techniques to account for rapidly varying vantage points located outside the ecliptic plane.


We use the N-body simulation package—MERCURY (Chambers 1999)—to numerically investigate the effects of photo-evaporation on the dynamical evolution of planet–satellite systems. We choose the Bulirsch–Stoer integration algorithm, which can handle close encounter accurately. It is important in the simulations, as we will see below, that many close encounters among moons and the planet are expected to happen. Collisions among moons, the planet, and the central star are also considered in simulations and treated simply as inelastic collisions without fragmentations. Each simulation consists of a central star, a planet, and some moons orbiting around the planet. The photo-evaporation is simply modeled as a slow (adiabatic) and isotropic mass-loss process of the planet. In reality, the photo-evaporation is a very slow process on a timescale of the order of 107–108 year (Owen & Wu 2013). However, it is impractical and unnecessary to perform a simulation on such a long timescale. Instead, we model the mass-loss process on a timescale of τevap, and each simulation typically lasts for several τevap. As long as the adiabatic requirement is met, i.e., the mass-loss timescale is much longer than the dynamical timescale of the system (τevap ≫ Pp, where Pp is the orbital period of the planet), one could study the dynamical effects of the mass-loss process equivalently. As we discussed in Section 3.3, the results converge if τevap > 102–103 Pp, indicating the adiabatic condition is met. Therefore, in all other simulations, we set τevap = 104 Pp. Other parameters are set to represent the typical values of Kepler planets. In particular, we consider a planet–satellite system orbiting a star of solar mass (M⋆ = M⊙) in a circular orbit (ep = 0.0) with semimajor axis of ap = 0.1 au. The orbit has a period of ∼10 days (typical value of Kepler planets), and it is sufficiently close to the central star to be subject to significant photo-evaporation effect (Owen & Wu 2013), which removes massive hydrogen envelopes of the planet. The planet has an initial mass of Mpi and a final mass of Mpf after photo-evaporation. In this paper, we adopt Mpi = 20 M⊕ and Mpf = 10 M⊕ nominally (close to the standard model adopted in Owen & Wu 2013). The mean density of the planet is set to the same as that of Neptune (1.66 g cm−3). The effect of changing the planetary density is discussed in Section 3.3. We performed a number of sets of simulations by considering different planet–satellite configurations. Similar to the definition in MERCURY, hereafter, we define “small moons” as test particles (TPs) whose mutual gravity and corresponding effects on the planet and the star are ignored, while “big moons” are gravitationally important enough that their gravitational effects are fully considered. Table 1 lists the initial setups and parameters of various simulations, whose results are presented in the following subsections.


Summarizing the discussion above: we have a number of suggested r-process sites, but only one of them is proven by a direct observation of the explosive event. Observations of low metallicity stars show essentially three types of patterns, a weak or limited r-process, a strong solar-type r-process, and an actinide-boosted r-process (in some publications, this is also referred to as a weak, main, and strong r-process). Whether the latter two types are produced in different sites or a result of variations within the same site (e.g., neutron star mergers) is still debated. The question is now how such observations can point back to the r-process sites, and whether it is possible to identify features which can provide additional insight. A promising approach is to look for correlations among different elements, which might directly identify the nucleosynthesis of a specific site (see e.g., Barklem et al. 2005; François et al. 2007; Mashonkina et al. 2007; Kratz et al. 2008). Cowan et al. (2005) compared the abundances of Fe, Ge, Zr, and r-process Eu in low metallicity stars. They found a strong correlation of Ge with Fe, indicating the same nucleosynthesis origin (core-collapse supernovae), a weak correlation of Zr with Fe – indicating that other sites than regular core-collapse supernovae (without or low Fe-ejection) contribute as well –, and no correlation between Eu and Fe, essentially pointing to a pure r-process origin with negligible Fe-ejection. More recent data from the SAGA and JINA databases (Suda et al. 2008; Abohalima & Frebel 2018) permit a correlation between Eu and Fe for [Eu/Fe]  0.3, that is for stars with lower than average r-process enrichment. If interpreted in a straightforward way, this would point to a negligible Fe/Eu ratio (in comparison to solar ratios) in the major r-process sources, while a noticeable coproduction of Fe with Eu is possible in less strong r-process sources, for example with a weak r-process. Such cases could again be identified with the limited-r entry in observations (Hansen et al. 2018).


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.


Figure 24 shows that the median Re increases for increasing mass (from ~5 Kpc to ~20 Kpc) and, given a stellar mass, our passive ETGs have median sizes smaller than those of the parent sample even by ~15% (at the highest masses). Furthermore, the entire Re distribution is extended to smaller radii in the case of passive ETGs, especially for log (M/M⊙) ≳ 11.5. Remembering that small differences in galaxy size imply large differences in stellar mass density, the derived trends suggest that the ETGs analyzed in this work should have formed from higher density progenitors which, in the hypothesis of no coeval mergers, do not increase their mass during the evolution. On the other hand, we cannot exclude the possibility that galaxies in the parent sample have experienced more dry mergers than our massive and passive galaxies, which have increased their size across cosmic time (Naab et al. 2009; Johansson et al. 2012a). The observed trend is also in agreement with some literature studies at low redshift which also suggest that more compact galaxies contain older stellar populations than larger ones (e.g. Saracco et al. 2009; Shankar & Bernardi 2009; Williams et al. 2010; Poggianti et al. 2013; McDermid et al. 2015). In general, this is qualitatively consistent with the high zF inferred by our analysis (z> 5) since, according to the cosmological evolution of the baryonic matter density, gas was denser at these cosmic epochs. These findings also agree with recent observations of compact systems (with various level of SF) at z ~ 2−3, which could be identified as local massive ETGs progenitors (e.g. Daddi et al. 2004; Cattaneo et al. 2013; Finkelstein et al. 2013; Marchesini et al. 2014; Nelson et al. 2014; Williams et al. 2015). Moreover, recent models of elliptical galaxy formation also predict the formation of compact and dense progenitors at high redshifts (e.g. Johansson et al. 2012a; Naab et al. 2014 and references therein).


Gravitational-wave astronomy has recently become a reality with the first detection of gravitational waves (GW hereafter) by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo ground-based interferemeters. To date, eleven events have been reported by the LIGO and Virgo detectors (Abbott 2018), and this number will quickly increase to tens of events in the coming years. Some of these events may correspond to gravitationally lensed events with magnification factors ranging from a few tens to a few hundreds (Dai et al. 2017; Ng et al. 2018; Li et al. 2018a; Smith et al. 2018a,b; Broadhurst et al. 2019). Recent works have studied lensing effects in the existing LIGO/Virgo O1 and O2 events (Hannuksela et al. 2019; Broadhurst et al. 2019), while Smith et al. (2018c) searched for candidate galaxy cluster lenses for the GW170814 event. The most likely lenses for such events would be massive galaxies or galaxy clusters (Ng et al. 2018; Dai et al. 2017; Smith et al. 2018b; Broadhurst et al. 2019). On the other extreme of the lens mass regime, compact objects with masses of a few hundreds to a few tens M⊙ can also act as lenses (Lai et al. 2018). In this case, the geometric optics limit is not valid since the Schwarszchild radius of the lens is comparable to the wavelength of the wave. For these relatively low masses, the lensing effect has a modest impact on the average magnification, but it can introduce a frequency dependence on the magnification (see for instance, Jung & Shin 2019; Lai et al. 2018). An even smaller mass regime was considered in Christian et al. (2018) where the authors find that lenses with a mass as low as 30 M⊙ could be detected with current experiments. They also consider future, higher-sensitivity experiments and show how they can push the limit to even smaller masses of order 1 M⊙. These conclusions are, however, obtained assuming isolated microlenses and without accounting for the effect of the macromodel, or other nearby microlenses. In the small mass regime, microlenses such as neutron stars have been also considered as scattering sources of GWs, and it is found that a GW can be focussed at a focal point near the neutron star surface (Halder et al. 2019; Stratton & Dolan 2019).


Classic examples of this approach to investigating solar eruptions have been the many simulations of the magnetic breakout model, which uses reconnection as the eruption mechanism (Antiochos 1998; Antiochos et al. 1999). In typical breakout simulations magnetic energy is built up in the corona by prescribed surface motions at the lower boundary, either large-scale shearing flows (e.g., Karpen et al. 2012) or small-scale randomized motions leading to helicity condensation (e.g., Dahlin et al. 2022). The normal component of the coronal field is held fixed at this lower boundary, which is presumed to represent the high-beta photosphere, and the coronal flux is assumed to be multipolar so that a separatrix surface and null point are present. Note that even a bipolar AR implies the presence of a coronal separatrix surface and null when the field of the bipole is embedded in the solar global dipole (e.g., Lynch et al. 2008). The initial conditions in most breakout simulations are taken to be the minimum-energy potential field (
J
 ≡ ∇ ×
B
/μ
0 = 0 where
B
 is the magnetic field), but the imposed boundary motions inject magnetic free energy into the corona, leading to the formation of a sheared-arcade filament channel with current sheets at the overlying separatrix surface and null between the filament flux system and neighboring flux systems. In the breakout model, magnetic reconnection (often called breakout reconnection) at the separatrix current sheet is necessary so that the sheared filament flux can expand upward sufficiently for a vertical current sheet to form below/inside this flux system. The onset of magnetic reconnection in this vertical current sheet (often loosely described as flare reconnection) greatly accelerates the eruption, leading to the ejection of the shear and the relaxation of the corona back down to a near-potential state (e.g., Karpen et al. 2012; Wyper et al. 2017). A related but physically distinct reconnection-driven eruption model is the so-called tether cutting, which posits that with sufficient boundary shear a vertical current sheet can form spontaneously in the filament channel, without the need for breakout reconnection, leading to an eruption (e.g., Moore et al. 2001). Recent simulations using the same approach as the breakout ones just described appear to support this scenario (Jiang et al. 2021).


Cygnus A, at z = 0.0562, is 10 times closer than the next radio galaxy of similar radio luminosity.4

4
Radio luminosity >1045 erg s−1.
 The nuclear regions in Cygnus A have been observed extensively at radio through X-ray wavelengths (Carilli & Barthel 1996). The inner few arcseconds is a complex mix of optically obscuring dust clouds (Vestergaard & Barthel 1993; Whysong & Antonucci 2004; Lopez-Rodriguez et al. 2014; Merlo et al. 2014), atomic gas seen in narrow line emission (Stockton et al. 1994; Taylor et al. 2003), H i 21 cm absorption toward the inner radio jets, with a neutral atomic column density >1023 cm−2, depending on H i excitation temperature (Struve & Conway 2010), polarized, broad optical emission lines due to scattering by dust (Antonnuci et al. 1994; Ogle et al. 1997), and a highly absorbed hard X-ray spectrum with a total gas column density of ∼3 × 1023 cm−2 (Ueno et al. 1994; Reynolds et al. 2015). VLBI radio observations at 0.05 mas resolution reveal highly collimated jets originating on scales ∼200 times the Schwarzschild radius (Boccardi et al. 2016). Tadhunter et al. (2003), derive a black hole mass of 2.5 ± 0.7 × 109 M⊙ from HST and Keck spectroscopy of Pa-α and [O iii], and conclude that Cygnus A contains an AGN with a bolometric luminosity of order 1046 erg s−1, comparable to high redshift quasars (Runnoe et al. 2012). This AGN is highly obscured in the optical due to dust along our line of sight, with Av > 50 magnitudes, based on near-IR spectroscopy (Imanishi & Ueno 2000). Studies of the mid- to far-IR spectral and polarization properties have led to a model of a clumpy, dusty torus obscuring the AGN in Cygnus A, with a radius of at least 130 pc, although these conclusions are based on spatially integrated properties; these observations did not have the spatial resolution to resolve the torus, and hence are partially contaminated by emission from the radio core-jet (Privon et al. 2012; Lopez-Rodriguez et al. 2018).


Variable stars have a long tradition of being tracers of different stellar populations. The most well known of the pulsating variable stars in dwarf galaxies are RR Lyrae stars, which unequivocally trace an old population (>10 Gyr, Smith 1995). RR Lyrae stars have been found in almost all of the satellites of the Milky Way (recent compilation in Martínez-Vázquez et al. 2019), even in low-luminosity systems such as Segue I (Simon et al. 2011). This is a clear indication that an old population is ubiquitous among dwarf galaxies. On the other hand, anomalous Cepheids, which are pulsating stars above the horizontal branch, may trace an intermediate age population. Their progenitors are likely massive (1–2 M⊙) stars that have evolved off the main sequence (Fiorentino & Monelli 2012). These stars have been commonly found in the classical satellites of the Milky Way but are rare in globular clusters (Clement et al. 2001), which contain exclusively old populations. Since they have been observed also in dwarf spheroidal (dSph) galaxies with predominantly old stellar populations like Draco and Ursa Minor (Nemec, Wehlau & Mendes de Oliveira 1988; Kinemuchi et al. 2008), other formation channels are needed for these stars. Binary evolution can also bring stars to the region of the instability strip where anomalous Cepheids live (Gautschy & Saio 2017). Thus, old progenitors are also possible. Dwarf Cepheid stars (a.k.a. SX Phoenicis and/or δ Scuti stars) are also pulsating stars in the instability strip, but they are found below the horizontal branch (Breger 2000). Their very short periods (just a few hours) and small amplitudes make them very hard to detect, especially in distant systems. They may trace either intermediate-age populations (massive main sequence stars in the instability strip) or old populations (pulsating blue stragglers). Finally, Classical Cepheids indicate the presence of young populations (0.03–0.7 Gyr). They are rare in dSph galaxies, with Leo I being an exception (Fiorentino et al. 2012).


The column S in the table shows that at least two minima of line-of-sight velocity irregularity are present for all numbers m considered: the first short-wavelength minimum with the radial scale λrad ≈ 1 kpc and the second long-wavelength minimum with the scale λrad ≈ 2.5 kpc. There are three possible ways to explain these scales. In the first place, one can identify the scales as fully independent global modes. This is because for a fixed number of spiral arms m, in a self-gravitating rotating astrophysical disc configuration, there usually exists a sequence of radial wavelengths (Bertin et al. 1977; Griv & Chiueh 1998; Griv et al. 2000, 2006, Griv et al. 2012; Fujii et al. 2011; Griv & Wang 2014). The non-negative azimuthal mode number m gives the number of spiral arms, whereas the real radial wavenumber krad = 2π/λrad determines the radial structure.4 Secondly, one can identify these scales as Fourier harmonics of a single wave (Mishurov et al. 1979, p. 151). And thirdly, the phase ϕ0 that we found is between −48° and −70° and/or between 327° and 351° for all m. To be consistent with the current ideas as to the Galactic spiral structure (Vallée 2008, fig. 1 therein; Xu et al. 2013, fig. 12 therein; Hou & Han 2014, fig. 5 therein; Nakanishi & Sofue 2016, fig. 7 therein), we may interpret this finding to mean that the kinematics of 223 Cepheids investigated reveals the segments of different large-scale arms. Namely, whatever spiral m models we consider, the Sun is located at the outer edge of a local spiral arm (at the outer edge of the Cygnus–Orion arm; ϕ0 ≈ −60° for the first minimum) and/or at the outer edge of an inner spiral arm (at the outer edge of the Carina–Sagittarius arm, very close to the arm centre; ϕ0 ≈ 330° for the second minimum) (for notation, see Reid et al. 2009, fig. 1 therein; Choi et al. 2014, fig. 14 therein; Sanna et al. 2014, fig. 6 therein; Camargo et al. 2015, fig. 12 therein; Sato et al. 2014, fig. 3 therein). Basharina et al. (1980) have already confirmed the Sun to be located in the local arm. Further studies are needed to clarify the issue (see also Hou & Han 2014).


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

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

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

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


Brown dwarfs and giant exoplanets populate the same temperature range and share many physical properties, such as their molecule-dominated atmospheres and gradual cooling from ~3000 K at formation to ~100 K like the solar system gas-giant planets. Recent discoveries of very massive planets (Chauvin et al. 2005; Marois et al. 2010; Delorme et al. 2013), some possibly more massive than the 13 MJup deuterium burning mass limit, hint that planets could overlap with brown dwarfs in mass. On the other hand, the discovery of isolated L dwarfs in young clusters (Zapatero Osorio et al. 2002, 2014; Peña Ramírez et al. 2012), in young moving groups (Liu et al. 2013; Gagné et al. 2015; Gauza et al. 2015), and very cold very nearby Y dwarf objects (e.g., Kirkpatrick et al. 2012; Luhman 2014) show that very low-mass isolated brown dwarfs exist and overlap with the planetary masses. When these low-mass brown dwarfs are close enough and bright enough to be observed spectroscopically their atmospheres are much easier to study than similar exoplanets that lie near their very bright host stars. Liu et al. (2013) notably showed that the ~8 MJup brown dwarf PSO J318.5−22, a β-pictoris moving group member shares the spectral characteristics of the young directly imaged exoplanets, as well as atypically red late-L spectral type objects (e.g., Faherty et al. 2013; Gizis et al. 2015; Kellogg et al. 2016; Schneider et al. 2014, 2016; Bonnefoy et al. 2016). When CFBDSIR J214947.2−040308.9, hereafter CFBDSIR 2149, was identified (Delorme et al. 2012), it seemed to be a candidate member of the AB Doradus young moving group and, together with the low-gravity features in its spectrum, made it a unique T-type isolated planetary-mass candidate. Another earlier-type, isolated young planetary-mass T-dwarf, SDSS J111010.01+011613.1, has been identified as a bona fide member of AB Doradus moving group (\hbox{$149^{+51}_{-19}$}149-19+51 Myr; Bell et al. 2015) by Gagné et al. (2015). The late-T spectral type of CFBDSIR 2149 is typical of the coolest known directly imaged exoplanets, such as GJ 504 b or 51 Eri b (Kuzuhara et al. 2013; Macintosh et al. 2015), that the latest generation of adaptive optics systems are detecting. We therefore carried out a multi-wavelength, multi-instrument follow-up of CFBDSIR 2149 to fully characterise it and constrain its nature.


FRBs have been detected in the radio band. Circular polarization of FRB 140514 was measured at a level of

 degree, while linear polarization is less than 10% as a 1σ upper limit (Petroff et al. 2015). We apply our model to self-consistently get both circular and linear polarization degrees of FRB 140514. The case of B = 1010 G, Te = 108 K, and γth = 104 shown as the solid line in the right panels of Figure 3 seems to be one solution to explain the polarization observations. Thus, we may consider FRB 140514 to be associated with strongly magnetized sources. A neutron star can be one candidate for FRB origin. Here, we assume that the polarized emission is pointing toward observers, as usual neutron star models assumed, but we do not include additional jet view-angle effects. We note one recent theoretical work on the polarization detection of neutron stars in the soft X-ray band (Yatabe & Yamada 2017), and the relatively low electron temperature from our analysis indicates that the radiation of FRB 140514 may not occur near the neutron star magneto-atmosphere above the neutron star surface. On the other hand, the alternative case of B = 1 G, Te = 1010 K, and

 in our model can obtain the circular polarization degree of 20%. However, in this case, the intrinsic linear polarization degree is about 76%. This seems to be in contrast with the observation of FRB 140514. Therefore, we are inclined to believe from our polarization analysis that FRB may have a neutron star origin. Besides FRB 140514, FRB 110523 has the linear polarization degree of

, but the circular polarization degree of about 23% due to instrumental leakage was not confirmed to be an astronomical result (Masui et al. 2015). FRB 081507 has the high linear polarization degree of 80% (Ravi et al. 2016) and FRB 150215 has the linear polarization degree of

 (Petroff et al. 2017). If we can detect both linear and circular polarization for FRBs, we may further constrain the FRB physics.


To this we can add that Zimbardo and coworkers reported in a series of papers that spacecraft observations of SEP intensity-time profiles ahead of interplanetary shocks yielded power laws instead of the exponential profiles predicted by standard DSA. They interpreted this as a sign of superdiffusive spatial SEP transport in the shock vicinity resulting in superdiffusive shock acceleration. They predicted the superdiffusive shock acceleration to be more efficient, producing a harder accelerated power-law spectrum for SEPs, than standard DSA (Zimbardo et al. 2006; Perri & Zimbardo 2007, 2008, 2009; Zimbardo & Perri 2013; Zimbardo et al. 2017, 2020; Zimbardo & Perri 2020). Zimbardo & Perri (2020) explained such superdiffusive transport as a product of subdiffusion in pitch-angle space arising from the observation that Alfvén-wave pitch-angle scattering times in the solar wind have a power-law distribution instead of a single value. Another possibility is that there is a strong presence of SMFRs in the vicinity of heliospheric shocks so that particle trapping effects could result in anomalous diffusive transport and shock acceleration. Evidence is increasing that, in a space plasma with a significant guide/background magnetic field like the solar wind, SMFRs naturally form as part of a self-generated, quasi-two-dimensional (quasi-2D) MHD turbulence component that might dominate other MHD wave turbulence modes. This is supported by observations in the slow solar wind near 1 au (e.g., Matthaeus et al. 1990; Bieber et al. 1996; Greco et al. 2009; Zheng & Hu 2018), MHD simulations (e.g., Shebalin et al. 1983; Dmitruk et al. 2004), and nearly incompressible MHD turbulence transport theory (e.g., Zank & Matthaeus 1992, 1993; Zank et al. 2017, 2018, 2020). It is plausible that SMFRs can have a strong presence ahead of interplanetary shocks. Furthermore, there is evidence that the occurrence of SMFRs peaks at large-scale current sheets in the solar wind where magnetic reconnection produces additional SMFRs that can trap energetic particles (Khabarova et al. 2015, 2016; Hu et al. 2018). Many of these current sheets occur behind traveling shocks (Khabarova & Zank 2017). Recently, a theoretical investigation was launched to determine the transmission of quasi-2D SMFRs through a perpendicular shock (Zank et al. 2021). The results show a strong enhancement in the magnetic energy density of the SMFR magnetic island component behind the shock, thus confirming a strong presence of SMFRs downstream of the shock as well.


Analytical insight into the motion of the inner planets requires an appropriate dynamical modelling of the long-term evolution of their orbits. On the one hand, such a model must be consistent with the predictions of the reference numerical integrations available in literature (Laskar 1990c, 2008; Laskar et al. 2004; Laskar & Gastineau 2009) to ensure that it reproduces the dynamical features of the inner system with sufficient precision. On the other hand, the corresponding Hamiltonian should be set in a form suitable for the systematic application of canonical perturbation techniques (Hori 1966; Deprit 1969), which is essential to an unbiased analysis of such a high-dimensional dynamics. Moreover, the possibility of numerically integrating the equations of motion in an efficient way is fundamental for studying the chaotic evolution of the orbital solutions in a statistical way. Unfortunately, the construction of such a model is a delicate task. In principle, we might just consider the full N-body Hamiltonian of the Newtonian gravitational interactions among the Solar System planets, with the addition of the leading corrections coming from general relativity and the Earth–Moon interaction. This already reproduces the precession frequencies of the inner orbits with a precision better than 0.01′′ yr−1 (Laskar 1999). However, this Hamiltonian is unnecessarily complicated because it includes short-time harmonics, with periods shorter than 5000 yr (e.g. Carpino et al. 1987), which are known to generate small quasi-periodic oscillations in the inner orbits, without being implied in chaos generation. The inner planets are not, indeed, involved in any relevant mean-motion resonance. At the same time, the long-term numerical integration of the corresponding equations of motion is very time consuming, the resulting solutions needing to be filtered to extract the secular trend of the orbits (Carpino et al. 1987; Nobili et al. 1989). These facts suggest considering a secular Hamiltonian to directly describe the slow movement of the planet perihelia and nodes after proper averaging over the short-time orbital motion (Laskar 1984, 1985). Secular dynamics includes the essential planet interactions responsible for chaos in the inner Solar System and allows performing the fastest long-term numerical integrations (Laskar 1988, 1989, 1994, 2008). This enabled the discovery of chaos in the inner system before the use of symplectic integration schemes (Sussman & Wisdom 1992). Unfortunately, an effective secular model for the entire Solar System has to be of high order in planet masses, principally because of the 5:2 near mean-motion resonance between Jupiter and Saturn, the so-called great inequality (Laplace 1785; Laskar 1996). A simple averaging of the N-body Hamiltonian over the planet mean longitudes, resulting in a first-order secular dynamics in planet masses, would reproduce the fundamental frequencies g5 and g6 (which dominate the perihelion precession of Jupiter and Saturn, respectively) very poorly1 (Laskar 1988). The construction of higher-order models requires the manipulation of large Poisson series and the use of sophisticated computer algebra systems. This is probably the reason why they are still not widely used, at least as a basis of extensive research.


The first SMGs were detected using SCUBA at 850 μm (Smail et al. 1997; Barger et al. 1998; Hughes et al. 1998), which remains one of the prime wavelengths to detect these galaxies (e.g., Geach et al. 2017), thanks to a combination of available instruments, spectral window, and the negative k-correction at that wavelength. Other single-dish samples of SMGs have also been obtained at 1.1–1.3 mm using MAMBO (e.g., Eales et al. 2003; Bertoldi et al. 2007; Greve et al. 2008) and AzTEC (e.g., Aretxaga et al. 2011; Yun et al. 2012), at 1.4 mm/2 mm with the SPT (Vieira et al. 2010), and at 2 mm with GISMO (Staguhn et al. 2014; Magnelli et al. 2019). Selecting SMGs from observations at longer wavelengths is thought to favor galaxies at higher redshifts (e.g., Smolčić et al. 2012; Vieira et al. 2013; Staguhn et al. 2014; Magnelli et al. 2019; Hodge & da Cunha 2020), although it is difficult to compare the redshift distributions in an unbiased way (see, e.g., Zavala et al. 2014 for a discussion), and account for intrinsic variations of galaxy far-IR spectral energy distributions (SEDs). Nevertheless, the 2 mm band has been put forth as a potential candidate to detect high-redshift (z > 3) galaxies (e.g., Casey et al. 2018a, 2018b, 2019; Zavala et al. 2021). The negative k-correction is stronger at 2 mm than at 850 μm; thus, for a fixed SED, the 2 mm band should pick up more high-redshift galaxies than at 870 μm. In addition, better atmospheric transmission and larger fields of view can be achieved at 2 mm (but corresponding poorer resolution). Such an effort is currently ongoing (see Zavala et al. 2021 for first results). To understand the relationship between the populations detected at 850 μm and at 2 mm, we require a detailed characterization of the (sub)millimeter SEDs of these sources. Multiwavelength submillimeter observations are still rare, with most observations focusing on a single wavelength. Only a handful of sources observed at 2 mm have complementary shorter-wavelength detections (Staguhn et al. 2014; Magnelli et al. 2019). Thus, a more systematic multiwavelength dust continuum investigation is warranted in order to reveal the dust properties of (sub)millimeter-detected sources.


To test IADI, we made a model of a disk in scattered light. This model is 400 × 400 pixels, each pixel having a physical size of 1 × 1 au. Multiple rings are implemented, inspired by observations of disks (e.g., HD 97048 Ginski et al. 2016; RX J1615 de Boer et al. 2016 and TW Hydrae van Boekel et al. 2017), see panel a in Fig. 2. A specific inclination and rotation is achieved using the warpAffine function from OpenCV (Bradski 2000). Young planet-forming disks are still gas rich and dust particles are stratified due to gas pressure along the vertical axis. Therefore, flaring is implemented in the model via an offset of the rings with respect to the center of the ring (see the detailed discussion in de Boer et al. 2016). For our disk model, we are using the power-law profile for the scattering surface height H and the separation r found by Ginski et al. (2016) for the disk around HD 97048. This profile describes the flaring discovered in this source reasonably well up to a separation of ~270 au. Considering that the model disk used will have a separation of 200 au, this formula will be sufficient to simulate the disk height2. Illumination effects of the central star are implemented via a ~1/r2 intensity dependence from the center of the disk, making the inner part of the disk brighter compared to the outer part. Moreover, the intensity also depends on the light scattering angle via the phase function. Because a physical model is beyond the scope of this work, a “pseudo” phase function is implemented to mimic the same asymmetries in light distribution seen in observed disks via I = cos ϕ, where the intensity I depends on the cosine of the azimuthal angle ϕ. This pseudo phase function depends on the azimuthal angle instead of a scattering angle on which a real phase function would depend. This makes the part of the disk facing toward the observer appear brighter than the part facing away in a fairly simple way. Lastly, the model is put through a Gaussian convolution kernel from the scipy ndimage package (Virtanen et al. 2020) to remove sharp edges and give a finite resolution to the model. The final three steps are shown in the top row of Fig. 2.


AGN While—starting from the very early works (e.g., Seldner and Peebles 1978; Longair and Seldner 1979; Hill and Lilly 1991; Peacock and Nicholson 1991; Allington-Smith et al. 1993; Zirbel 1997)—virtually all the studies presented in the literature converge at indicating that radio-AGN preferentially reside within overdense structures, the three (or rather five if one also includes cross-correlation studies) methods presented in Sect. 4 provide different information on the large-scale structure behaviour of these objects. To summarize them in a few words, we might say that the method based on clustering returns more information on the very large/cosmological (i.e., at Mpc level and beyond) scales traced by radio sources and also on the dark matter content of the regions that host them. On the other hand, very different results are obtained if one searches for structures around known radio-AGN or if one pinpoints radio-AGN within known structures. Indeed, in the first case one finds that virtually all radio-AGN are surrounded by over-densities (e.g., Venemans et al. 2007; Mayo et al. 2012; Galametz et al. 2012; Castignani et al. 2014; Wylezalek et al. 2013; Rigby et al. 2014), while the second method shows that only about 20–30% of them inhabit rich (group- and cluster-like) structures (e.g., Best et al. 2007; Magliocchetti and Brüggen 2007; Lin and Mohr 2007; Croft et al. 2007; Magliocchetti et al. 2018b; Croston et al. 2019). The reason for this discrepancy is not known, but it is likely related to the different redshift ranges probed by the two methods (much more local sources are considered in the second one), and/or—under the assumption of a strong correlation between radio luminosity and environmental density (e.g., Bardelli et al. 2010; Magliocchetti et al. 2018b; Croston et al. 2019; Mo et al. 2020, but see further in this section for different points of view)—to the fact that generally the first method images much brighter radio sources than the second one. In any case, we note that these findings also have implications for the life-time of the radio-AGN phenomenon, and it is therefore of no surprise if works based on the different methods illustrated above find different values, ranging from ∼60\documentclass[12pt]{minimal}
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				\begin{document}$$\sim 60$$\end{document} Myr up to a few Gyr (e.g., Lin and Mohr 2007; Smolčić et al. 2011; Hatch et al. 2014; Magliocchetti et al. 2017). We also note that recent studies based on direct LOFAR observations which—we remind—sample lower frequencies and therefore older emission, would tend to better agree with the high-end values provided above for the radio-active phase of an AGN (τ>200\documentclass[12pt]{minimal}
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				\begin{document}$$\tau > 200$$\end{document} Myr – Heesen et al. 2018).


In Section 3.2, it was noted that the long range structure observed in the reaction between the formamide and amino radicals was that of neutral hydrogenated isocyanic acid. However, instead of hydrogenation, protonation could be occurring. Isocyanic acid (HNCO) has been detected in the ISM and can be formed from simple building blocks like atomic nitrogen and CO (Snyder & Buhl 1972; Buhl, Snyder & Edrich 1973; Nourry, Zins & Krim 2015). It has been used in the study of the formation of urea in irradiation studies, where its irradiation is shown to lead to the formation of formamide and urea (Ferus et al. 2018; Raunier et al. 2003, 2004). In addition, it has been shown to be a product of the dissociation of formamide and has even been suggested to be a catalyst for the formation of H2 in the ISM (Lundell, Krajewska & Räsänen 1998; Duvernay et al. 2005; Haupa, Tarczay & Lee 2019). Moreover, there is a clear correlation with the abundances of formamide (Bisschop et al. 2007; López-Sepulcre et al. 2015). There is ample evidence of HNCO molecules functioning as an imine base, both in the gas phase and in the solid state (Dekock & Jasperse 1983; Hop et al. 1989; Hunter & Lias 1997; Hudson, Khanna & Moore 2005; Gupta et al. 2013; Bouchoux 2018; Marcelino et al. 2018). The proton affinity of HNCO is higher than that of water, so that one would expect protonation to occur even in water-based ices (Dekock & Jasperse 1983; Bouchoux 2018). Thus, in this section, calculations starting from protonated isocyanic acid are reported. Only DFT calculations were performed on these reactions, since multiconfigurational effects can be assumed to be small for these non-radical charged species. The first step that was investigated is the protonation of isocyanic acid. There are multiple options for protonation in this case: Protonation can occur on the nitrogen, carbon, or oxygen atoms. Hereby, we note that N-protonated isocyanic acid has been detected in laboratory experiments and in the ISM in the dense core L483 with a more tentative detection towards Sgr B2(N) (Hudson et al. 2005; Gupta et al. 2013; Marcelino et al. 2018). Moreover, O-protonated isocyanic acid has also been detected in laboratory experiments (Lattanzi et al. 2012). The potential energy curves for protonating on each of these atoms is shown in Fig. 7. Protonation on the nitrogen and oxygen atoms is barrierless. The well depths are 603.1 and 603.9 kJ mol−1, respectively, making them equally likely. Protonation on the carbon atom, however, is not barrierless, but requires an energy input of 14.4 kJ mol−1. It also results in a much less stable species, with a well depth of only 172.8 kJ mol−1, making it the least likely of the three pathways. Nitrogen protonation is the product that most naturally leads on to the formation of urea as it creates one of the amino groups found in urea. None the less, the similarity in energies for the nitrogen- and oxygen-protonated species means that the oxygen-protonated species could also be formed. The latter is the species we will consider first.


In a quasi-isothermal jet, Uj is (17)\begin{equation} \label{eq:U_j_quasi} U_{\rm j} = \zeta n_0 m_{\rm p} c^2\left(\frac{\gamma_{\rm j}\beta_{\rm j}}{\gamma_0\beta_0}\right)^{-\Gamma}\left(\frac{z}{z_0}\right)^{-2} \cdot \end{equation}Uj=ζn0mpc2γjβjγ0β0−Γzz0-2·Substituting Eqs. (17) and (13) into Eq. (10), and assuming the jet is launched with an initial γ0β0 equal to the sound speed (Eq. (16)), the 1D Euler equation that results is \begin{eqnarray} \label{eq:AGNJET_Corrected} &&\left\{\gamma_{\rm j}\beta_{\rm j}\frac{\Gamma+\xi}{\Gamma-1}-\Gamma\gamma_{\rm j}\beta_{\rm j}-\frac{\Gamma}{\gamma_{\rm j}\beta_{\rm j}}\right\}\frac{\partial \gamma_{\rm j}\beta_{\rm j}}{\partial z} = \frac{2}{z}; \\ &&\xi = \frac{1}{\zeta}\left(\frac{\gamma_{\rm j}\beta_{\rm j}}{\gamma_0\beta_0}\right)^{\Gamma-1}; \qquad \gamma_0\beta_0=\sqrt{\frac{\zeta\Gamma(\Gamma-1)}{1+2\zeta\Gamma-\zeta\Gamma^2}} \cdot \end{eqnarray}γjβjΓ+ξΓ−1−Γγjβj−Γγjβj∂γjβj∂z=2z;ξ=1ζγjβjγ0β0Γ−1; γ0β0=ζΓ(Γ−1)1+2ζΓ−ζΓ2·The above equation should reduce to the jet Lorentz factor profile used in Falcke (1996), Markoff et al. (2005) when ζ = 1. However, it differs from Eq. (2) in Falcke (1996): (20)\begin{equation} \label{eq:Heino96} \left\{\gamma_{\rm j}\beta_{\rm j}\frac{\Gamma+\xi}{\Gamma-1}-\frac{\Gamma}{\gamma_{\rm j}\beta_{\rm j}}\right\}\frac{\partial \gamma_{\rm j}\beta_{\rm j}}{\partial z} = \frac{2}{z}; \end{equation}γjβjΓ+ξΓ−1−Γγjβj∂γjβj∂z=2z;(21)\begin{equation} \xi = \left(\gamma_{\rm j}\beta_{\rm j}\frac{\Gamma+1}{\Gamma(\Gamma-1)}\right)^{1-\Gamma} \cdot \end{equation}ξ=γjβjΓ+1Γ(Γ−1)1−Γ·The difference between our equation and the equation in Falcke (1996) can be accounted for as follows: the − Γγjβj term in Eq. (18) results from a neglected \hbox{$\frac{\partial}{\partial z}(U_{\rm j}/n)$}∂∂z(Uj/n) term, the difference in the exponent in ξ results from an arithmetic error, and finally the difference in the inside of the parenthesis of ξ terms is from setting \hbox{$\gamma_0\beta_0 = \beta_{\rm s0}^{2}$}γ0β0=βs02 instead of using the proper value given in Eq. (16). The difference between the solutions of Eqs. (18) and (20) are small and shown in Fig. 1. In Fig. 1, we also include solutions to the 1D Euler equations when the jet is isothermal (Tj = const., i.e., Eq. 20 with ξ = 1) and adiabatic (Tj ∝ (γjβj)1 − Γz2 − 2Γ, see Eq. (25)).


It has been also suggested that the X-ray emission from SNe is dominated by inverse Compton (IC) scattering of photospheric optical photons by relativistic electrons accelerated by the SN shock on a timescale of weeks to a month after the explosion (see Chevalier & Fransson 2006). The X-ray luminosity strongly depends on the structure of the SN ejecta (ρSN ∝ r− n), the density structure of the CSM and the relativistic electron distribution responsible for the up-scattering (Chevalier & Fransson 2006; Margutti et al. 2012). Assuming a wind-like CSM (ρCSM ∝ r-2) and an ISM-like CSM (ρCSM = constant), Margutti et al. (2012) developed two generalized formalisms to calculate the IC luminosity. Their formalisms are strongly sensitive to the SN bolometric luminosity, Lbol (see Appendix A of Margutti et al. 2012). Here, it is assumed electrons are accelerated according to a power-law distribution n(γ) ∝ γ− p with index p = 3, as suggested by the radio observations of SN shocks in Type Ib/Ic explosions (see Soderberg et al. 2006; Margutti et al. 2014). Then, an IC luminosity in the wind-like CSM case is (see Margutti et al. 2012, their Appendix A) (1)\begin{eqnarray} \label{eq:1}  \frac{\mathrm{d} L_{\rm{IC}}}{\mathrm{d} \nu} \approx 2.1\times10^{-2}\left(\frac{\epsilon_{\rm e}}{0.1}\right)^{-2}\left(\frac{M_{\rm{ej}}}{1.4\,M_{\odot}}\right)^{-0.93}\left(\frac{A}{\rm{g\,cm^{-1}}}\right)^{0.64}  \nonumber \\\times\left(\frac{E}{10^{51}\,\rm{erg}}\right)^{1.29}\left(\frac{t}{\rm{s}}\right)^{-1.36}\left(\frac{L_{\rm{bol}}}{\rm{erg\,s^{-1}}}\right)\,\nu^{-1}, \end{eqnarray}dLICdν≈2.1×10-2ϵe0.1-2Mej1.4 M⊙-0.93Ag cm-10.64×E1051 erg1.29ts-1.36Lbolerg s-1 ν-1,where A = Ṁ/ (4πυwind), and ϵe is the fraction of thermal energy in the shock used for the electron acceleration (~0.1 see Chevalier & Fransson 2006). Theoretical IC X-ray luminosities with different mass-loss rates (for a wind velocity of 100 km s-1) are compared to the observations in Fig. 5. Here, both the observed bolometric light curve of SN 2005hk and the predicted bolometric light curve for the “N5def model” (see Fig. 8 of Kromer et al. 2013) are used as input for Lbol. The “N5def model” was shown to provide a good fit to the observations of the SN 2005hk event (Kromer et al. 2013). Moreover, E = 1.34 × 1050 erg, and Mej = 0.37 M⊙ (these parameters are consistent with the N5def model) are used in Eq. (1) to estimate the X-ray luminosities. Here, we note that SNe Iax have a range of luminosities, ejecta velocities, and inferred ejecta masses (Foley et al. 2013). Different bolometric luminosity light curves and ejecta masses of different SNe Iax may change the results shown in Fig. 5.


Our model consists of four zones; an inner disk (zone 1, as in Matter et al. 2016), and three zones into which the outer disk is divided (zones 2–4) in order to produce the azimuthal asymmetries seen in our SPHERE observations. The radial extent of these zones were constrained from our images: zone 2 corresponds to the component inside ~14 au observed in the noncoronagraphic J-band image, zone 3 corresponds to the bright ring at 16 au, and zone 4 corresponds to the asymmetrical outer disk. The radial extent of each of these zones, as well as their disk masses, is summarized in Table 2. No gaps were introduced between the three outer disk zones, but the gap between zones 1 and 2 from the Matter et al. (2016) model was kept. We note that these radii are only loosely constrained from our data, and are determined by eye from both the coronographic and noncoronographic data. We ran a grid of models with different inclinations and position angles for zones 1–2 (note that we systematically use the same inclination and position angle for these two zones) and for zone 3 – that is, a total offour free parameters, keeping in mind that the relative inclination between components must be small to allow a single broad shadow to be cast (as opposed to two narrow shadow lanes). The inclination and position angle of zone 4 is set to the values provided in Sect. 3. The grid was sampled in steps of 1° for inclination, and 2° for PA, and later refined to 0.5° steps for inclination and 0.5° for PA after a good initial agreement is found between the average azimuthal profile of the model and the scattered light images. The best fitting model was picked not only based on the location of the shadows cast by the inner components on the outer disk, but also on the shape (slope) of the resulting azimuthal profile of the outer disk. There is also a degeneracy if we consider that the inclinations and PAs of the two inner components (zones 1–2 and zone 3) can be exchanged and produce very similar results. However, doing this would cast a shadow in a different location, and thus produce a different azimuthal profile for zone 3.


After the LVC announcement, a multi-wavelength campaign immediately started. The campaign involved the X-ray and gamma-ray satellites first, and radio/IR–optical/TeV ground observatories at later times. The detection of a new optical transient (OT) was first announced by the One-meter, Two-hemisphere (1M2H) team discovered with the 1 m Swope telescope on August 18 01:05 UT (Coulter et al. 2017a, 2017b; Drout et al. 2017), named Swope Supernova Survey 2017a (SSS17a, now with the IAU designation AT 2017gfo). The OT was also detected independently by five other teams, the Dark Energy Camera (Allam et al. 2017; Cowperthwaite et al. 2017), the Distance Less Than 40 Mpc Survey (L. Tartaglia et al. 2017, in preparation; Valenti et al. 2017; Yang et al. 2017), Las Cumbres Observatory (Arcavi et al. 2017a, 2017b, 2017c), the Visible and Infrared Survey Telescope for Astronomy (Tanvir et al. 2017a, 2017b), and MASTER (Lipunov et al. 2017b, 2017a), REM-ROS2 (Melandri et al. 2017; Pian et al. 2017a, 2017b), Swift UVOT/XRT (Evans et al. 2017b, 2017a), and Gemini-South (Kasliwal et al. 2017; Singer et al. 2017), and for all see also MMA17. AT 2017gfo is located at 106 from the early-type galaxy NGC 4993, at a distance of ∼40 Mpc. A sequence of satellite high-energy observations started almost immediately, with exposures of the GW170817 LR depending on satellite position and operations. The X-ray and γ-ray observations included contributions by CALET (Nakahira et al. 2017), Konus-Wind (Svinkin et al. 2017), Insight-HXMT (Li et al. 2017; Liao et al. 2017), AstroSat CZTI (Balasubramanian et al. 2017), AGILE-GRID (see below), Fermi-LAT (Kocevski et al. 2017), MAXI (Sugita et al. 2017; S. Sugita et al. 2017, in preparation), Super-AGILE (MMA17; this work), Swift X-ray Telescope (Evans et al. 2017b, 2017a), NuSTAR (Harrison et al. 2017), INTEGRAL JEM-X (Savchenko et al. 2017b; V. Savchenko et al. 2017, in preparation), and Chandra (Fong et al. 2017; Margutti et al. 2017a; Troja et al. 2017b). An X-ray counterpart detection at the OT position was reported after 9 days and confirmed after 15 days by Chandra (Fong et al. 2017; Margutti et al. 2017b; Troja et al. 2017a, 2017b). Moreover, an important detection in the radio band has been reported by VLA (Alexander et al. 2017a, 2017b).