Although each one of the four aforementioned mechanisms has some observational support in certain systems, there is not a single mechanism that can explain all observed polarization in protoplanetary disks. Alignment with respect to the local radiation anisotropy (“k-RAT alignment” thereafter) is best supported by the azimuthal polarization pattern observed at ALMA Band 3 in the HL Tau system (Kataoka et al. 2017). However, it predicts a strong azimuthal variation of polarization and circular pattern (rather than elliptical pattern) (Yang et al. 2019). There is some tentative evidences for alignment with respect to the magnetic field, through either Radiative Alignment Torques (“B-RAT alignment”; Lazarian & Hoang 2007), or recently proposed Mechanical Alignment Torques (Hoang et al. 2018), in, e.g., the IRAS 4A system at cm wavelengths (Cox et al. 2015; Yang et al. 2016b) and BHB07-11 (Alves et al. 2018) at (sub)millimeter wavelengths. But there is no well-resolved system that matches the theoretical expectations (see, e.g., Cho & Lazarian 2007; Yang et al. 2016b; Bertrang et al. 2017) assuming the widely expected disk toroidal magnetic field yet (Flock et al. 2015). Mechanical alignment has recently received some attention. Hoang et al. (2018) claims that under MATs, grains can be aligned with respect to local dust-gas streaming direction, in the case of a weak or zero magnetic field, even if the velocity difference is sub-sonic. Within this picture, Kataoka et al. (2019) investigated the direction of streaming velocities for dust grains with different Stokes numbers, and the resulting polarization orientations. They found that their polarization pattern in the order-of-unity Stokes number case resembles that observed by Alves et al. (2018) in BHB07-11. The BHB07-11, however, is a binary system, and we expect more complicated velocity fields than the simple one assumed in Kataoka et al. (2019). Yang et al. (2019) investigated the observational features of another mechanical alignment mechanism, the Gold mechanism (Gold 1952), to address the circular versus elliptical pattern problem in the ALMA Band 3 polarization observations of HL Tau disk. However, they failed to explain the nonexistence of strong azimuthal variation, and suggested the scattering by dust grains aligned under the Gold mechanism may be the origin of the polarization at ALMA Band 3 in the HL Tau system.


Figure 13 shows the temporal evolution of the density, ρ, plasma flow velocity, vx, position of the wave crest, PosA, phase speed, vw, and magnetic field component in the z-direction, Bz, for the primary waves in every different case of initial amplitude, ρIA. In Figure 13(a), we observe that the amplitude of the density remains approximately constant at their initial values until the time when the shock is formed and the density amplitude of the primary wave starts decreasing (see Vršnak & Lulić 2000), i.e., at t ≈ 0.03 (blue), t ≈ 0.04 (red), and t ≈ 0.055 (green). For the case of ρIA = 1.3 (magenta), a decrease of the amplitude of the primary can hardly be observed, as expected for low-amplitude wave (Warmuth 2015). One can see that the larger the initial amplitude, ρIA, the stronger the decrease of the primary wave’s amplitude, which is consistent with observations (Warmuth & Mann 2011; Muhr et al. 2014; Warmuth 2015). The amplitudes decrease to values of ρ ≈ 1.6 (blue), ρ ≈ 1.5 (red), and ρ ≈ 1.4 (green) until the primary wave starts entering the CH. Due to the fact that the waves with larger initial amplitude enter the CH earlier than those with small initial amplitude, we can see in Figure 13(a) that the tracking of the parameters of the faster waves stops at an earlier time than the one for the slower waves. A similar behavior to the one of the density, ρ, can be observed for the plasma flow velocity, vx, in Figure 13(b) and the magnetic field component, Bz, in Figure 13(e). Here, the amplitudes decrease from vx = 0.75, Bz = 1.9 (for ρIA = 1.9, blue), vx = 0.6, Bz = 1.7 (for ρIA = 1.7, red), vx = 0.45, Bz = 1.5 (for ρIA = 1.5, green), and vx = 0.27, Bz = 1.3 (for ρIA = 1.3, magenta) to vx = 0.55, Bz = 1.6 (for ρIA = 1.9, blue), vx = 0.46, Bz = 1.5 (for ρIA = 1.7, red), vx = 0.36, Bz = 1.4 (for ρIA = 1.5, green), and vx = 0.25, Bz = 1.25 (for ρIA = 1.3, magenta). Figure 13(c) shows how the primary waves propagate in the positive x-direction. In all four cases of different initial amplitude, ρIA, the phase speed decreases slighty (consistent with observations; see Warmuth et al. 2004 and Warmuth 2015) until the waves enter the CH at different times, i.e., the values for the phase speed start at vw ≈ 2.2 (for ρIA = 1.9, blue), vw ≈ 1.9 (for ρIA = 1.7, red), vw ≈ 1.7 (for ρIA = 1.5, green), and vw ≈ 1.4 (for ρIA = 1.3, magenta) and decrease to vw ≈ 1.5 (for ρIA = 1.9, blue), vw ≈ 1.39 (for ρIA = 1.7, red), vw ≈ 1.2 (for ρIA = 1.5, green), and vw ≈ 1.13 (for ρIA = 1.3, magenta).


Another clear difference for Ark 120 with the NT thin disc predictions is the variability. From the best simultaneous fit of the 2013 and 2014 observations, we infer a significant increase in mass accretion rate through the disc from 0.03 to 0.07 Lbol/LEdd in only one year, but a standard thin disc around a SMBH cannot vary on such timescale. Indeed, the radial mass accretion rate change via viscous processes has a time-scale of torb(R)/[α(H/R)2]. For Ark,120, assuming an orbital time-scale at R = 100 Rg, a viscosity parameter of 0.1 and a H/R (H is the height scale of the disc) value of 0.1, this corresponds to ∼150 years. Moreover, the optical-UV flux significantly changes in less than a year, varying for example by a factor of 50% in the UVW2 band between 2013 and 2014 (e.g. see Fig. 1, Lobban et al. 2018). Similar rapid changes in the optical-UV flux are typically seen in other BLS1s, especially those at low Lbol/LEdd (e.g. MacLeod et al. 2010; Kozłowski 2016; Simm et al. 2016; Rakshit & Stalin 2017). These are generally assumed to be from reprocessing, where the X-ray flux illuminates the outer disc (e.g. Buisson et al. 2017), and adds to the intrinsic emission. An additional reprocessed component in the optical-UV would lead us to overestimate the value of the intrinsic Ṁ, so to an underestimate of BH spin via the efficiency argument (Kubota & Done 2018). Nonetheless, changes as large as about 50% in the UV flux are unlikely to be driven by X-ray reprocessing, as the UV flux in Ark 120 is much higher than in the X-ray band. Besides, detailed models of the expected optical-UV variability from X-ray reprocessing fail to fit the excellent long term simultaneous optical-UV-X-ray datasets, and would imply a larger disc size than expected by standard thin disc (e.g. NGC 5548: McHardy et al. 2014; Edelson et al. 2015; Gardner & Done 2017; NGC 4151: Edelson et al. 2017; Ark 120: Gliozzi et al. 2017; Fairall 9: Pal et al. 2017; NGC 4593: Cackett et al. 2018; Pal & Naik 2018; Microlensing studies: Morgan et al. 2010; Dai et al. 2010). Such large discs should be significantly brighter than observed and this discrepancy may be explained for example by a flatter temperature profile than in NT discs, from scattering of a significant part of the optical flux on larger scales, by electron scattering in the disc atmosphere (Dai et al. 2010; Morgan et al. 2010; Hall et al. 2018).


Thermonuclear explosions and AICs of WDs in AGN disks are potential sources for future joint gravitational wave (GW), EM, and neutrino multi-messenger observations. In addition to AIC of WDs, another possible formation channel of millisecond magnetars in AGN disks is mergers of BNSs. Such a merger may produce a millisecond magnetar if the NS equation of state is stiff enough (e.g., Ai et al. 2020). This would also drive a magnetar-powered explosion as discussed above. The mechanism by which a nascent millisecond magnetar might power a GRB jet has been studied in detail over the past decade (Bucciantini et al. 2008, 2012; Metzger et al. 2008, 2011; Siegel et al. 2014).8

8
Some indirect evidence for the magnetar mechanism in GRBs are the presence of a plateau in the early X-ray afterglow of long-duration GRBs, which may be explained as the continuous energy injection from the spindown of a magnetar (Dai & Lu 1998; Zhang & Mészáros 2001; Zhang et al. 2006).
 A putative jet may thus be launched from the AIC of WDs and BNS mergers occurring in AGN disks. However, Zhu et al. (2021b, 2021a) and Perna et al. (2021a) recently showed that GRB jets embedded in AGN disks would be usually choked by the dense material of the accretion disks. Although it is hard to observe gamma-ray signals, Zhu et al. (2021a) suggested that these choked GRBs may effectively produce TeVPeV neutrinos that could be detected by IceCube and IceCube-Gen2. Furthermore, the dissipation of magnetic energy during the merger of BWDs is expected to accelerate cosmic rays and produce high-energy neutrinos (Xiao et al. 2016). In the GW channel, BWD mergers are promising astrophysical GW sources for space-borne GW observatories, e.g., LISA (Amaro-Seoane et al. 2017), TaiJi (Ruan et al. 2020), and TianQin (Luo et al. 2016), while the GW signals from BNS mergers are readily detected with the ground-based GW detectors such as LIGO and Virgo (Abbott et al. 2017). Future joint observations of GW, EM, and neutrino signals can reveal the existence of WD and NS populations in AGN disks.


The most common approaches to observe SPI are spectral observations of typical emission lines for stellar chromospheres and coronae. The earliest approach to observe SPI dates back to the early 2000’s and focused on non-thermal chromospheric Ca II H and K emissions (Shkolnik et al. 2003). Subsequent studies by Shkolnik et al. (2005, 2008) of the system HD 179949 saw enhanced emissions in four out of six observational epochs that appeared to be periodic with the planetary orbital period. Other authors observed different systems and likewise saw chro-mospheric excess emissions (Walker et al. 2008; Staab et al. 2017). In addition, Cauley et al. (2019) estimated possible magnetic field strengths of hot Jupiters based on chromospheric excess emissions. The derived energy fluxes from chromospheric Ca II H and K emissions are larger than typical fluxes derived from Alfvén wing models and magnetohydrostatic models (Saur et al. 2013; Lanza 2015) and the observed periodicity only appears in some epochs, which was suggested to be alternatively explained by star spots (Miller et al. 2012). Recently, Strugarek et al. (2019) investigated how modeling and observations could reconcile by including the magnetic topology of stellar coronae based on the example of Kepler-78. In the UV range, France et al. (2016, 2018) conducted large surveys with the Hubble Space Telescope, however, the authors could not identify any signals related to SPI. At coronal X-ray wavelengths, several studies have investigated the influence of planets on stellar X-ray activity, such as Kashyap et al. (2008); Scharf (2010); Poppenhaeger et al. (2010). Some studies found correlations between planets and X-ray activity in stars and some did not. Poppenhaeger & Schmitt (2011a,b) explain previously observed correlations, attributed to SPI, as a result of selection effects due to planet detection methods and the limitations in X-ray observations. The radio wavelength range is particularly promising to search for SPI. Recent observations with LOFAR showed strong hints for the existence of SPI in several systems (Vedantham et al. 2020; Callingham et al. 2021; Pérez-Torres et al. 2021). In addition, a recent campaign in the radio range provided the first tentative direct observational hints of an intrinsic magnetic field on an exoplanet (Turner et al. 2021).


Active galactic nuclei (AGNs) are extragalactic sources that emit across the whole electromagnetic spectrum. Such systems are composite and each sub-structure has its own role in shaping the emerging spectrum (see Padovani et al. 2017, for a comprehensive review). It is ubiquitously accepted that the X-ray emission originates in the very inner regions of AGNs, near the central supermassive black hole (SMBH). Accretion of matter infalling on to the SMBH is responsible for the enormous amount of optical-UV photons, a fraction of which can be further energized via inverse-Compton (Sunyaev & Titarchuk 1980) off thermal electrons (the so-called hot corona: Haardt & Maraschi 1991, 1993; Madejski et al. 1995; Zdziarski et al. 1995) up to the X-rays. The maximum energy gain for these seed photons is mainly set by the hot plasma’s temperature, and, to a lower extent, by its opacity (e.g. Rybicki & Lightman 1979; Beloborodov 1999; Middei et al. 2019). In fact, the X-ray continuum in AGNs is well modelled by a power law with a high energy roll-over (e.g. Perola et al. 2002; Dadina 2007; Molina et al. 2009, 2013; Malizia et al. 2014; Fabian et al. 2015, 2017; Ricci et al. 2018; Tortosa et al. 2018). AGN X-ray spectra may show additional features due to reprocessing of the primary X-ray emission by the circumnuclear material. A fluorescence emission line from the Fe K-shell is commonly observed as the most prominent feature (e.g. Bianchi et al. 2009) and its analysis carries a wealth of information on the physics of the reflecting material. This emission line has an intrinsically narrow profile that can undergo distortions, such as broadening, due to special and general relativistic effects. In particular, the closer to the SMBH the reflectors, the more distorted (i.e. the broader) the neutral or ionized Fe line profile (e.g. Fabian et al. 1995). On the contrary, at larger distance, these effects are negligible, thus the Fe Kα shape is consistent with a narrow profile. Additionally, in the case of Compton-thick reflectors (i.e. NH ≳ 1.5 × 1024 cm−2) the X-ray spectra show a typical emission excess around 30 keV, the so-called Compton-hump (e.g. Matt, Fabian & Ross 1993). The effect of any absorbing matter crossing our line of sight can significantly attenuate the observed number of photons, especially in the soft X-rays (e.g. Cappi et al. 1999; Awaki et al. 2000; Matt 2002; Bianchi et al. 2009; Middei et al. 2021).


The measurement of clumps at redshifts beyond the peak of cosmic star formation is notoriously difficult. The identification of clumpy galaxies in the dominant population of irregular galaxies at high redshift dates back to the first deep Hubble Space Telescope (HST) images (e.g., Williams et al. 1996). Subsequent studies at z ~ 1−3 revealed that clumpy galaxies are more numerous than in the local Universe (e.g., Abraham et al. 1996; van den Bergh et al. 1996; Giavalisco et al. 1996; Elmegreen et al. 2004, 2007, 2008, 2009; Elmegreen & Elmegreen 2006; Elmegreen et al. 2013; Kubo et al. 2013, 2016; Glazebrook 2013; Tadaki et al. 2014; Murata et al. 2014; Guo et al. 2015; Garland et al. 2015; Bournaud 2016). The fraction of clumpy galaxies was studied from z = 0 up to the most distant galaxies identified today at z ~ 10 (Ravindranath et al. 2006; Guo et al. 2012, 2015; Shibuya et al. 2016). In the sample of galaxies with 0.5 z  3 in the CANDELS survey, Guo et al. (2015) find that galaxies with low mass log (M⋆/M⊙)  9.8 have a high fraction of off-center clumps fclumpy ~ 60% constant over the observed redshift range, while for intermediate and massive galaxies fclumpy decreases from ~40% at z ~ 3 to ~15% at z ~ 0.5. Combining deep HST imaging from the 3D-HST, CANDELS, HUDF and HFF surveys Shibuya et al. (2016) claim that \hbox{$f_{\rm clumpy}^{\rm UV}$}fclumpyUV follows an evolution similar to that of the star formation rate density (e.g., Madau & Dickinson 2014), increasing from z ≃ 8 to z ≃ 1−3 and decreasing from z ≃ 1 to z ≃ 0. In comparing these observed trends with the predictions of simulations, Guo et al. (2015) conclude that VDI are likely responsible for fclumpy at high mass and that minor mergers are a viable explanation for fclumpy at intermediate mass for z  1.5, while Shibuya et al. (2016) conclude that VDI is the main origin of all clumps. Both these studies exclude major mergers as a possible contribution to the evolution of the fraction of clumps. This is somewhat surprising as the major merger fraction for star-forming galaxies is observed to increase up to ~20% at z ≃ 1−2 (e.g., Lotz et al. 2011; López-Sanjuan et al. 2011, 2013), staying high at least to z ~ 3−4 (e.g., Conselice et al. 2008; Tasca et al. 2014a), and one would therefore expect that a fraction of the clumps is related to ex situ major merging.


Owing to their brightness at rest-frame FIR wavelengths, the ionized and neutral species of Carbon, Nitrogen, and Oxygen are powerful diagnostic lines for tracing the ISM of nearby and distant galaxies. When combined with photodissociation region (PDR) models (Tielens & Hollenbach 1985), measurement of the emission from different lines provide a means to constrain quantities such as the ionization rate and metallicity of the ISM of galaxies. Multilevel FIR transition lines have now been widely surveyed in local galaxies, originally by ISO (e.g. Luhman et al. 1998; Malhotra et al. 2001) and more recently using the PACS spectrometer (Poglitsch et al. 2010) on the ESA Herschel Space Observatory (Pilbratt et al. 2010). The [C ii]158 μm line is typically the brightest in star-forming galaxies, arising from ionized, and even neutral gas where it is the main coolant (Wolfire et al. 2003). Another commonly observed FIR line tracer of the ionized ISM is [N ii]122 μm. It has the advantage that it can be found associated with lower excitation gas, close to that observed in our own Galaxy (e.g. Goldsmith et al. 2015; Herrera-Camus et al. 2016). Another major coolant of the ISM is [O i]63 μm (Wolfire et al. 2003). Owing to its high excitation temperature and critical density, it can dominate the cooling in regions of starburst activity (Kaufman et al. 1999; Kaufman, Wolfire & Hollenbach 2006; Brauher, Dale & Helou 2008; Croxall et al. 2012; Narayanan & Krumholz 2017). When combined with measurements of the [C ii]158 μm line intensity and FIR luminosity, the [O i]63 μm line intensity can constrain the FUV field, G, and the gas density using PDR models. The luminosity in these FIR lines generally exhibits a deficit in the most FIR luminous galaxies compared to the trend expected from lower luminosity galaxies (e.g. Malhotra et al. 2001; Graciá-Carpio et al. 2011; Díaz-Santos et al. 2017). This has made the emission from lines like [O i]63 μm more challenging to detect at high-redshifts.


We first determined the orbital parameters for RS Ser, V449 Per, and V1095 Her. Further, we updated the parameters for V593 Cen and MR Del. Using the formula f  = (Ωin – Ω1)/(Ωin – Ωout), we calculated the contact factors f for RS Ser, V593 Cen, and V1095 Her as 6.5 per cent, 40 per cent, and 53 per cent, respectively. RS Ser is a contact binary with a small temperature difference of 131 K and a low contact factor. For V593 Cen, we updated the orbital parameters using more complete light curves. The orbital inclination of 83°.18 is similar to the result (82°.6) obtained by Zhao et al. (2019). The temperature of the secondary component (15 284 K) is higher than the previous result of 15 099 K. However, the mass ratio of 0.6 is lower than the previous result of 1.05 (Zhao et al. 2019). More spectroscopic observations are required to confirm the mass ratio. We confirmed that V593 Cen is an early-type contact binary with a deep contact factor as well as a black hole candidate. For MR Del, we revised the absolute parameters using its full light curve and the published radial velocities, which are similar to those published previously (Zhao et al. 2019; Pribulla et al. 2009; Djurašević et al. 2011). V1095 Her is also a contact binary with a deep contact factor of 40 per cent and a temperature difference of about 172 K. Looking over our four complete light curves, we found no evident starspot activity, and estimated variations exist over a long-term time-scale of years. V449 Per is an interesting target for detecting extra-solar and brown dwarfs using the minima timing variability of a low-mass eclipsing binary (Pribulla et al. 2012). Additional minima with higher precision are required to study its periodic variation further. Our physical parameters for RS Ser, V593 Cen, and V1095 Her are based on a light curve with a q-search-determined mass ratio. The nature of these parameters is speculative and preliminary. Radial velocities may eventually come to rescue them and provide a more definitive determination.


Previously it has been postulated that the SMS formation by DC is only possible in atomic cooling haloes both with intense FUV irradiation and with primordial gas composition. Here we have shown that SMSs can form also in slightly metal-enriched cases as long as FUV irradiation is intense enough. This relaxation of the condition will increase the expected number density of massive seed BHs. Several authors have estimated the number density of such seeds formed in the usual DC scenario, which requires metal-free gas composition. Using the critical intensity advocated by recent studies (Agarwal et al. 2014; Sugimura et al. 2014; Inayoshi & Tanaka 2015), this ranges from a few Gpc−3 (e.g. Dijkstra et al. 2008; Dijkstra, Ferrara & Mesinger 2014), to 10−6 to 10−4 Mpc−3 (e.g. Agarwal et al. 2012; Visbal, Haiman & Bryan 2014a; Chon et al. 2016; Habouzit et al. 2016; Valiante et al. 2016). The dynamical heating model by Wise et al. (2019) predicts the number density of 10−7 to 10−6 Mpc−3. Those seeds can account for the origin of the rare BHs in the high-z universe. If all the SMBHs down to z = 0 shares the universal origin, the seed density should be comparable to that of the SMBHs ubiquitously residing in massive galaxies, ∼0.01–0.1 Mpc−3 (Aller & Richstone 2002; Davis et al. 2014), which is much larger than the seed density predicted by the DC model. The DC in the primordial environment is terminated around z ∼ 10, as the metal enrichment proceeds (e.g. Trenti & Stiavelli 2009; Chon et al. 2016): once a Pop III star ends its life as a core-collapse SN, metallicity inside the host halo jumps up to 10−4 to 10−3 Z⊙ (e.g. Maio et al. 2010; Ritter et al. 2015; Sluder et al. 2016; Chiaki, Susa & Hirano 2018). According to our result, the SMS formation can continue even in such second-generation haloes. Since the second-generation haloes tend to be under stronger radiation field than the pristine ones (e.g. Dijkstra et al. 2014), we expect significant increase in the number density of the SMSs. For example, the first episode of star formation delays another star formation for a few hundred million years by the radiative and SNe mechanical feedback, which ejects a gas from the halo. If the haloes approach close enough to a luminous galaxy before another episode of star formation, they can be ideal sites for SMS formation. Not only the radiation sources outside the halo, but also those inside the same halo can trigger SMS formation in an irradiated massive cloud as long as the metallicity is low enough. With such new varieties of SMS formation sites, the expected seed BH number will be largely enhanced. We will pursue the validity of this scenario using samples from the cosmological simulations in the future studies.


In the context of RI imaging techniques, the standard clean algorithm implements a non-linear, greedy approach to perform deconvolution in an iterative manner (Högbom 1974). Working pixelwise, clean implicitly assumes sparsity of the sought image, removing at each iteration, a fraction of the maximum intensity pixel convolved with the dirty beam from the computed residual image. Over the past years, many variants of this celebrated algorithm have been developed, for instance, its multiscale version (Cornwell 2008). In addition to these clean-based approaches, recent developments in the field of compressive sensing (CS) applied for astronomical imaging have given birth to many imaging algorithms, particularly for RI (Wiaux et al. 2009; Carrillo, McEwen & Wiaux 2012; Garsden et al. 2015; Onose et al. 2016). Leveraging optimization frameworks, these methods aim to solve the underlying image recovery problem by enforcing sparsity of the image of interest in some suitable domain. These techniques have shown the potential to surpass the image reconstruction quality obtained by clean -based approaches (Carrillo, McEwen & Wiaux 2014; Onose et al. 2016; Pratley & Johnston-Hollitt 2016; Onose, Dabbech & Wiaux 2017; Dabbech et al. 2018). While the aforementioned methods have been developed mainly for Stokes I imaging, as previously mentioned these can be extended to polarimetric imaging by following the same imaging approach for all the Stokes parameters. In the context of sparsity regularized approaches, one such extension for polarimetric imaging has been presented in Akiyama et al. (2017), promoting sparsity of each of the Stokes parameters using ℓ1 norm combined with total variation (TV) regularization (Rudin, Osher & Fatemi 1992). A point worth noting here is that the above-mentioned approaches, whether clean and its variants or the sparsity regularized method, solve for the Stokes parameters totally independently. However, these images are physically linked via polarization constraint, i.e. the polarized intensity cannot be greater than the total intensity. Within the CS framework, this constraint has been exploited by a recently proposed approach, namely Polarized SARA, estimating jointly the Stokes parameters (Birdi, Repetti & Wiaux 2018a, b). This approach has been shown to provide better reconstruction quality in comparison with the case when the constraint is not accounted for.


Various outbursts in GeV–TeV energies from 1ES 1959+650 have been reported by Fermi-LAT and several ground-based Cherenkov experiments like VERITAS, MAGIC, FACT (Albert et al. 2006; Aliu et al. 2014; Biland et al. 2016) including a new highest historical γ-ray activity, detected by MAGIC collaboration on 2016 June 13–14, when the VHE flux above 100 GeV reached up to 3 Crab unit (C.U) (Bhattacharyya et al. 2019). Many multiwavelength campaign from radio to TeV γ-ray energies have been conducted since its discovery (Krawczynski et al. 2004; Biland et al. 2016) and this source has exhibited a number of outbursts across all energies. One interesting VHE outburst was detected on 2002 June 4 by the Whipple telescope without any activity in contemporaneous X-ray energies, called ‘orphan flare’, during a multiwavelength campaign (Krawczynski et al. 2004). In the recent past, 1ES 1959+650 has undergone a few major outbursts in all wavelengths specially in X-ray energies since 2015 (Kapanadze et al. 2016). Unprecedented flux and spectral variability during these episodes have been observed (Kapanadze 2015; Kaur et al. 2017; Kapanadze et al. 2018; Patel et al. 2018). Such flux and spectral variations in different energy bands over time provide an opportunity to study underlying physical processes in terms of particle acceleration processes, evolution of the accelerated particles (leptons/hadrons) within the source, and their radiative cooling and escape processes. Many authors explained the broad-band emission from this source with leptonic one-zone SSC process (Krawczynski et al. 2004; Tagliaferri et al. 2008). But the lack of correlation between X-ray and VHE γ-rays several times and also during the orphan flare, mentioned earlier, challenges the leptonic one-zone SSC model of emission. Alternatively, EC, lepto-hadronic and two-zone SSC models have been also tried to explain the broad-band SED of the source (Backes et al. 2012; Aliu et al. 2014; Asano & Hayashida 2018; Patel et al. 2018). Recently, the MAGIC collaboration again introspected the VHE flaring episodes in 2016, mentioned earlier, to study the feasibility of neutrino emission from 1ES 1959+650 as well under the framework of mixed lepto-hadronic model (MAGIC Collaboration 2020a). Although they (MAGIC collaboration) have concluded that it is difficult to detect neutrinos from the same source during extreme γ-ray flares, it is customary to mention that more study with well-sampled data from multiple experiments are inevitable to understand the true physical processes inside this type of astrophysical sources in a better way.


While both Suprime-Cam/NB359 and HST/F336W trace LyC for sources at z > 3.06, NB359 has a narrower filter bandpass, and it preferentially captures ionizing photons closer to the Lyman limit (see Fig. 1). Because IGM attenuation varies as a function of wavelength, expected transmissions of photons through the IGM (here we denote the ratio of flux density with and without IGM attenuation as ‘IGM transmission’) are different for different filters. In Fig. 2 we show the median and 68 percentile IGM transmission values of NB359 andF336W for a source at a redshift range of 3.1 ≤ z ≤ 3.8. These IGM transmissions are estimated from Monte Carlo simulations (Inoue & Iwata 2008) which generate 10 000 sightlines for redshifts consistent with the H i cloud distribution defined analytically by Inoue et al. (2014). For each sightline we calculate IGM transmission through NB359 or F336W for an object with a flat SED in fν (i.e. fν = constant) and obtain median and 68 percentile values from the 10 000 instances. These calculations are repeated from z = 3.1 to 3.8 with a redshift step of 0.1. The median values of IGM transmission for NB359 are higher than those for F336W, especially at the lower redshift range. This is because NB359  traces a rest-frame wavelength range close to the Lyman limit where IGM transmission is higher than that for photons with shorter wavelengths. If the same limiting magnitude is achieved, NB359 is more sensitive for detecting LyC photons from z > 3 galaxies than F336W. Median values of IGM transmission for both NB359 and F336W rapidly decrease as the source redshift increases, which indicates that the detection of LyC photons becomes increasingly difficult due to increasing IGM opacity. However, higher-side 68 percentile IGM transmission values at z = 3.5 are 0.33 for NB359 and 0.20 for F336W, respectively. The fluctuation of IGM transmission among different sightlines is large, and there are still a reasonable number of sightlines with significant IGM transparency for LyC in the redshift range studied in this paper.


It is well known that the accretion on to compact objects may influence the nearby ambient around SMBHs in the centre of galaxies (e.g. Salpeter 1964; Fabian 1999; Barai 2008; Germain, Barai & Martel 2009). Together with the outflow phenomena, it is believed to play a major role in the feedback processes invoked by modern cosmological models (i.e. Λ-Cold Dark Matter) to explain the possible relationship between the SMBH and its host galaxy (e.g. Magorrian et al. 1998; Gebhardt et al. 2000) as well as in the self-regulating growth of the SMBH. The problem of accretion on to an SMBH has been studied via hydrodynamical simulations (e.g. Ciotti & Ostriker 2001; Di Matteo, Springel & Hernquist 2005; Li et al. 2007; Ostriker et al. 2010; Novak, Ostriker & Ciotti 2011). In numerical studies of galaxy formation, spatial resolution permits resolving scales from the kpc to the pc, while the sub-parsec scales of the Bondi radius are not resolved. This is why a prescribed sub-grid physics is employed to solve this lack of resolution. With sufficiently high X-ray luminosities, the falling material will have the correct opacity, developing outflows that originate at sub-parsec scales. Therefore, calculations of the processes involving accretion on to SMBH have become of primary importance (e.g. Proga, Stone & Kallman 2000; Proga 2000, 2003; Proga & Kallman 2004; Proga 2007; Ostriker et al. 2010). Numerical calculations of the accretion of matter on to SMBHs, including the radiative-outflow component, have been mostly performed using Eulerian finite-difference methods (Mościbrodzka & Proga 2013) [see also the overviews by Edgar (2004) and Foglizzo et al. (2005) and references therein for earlier work], while only a few calculations have been reported using smoothed particle hydrodynamics (SPH) techniques (Barai 2008; Barai, Proga & Nagamine 2011, 2012; Nagamine, Barai & Proga 2012), where results for the accretion rates, outflow rates, thermal instabilities, and impact of the thermal, mechanical, and X-ray feedbacks have been obtained for evolutions up to 5 Myr and scales from 0.1 to 200 pc.


As well as being directly excited from the ground state, Balmer lines (intensity, line profile, polarization and so on) are affected by the conversion of Lyman lines to Balmer lines. For example, the absorption of Ly β by a hydrogen atom results in radiative excitation from 1s to 3p, and the excited atom can emit H α by the spontaneous transition from 3p to 2s. Simultaneously, the conversion yields the 2s-state hydrogen atom, which creates the two-photon continuum by the spontaneous transition from 2s to 1s. Thus, the Ly β to H α conversion impacts the total intensity, line profile, and net polarization of H α. Moreover, an adequate density of 2s-sate atoms can further scatter H α photons. Although such fundamental physics is well known, it has not been well studied in SNR shocks. In fact, it is usually assumed that the Ly β photons are at the limits of either completely optically thick or optically thin at SNR shocks, i.e. they are completely converted to H α photons or not at all (e.g. Heng & McCray 2007; van Adelsberg et al. 2008; Morlino et al. 2012, 2013b; Shimoda et al. 2018). Contrary to this, Ghavamian et al. (2001) studied the conversion of Ly β and Ly γ to H α and H β by Monte Carlo simulations and claimed that intermediate conversion occurs. However, they and previous studies did not consider the population of 2s-state hydrogen atoms. In this paper, we provide a formulation of the radiative line transfer with the rate equation of atomic population and study the nature of Balmer line emissions from SNR shocks. In this paper we do not consider the polarization, deferring that instead to a later work. Note that as a first step, our model makes several simplifications in the treatment of the SNR shock, handling the hydrogen atoms as fluids and supposing no particles leaking back upstream (e.g. cosmic rays). Our calculation of radiative transfer is based on so-called the ray-tracing method and uses updated atomic data from the literature (e.g. Heng & Sunyaev 2008; Tseliakhovich, Hirata & Heng 2012). Moreover, we consider only hydrogen line emissions and ignore bremsstrahlung radiation, thermal emissions from the SNR ejecta, and external radiation sources. Thus, our model possibly predicts somewhat smaller population of 2s-state hydrogen atoms than would be the case in a realistic SNR shock.


The energy dependent pulse arrival time can usually be observed in AMXPs. Soft lags are most often seen in AMXPs, where the pulse arrival times of the pulsations from softer energy bands lag compared to the ones from the harder energy bands. This phenomenon was first discovered by Cui et al. (1998) during the 1998 outburst of the SAX J1808.4–3658. The soft lag tendency can clearly be detected from 2 keV extended up to 10 keV (hereafter, the break point) for about 200 μs (∼0.08 cycles) but saturated for harder X-ray bands. Similar energy dependent pulse arrival time behavior can also be found in XTE J1751–305 (Gierliński & Poutanen 2005), XTE J1814–338 (Watts & Strohmayer 2006), HETE J1900.1–2455 (Galloway et al. 2007), and XTE J1807–294 (Chou et al. 2008) with different break point energies. However, the energy dependent pulse arrival time acts differently in IGR J00291+5934. Falanga et al. (2005) found that the soft lags can extend to the break point energy at ∼6 keV but the tendency reverses instead of saturation for the pulse of energy bands harder than the break point (hereafter hard lags) during its 2005 outburst. Similar behaviors are also observed during its 2015 outburst (Sanna et al. 2017) with a different break point energy at ∼8 keV. Such hard lags are also marginally detected in IGR J17511–3057 (Falanga et al. 2011) and IGR J17498–2921 (Falanga et al. 2012). On the other hand, the energy dependent pulse arrival times for two AMXPs are rather peculiar. The pulse arrival times seem independent of energy bands below ∼17 keV for SAX J1748.9–2021 (Patruno et al. 2009a) and only hard lags are detected in IGR J18245–2452 (De Falco et al. 2017). The newly discovered AMXP IGR J17379-3747 also shows unusual energy dependent pulse arrival times. Regular soft lags can be observed between 0.5 and 6 keV with no break point being detected; however, the phase difference between the softest and hardest bands can be as high as ∼0.3 cycles (or ∼110°; Bult et al. 2019).


Solar prominences or filaments are cool, dense plasmas embedded in the million-Kelvin corona (Mackay et al. 2010). The plasmas originate from the direct injection of chromospheric materials into a pre-existing filament channel, levitation of chromospheric mass into the corona, or condensation of hot plasmas from the chromospheric evaporation due to the thermal instability (Xia et al. 2011, 2012; Keppens & Xia 2014; Zhou et al. 2014). Prominences are generally believed to be supported by the magnetic tension force of the dips in sheared arcades (Guo et al. 2010b; Terradas et al. 2015) or twisted magnetic flux ropes (MFRs; Cheng et al. 2012, 2014a; Su & van Ballegooijen 2012; Sun et al. 2012a; Zhang et al. 2012a; Xia et al. 2014a, 2014b). They can keep stable for several weeks or even months, but may get unstable after being disturbed. Large-amplitude and long-term filament oscillations before eruption have been observed by spaceborne telescopes (Chen et al. 2008; Li & Zhang 2012; Zhang et al. 2012b; Bi et al. 2014; Shen et al. 2014) and reproduced by numerical simulations (Zhang et al. 2013), which makes filament oscillation another precursor for coronal mass ejections (CMEs; Chen 2011) and the accompanying flares. When the twist of a flux rope supporting a filament exceeds the threshold value (2.5π–3.5π), it will also become unstable and erupt due to the ideal kink instability (KI; Hood & Priest 1981; Kliem et al. 2004; Török et al. 2004, 2010; Fan 2005; Srivastava et al. 2010; Aschwanden 2011; Kumar et al. 2012). However, whether the eruption of the kink-unstable flux rope is failed or ejective depends on how fast the overlying magnetic field declines with height (Török & Kliem 2005; Liu 2008; Kumar et al. 2010). When the decay rate of the background field exceeds a critical value, the flux rope loses equilibrium and erupts via the so-called torus instability (TI; Kliem & Török 2006; Amari et al. 2014; Jiang et al. 2014). On the other hand, if the confinement from the background field is strong enough, the filament will decelerate to reach the maximum height before falling back to the solar surface, which means the eruption has failed (Ji et al. 2003; Liu et al. 2009; Guo et al. 2010a; Kumar et al. 2011; Joshi et al. 2013, 2014; Song et al. 2014).


Starting from the four aforementioned materials, we consider several composition mixtures and grain structures. For the sake of comparison, we first consider compact grains of purely a-Sil, a-C, or a-C:H. Subsequently, according to Köhler et al. (2015), we consider compact grains made of two thirds a-Sil and one third a-C (Mix 1) or one third a-C:H (Mix 2), in terms of volume fractions. These allow reproduction of the mass fractions derived by Jones et al. (2013) for the diffuse ISM. The effect of porosity is tested for the Mix 1 mixture, with a porosity degree of 50% (Mix 1:50). We also evaluate theimpact of the presence of a water ice mantle on compact Mix 1 grains (Mix 1:ice). We further consider two material compositions defined in Pollack et al. (1994) based on depletion measurements: (i) 21% a-Sil and 79% a-C (Mix 3); and (ii) 8% a-Sil, 30% a-C, and 62% water ice (Mix 3:ice). The various grain compositions are summarised in Table 1. For each grain composition, we derive the absorption and scattering efficiencies Qabs and Qsca, respectively, and the asymmetry factor of the phase function g = ⟨cosθ⟩. To allow fast calculations, we make the major assumption that the grains are spherical and compute their optical properties using the Mie theory (Mie 1908; Bohren & Huffman 1983) with the Fortran 90 version of the BHMIE routine given in Bohren & Huffman (1998). For grains consisting of two or three materials, we first derive effective optical constants following the Maxwell Garnett mixing rule (Maxwell Garnett 1904; Bohren & Huffman 1998). Indeed, we assume that in Mix 1 grains, for example, carbon appears as proper inclusions in the silicate matrix rather than assuming a completely random inhomogeneous medium. Mishchenko et al. (2016a,b) performed exhaustive studies of the applicability of the Maxwell Garnett mixing rule to heterogeneous particles. These latter authors showed that this rule can provide accurate estimates of the scattering matrix and absorption cross-section of heterogeneous grains at short wavelengths (typically up to the visible for a 0.1 μm grain and to the mid-infrared(MIR) for a 10 μm grain) if twocriteria are met: both the size parameter of the inclusions and the refractive index contrast between the host material and the inclusions have to be small. Moreover, Mishchenko et al. (2016a) demonstrated that the extinction and asymmetry-parameter errors of the Maxwell Garnett mixing rule are significantly smaller than the scattering-matrix errors, remaining small enough for most typical applications and in particular the kind of applications we perform here. It is however well known that this kind of mixing rule systematically underestimates the absorption efficiency in the FIR to millimetre wavelength range, the implications of which are discussed in Sect. 3.2. We perform our computations with the emc routine of V. Ossenkopf3. For Mix 1 and Mix 2, we assume a matrix of a-Sil with inclusions of a-C or a-C:H, and for Mix 3 a matrix of a-C with inclusions of a-Sil. For grains surrounded by an ice mantle, the optical properties are derived with the core-mantle Mie theory using the BHCOAT routine given in Bohren & Huffman (1998).


The dynamics of stars can be related to the gravitational potential that they inhabit via the collisionless Boltzmann equation. For systems in a steady state with certain symmetry properties (typically spherical or axisymmetric) it is possible to find solutions to the phase-space distribution of a stellar tracer population, either through distribution function modelling or via the moments of the Boltzmann equation (Kapteyn 1922; Oort 1932; Bahcall 1984a,b; Kuijken & Gilmore 1989; Crézé et al. 1998; Holmberg & Flynn 2000; Bienayme et al. 2006; Binney & Tremaine 2008; Garbari et al. 2012; Bovy & Rix 2013; Salomon et al. 2020; Guo et al. 2020; Widmark et al. 2021a). Given the relatively quiet conditions necessary to form disk galaxies, the assumption of equilibrium for near-equilibrium systems has been widely and favourably applied to the Milky Way and other galaxies (McMillan 2011; Binney & McMillan 2011). Our place in the Milky Way makes it ideal to accurately measure its gravitational potential and mass distribution, since it is the only system where we have access to full six-dimensional phase space information, from its inner regions all the way to its outermost edge (e.g. Deason et al. 2021). A precise and robust measurement of the gravitational potential is crucial for our general understanding of the Milky Way (Dehnen & Binney 1998; Klypin et al. 2002; Widrow et al. 2008; Weber & de Boer 2010; McMillan 2011, 2017; Kafle et al. 2014; Cole & Binney 2017), and also for probing its distribution of dark matter (Read 2014; Nitschai et al. 2020; Cautun et al. 2020; Li et al. 2020; de Salas & Widmark 2021). The local dark matter density is of fundamental importance for direct and indirect dark matter detection experiments (Jungman et al. 1996; Klasen et al. 2015). In a broader sense, dark matter’s gravitational signatures, studied via stellar dynamics and gravitational lensing, is one of the most competitive avenues for constraining its thus far elusive particle nature (Bertone & Tait 2018; Ferreira 2021). The Gaia satellite has been instrumental to this field, pushing the size of the astrometric sample from a few hundred thousand stars (Perryman et al. 1997) to roughly two billion (Gaia Collaboration 2018a).


In addition to the galaxy mergers, the ram pressure may also induce AGN activity together to star formation in cluster galaxies (e.g., Poggianti et al. 2017; Marshall et al. 2018; Ramos-Martínez et al. 2018). The ram pressure, acting on galaxies in a galaxy cluster moving through the intra-cluster medium (ICM), can strip (ram pressure stripping) gas out of the galaxy where the gas is gravitationally bound to the galaxy less strongly than the force from the ICM medium wind due to the ram pressure. A typical effect of the ram pressure stripping is the formation of long tails of stripped gas behind galaxies. A good example of this effect is the Virgo cluster, the closest rich galaxy cluster, considered a ram pressure stripping laboratory since a number of clearly ram pressure stripped galaxies have been observed (e.g., Kenney et al. 2004; Crowl et al. 2005; Chung et al. 2007). Another example of long tails of stripped gas is the Norma cluster (Abell 3627), containing a very extended multi-phase gas stripped tail of a late-type galaxy (ESO137-001 Sun et al. 2007, 2010). In the literature, there is an open debate on the role of the ram pressure stripping on the AGN activity. Observations suggest that ram-pressure stripping tends to produce a decreasing of the radiative-mode AGN activity in the centres of clusters with respect to low density regions (e.g., Ellison et al. 2011; Ehlert et al. 2014; Khabiboulline et al. 2014). This happens because the ram pressure has depleted the gas supply of the central galaxies. However, models and hydrodynamical simulations show that a moderate ram pressure is also able to compress the gas in the galaxy and trigger star formation (e.g., Fujita & Nagashima 1999; Kronberger et al. 2008; Kapferer et al. 2009; Tonnesen & Bryan 2009; Bekki 2014). This effect, produced by a low level of ram pressure, is observationally supported (e.g., Lee et al. 2017). Moderate ram pressure can also produce the removal of angular momentum from the disk gas (Tonnesen & Bryan 2009), producing gravitational instability in the galactic disk (Schulz & Struck 2001) and consequentially the gas fueling towards the central AGN.


Molecular line ratio diagrams for NGC 4710, NGC 5866 and a variety of other galaxies. Our data for NGC 4710 and NGC 5866 are shown as filled circles and squares, respectively, while our data for the nuclear discs and inner rings are shown in blue and red, respectively (black for the intermediate region). Upper and lower limits are represented by arrows. Other lenticular galaxies are indicated by magenta filled stars (Krips et al. 2010; Crocker et al. 2012), starburst nuclei by dark green filled stars, Seyferts by brown filled stars, spiral arm GMCs by black circles with an X (see Baan et al. 2008; table 3 in Krips et al. 2010 and references therein), NGC 6946 (starburst) GMCs by black circles with a cross (Topal et al. 2014), and M31 GMCs by turquoise circles with an X (Brouillet et al. 2005). The data for NGC 1266 (a lenticular galaxy with a molecular outflow) are shown by magenta squares with a filled star (Alatalo et al. 2011). The green shaded region in panel a indicates the typical range of 12CO(1–0)/HCN(1–0) ratios in starbursts with LFIR > 1011 L⊙ (see table B2 in Baan et al. 2008). The range of R11 ratios in the nuclear disc and inner ring of NGC 5866 (this work) are indicated by respectively the blue and red horizontal lines in panel b, while the typical range in spirals with LFIR  1011 L⊙ (Paglione et al. 2001) is indicated by the pale grey shaded region. In panels a and b, Crocker et al.'s (2012) single-dish observations of NGC 4710 and NGC 5866 are shown as an open black circle and an open black square, respectively (see table 4 of Crocker et al. 2012). The HCN(1–0)/HCO+ ratios for M31 GMCs (Brouillet et al. 2005) are indicated by the turquoise shaded region in panels c and d. The green shaded region in panel d indicates the typical range of 13CO(1–0)/HCO+(1–0) ratios in the disc of M82 (starburst; Tan et al. 2011). The 12CO(1–0)/HCN(1–0) ratios in spirals (Gao & Solomon 2004a) are indicated by the dark grey shaded region in panels a, e and f, respectively. The black solid lines in a number of panels show the 1 : 1 relation and are there to guide the eye. Similarly, the black dashed lines show a ratio of 1 in panels c, d and f.


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


It was found that the complex dielectric function from Pecharromán et al. (1999) for the sample obtained by heating bayerite at 1273 K, assuming a spheroid with depolarization parameters of (0.35, 0.003), produced an opacity with 11, 20, 28, and 32 μm features, so this component was included in the models. However, with only this component, the observed 20 μm features in the residual spectra were found to be wider than those in the models. By adding the opacity of the sample obtained by heating boehmite at 1173 K, the width of the 20 μm feature could be matched. This was done using the complex dielectric function for the sample obtained by heating boehmite at 1173 K from Pecharromán et al. (1999), assuming a spheroid with depolarization parameters of (0.35, 0.035). The complex dielectric functions of the samples obtained by heating bayerite and boehmite to various temperatures (Pecharromán et al. 1999) were derived by modeling the reflectance spectra of pellets obtained by pressing powders of these materials under great pressure. This method required Pecharromán et al. (1999) to assume an effective medium theory, such that a pellet is a mixture of one of their samples with a matrix of air. Pecharromán et al. (1999) noted that heating bayerite at 500°C eliminates the XRD pattern of bayerite, and they note that at 700°C, the infrared reflectance spectrum of the boehmite sample no longer shows OH− stretching bands. This must mean that the samples obtained from heating bayerite at 1273 K and from heating boehmite at 1173 K are no longer bayerite or boehmite, respectively. XRD performed by Pecharromán et al. (1999) of the sample of bayerite prepared at 1273 K suggests only θ-alumina was present, and their infrared and NMR spectroscopy confirms this. XRD of their sample obtained from heating boehmite to 1173 K (Pecharromán et al. 1999) suggests δ-alumina to be present, though some amounts of θ-alumina and α-alumina are present, as they deduce from XRD and infrared and NMR spectroscopy.


Many of the earliest simulations of core-collapse supernovae used or were concerned with a general relativistic (GR) approach (Misner & Sharp 1964; Colgate & White 1966; May & White 1966; Wilson 1971; Bruenn 1985; Burrows 1988), and rightly so since neutron stars are sufficiently compact that GR dramatically effects their equilibrium structure. While the importance of including GR gravity in simulations of core-collapse supernovae has always persisted in the literature and is in use in many current and state-of-the-art multidimensional, core-collapse supernova calculations (Marek & Janka 2009; Kuroda et al. 2012; Müller et al. 2012a; Bruenn et al. 2013, 2016; Ott et al. 2013; Lentz et al. 2015; Skinner et al. 2016; Burrows et al. 2018), many modern simulations have used a purely Newtonian approximation for gravity (Takiwaki et al. 2014; Couch & O’Connor 2014; Handy et al. 2014; Couch & Ott 2015; Dolence et al. 2015; Nakamura et al. 2015; Pan et al. 2016; Suwa et al. 2016). Liebendörfer et al. (2001) extensively compared GR gravity and Newtonian gravity in spherical symmetry with a full Boltzmann neutrino transport solver. While their baseline simulations in both prescriptions of gravity fail to explode in 1D, their conclusion is that, overall, GR is helpful for the development of the core-collapse supernova explosion. This conclusion comes out of serendipitous simulations where incorrect nucleon isoenergetic scattering cross sections were used. In these simulations, when GR gravity was used, the simulation predicted an explosion, but when Newtonian gravity was used, the simulations failed to achieve explosions. Bruenn et al. (2001), Buras et al. (2006b), and Lentz et al. (2012) also compared Newtonian and GR simulations in spherical symmetry with energy-dependent neutrino transport. Like Liebendörfer et al. (2001), they observe higher neutrino luminosities and energies but do not extensively study the differences, in part because both simulations still fail to explode owing to the 1D nature of the simulations. Kuroda et al. (2012) examined the difference between special relativistic hydrodynamics and GR hydrodynamics in both 1D and 3D core-collapse simulations using approximate neutrino transport (a gray M1 scheme). However, while the 3D GR simulations show signs of increased susceptibility to explosion, the simulated time was not long enough to observe an explosion. Müller et al. (2012a) also investigated the influence of Newtonian gravity, GR gravity, and GR effective potential gravity in 2D core-collapse simulations using a variable-Eddington-factor, two-moment, energy-dependent neutrino transport scheme and the ray-by-ray+ approximation (where the neutrino transport is done along radial rays assuming spherical symmetry and with minimal coupling between neighboring rays). For the classic 15 M⊙ model from Woosley & Weaver (1995), Müller et al. (2012a) find a late and asymmetric explosion when using fully GR gravity, but not with Newtonian gravity, GR effective potential gravity, or reduced set neutrino opacities. This was, and still is, the most direct evidence that GR aids in the explosion mechanism. It is important to validate the hypothesis that GR gravity does indeed lead to more favorable conditions for explosion in modern-day simulations, with updated progenitor models, and loosening the assumption of spherically symmetric.


The basic idea, summarized in Dekel et al. (2009), is that during VDI, the high surface density of gas and ‘cold’ young stars, Σ, drives the Toomre Q parameter below unity, Q ∼ σΩ/(πGΣ) ≲ 1, where σ is the 1D velocity dispersion and Ω is the angular frequency, a proxy to the epicyclic frequency κ, which is related to the potential well (Toomre 1964). It has been established that under such conditions, the disc will fragment and produce large star-forming clumps. This has been shown using idealized simulations of isolated galaxies (Noguchi 1999; Gammie 2001; Immeli et al. 2004a,b; Bournaud, Elmegreen & Elmegreen 2007; Elmegreen, Bournaud & Elmegreen 2008; Bournaud & Elmegreen 2009; Hopkins et al. 2012b), as well as cosmological simulations (Agertz, Teyssier & Moore 2009; Ceverino et al. 2010; Ceverino et al. 2012; Genel et al. 2012; Mandelker et al. 2014; Oklopcic et al. 2016). The ratio of clump mass to the mass of the cold disc scales as Mc/Md ∝ δ2, where δ = Md/Mtot is the ratio of the cold disc mass to the total mass within the disc radius, which includes the bulge and dark matter halo (e.g. Dekel et al. 2009). This leads to much larger clumps at z ∼ 2 than the low-redshift giant molecular clouds (GMCs). Gravitational interactions in the perturbed disc drive turbulence causing the disc to self-regulate in a marginally stable state with Q ≲ 1 (Dekel et al. 2009; Ceverino et al. 2010; Krumholz & Burkert 2010; Cacciato, Dekel & Genel 2012; Forbes, Krumholz & Burkert 2012; Forbes et al. 2014) that can last for more than a Gyr so long as the accretion is not interrupted. Some recent works have called into question the validity of linear Toomre analysis in the context of these highly non-linear galaxies (Behrendt, Burkert & Schartmann 2015; Tamburello et al. 2015; Inoue et al. 2016) and others have suggested alternate fragmentation mechanisms related to turbulence (e.g. Hopkins 2013). However, since clump formation is largely determined by the balance between self-gravity, turbulent pressure and the centrifugal force, the largest clumps are always roughly at the Toomre scale. Larger clumps would be disrupted due to the shear and/or tidal forces within the disc, or would not collapse in the first place due to the centrifugal force. Therefore, regardless of the full validity of linear Toomre analysis, it is plausible that the Toomre Q parameter can serve as a crude criterion for instability, possibly with a critical value that is larger than unity.

This has been shown using
as well as cosmological simulations


Large numbers of works have extensively studied the binary-disk system in the Newtonian regime with analytic methods (Paczynski 1977; Papaloizou & Pringle 1977; Kocsis, Haiman & Loeb 2012a, b) and hydrodynamical simulations (Lin & Papaloizou 1979; Artymowicz & Lubow 1994; MacFadyen & Milosavljević 2008; Mayama et al. 2010; de Val-Borro et al. 2011; Shi et al. 2012; D’Orazio et al. 2013; Farris et al. 2014; Ju, Stone & Zhu 2016; Muñoz & Lai 2016; Nelson A. & Marzari 2016; Miranda, Muñoz & Lai 2017; Tang, MacFadyen & Haiman 2017; Tang, Haiman & MacFadyen 2018; Muñoz, Miranda & Lai 2019). Simulations within the Newtonian regime during the inspiral of the binary black hole have also been investigated (Baruteau, Ramirez-Ruiz & Masset 2012; Farris et al. 2015; Cerioli, Lodato & Price 2016; Tang et al. 2018). Two-dimensional simulations by Noble et al. (2012) and three-dimensional ones by Zilhão et al. (2015) conducted the fully relativistic magnetohydrodynamic evolution of a circumbinary disk surrounding two non-spinning black holes with equal mass using the near zone metric. Later on, the fully relativistic magnetohydrodynamic simulations of SMBBH–disk interaction with both the near zone metric and the inner zone metric have been performed (Bowen et al. 2017, 2018, 2019; d’Ascoli et al. 2018) and these simulations are limited to several binary orbits. In particular, Bowen et al. (2017) showed that the gravitational potential of the binary black hole in the post-Newtonian (PN) regime is shallower than that in the Newtonian regime, and that such shallow potential in the PN regime has significant effects on the dynamics of the mini-disk around each SMBH. Simulations of SMBBH–disk interaction with full numerical relativity are so computationally expensive that the evolution of disk around SMBBH is constrained within the stage near merger (Farris et al. 2012; Giacomazzo 2012). In this work, we present hydrodynamical simulations of accretion of equal mass SMBBH by using PN hydrodynamics in which the near zone metric of SMBBH is used.


Similar results of the on-disk condensations are obtained to those of the on-disk quiescent coronal rain in AR closed loops in Hα (see Section 3.2). If we considered the AIA 304 Å observations alone, the on-disk condensation, and hence coronal rain events we report here would resemble those occurring in magnetically closed field lines (Antolin & Rouppe van der Voort 2012; Antolin et al. 2012; Ahn et al. 2014), which are generally interpreted as a manifestation of the heating-condensation cycles due to thermal nonequilibrium (Schrijver 2001; Müller et al. 2003, 2004; Antolin 2020). However, combining the observations of SDO and STEREO A and B at different viewing angles, we find that the on-disk coronal rain in this study corresponds to the downflows of condensations facilitated by reconnection between open and closed structures. Similarly, if we analyze only the on-disk observations as recorded by the AIA as shown in Figure 7, it appears that the structures gradually brighten first in the 171 Å channel and then in the 131 Å channel. Such sequential appearance of coronal structures in the AIA channels sensitive to emission from progressively cooler plasma could be interpreted as a case of loop cooling after nanoflare heating (e.g., Viall & Klimchuk 2012; Li et al. 2015), for instance. In contrast, by employing observations from multiple vantage points, we show that the on-disk structure brightening in the AIA images is actually due to cooling and condensation of plasma facilitated by reconnection in the high corona that is not necessarily regulated by any heating mechanism. To search for the origination of structures harboring on-disk flow, e.g., coronal rain, in the transition region or chromospheric lines, observations from different viewing angles are thus quite important. If there is no observation from other viewing angles, evolution of the associated structures, that may be difficult to observe on the disk, in multiwavelength images during the cooling and condensation process needs to be examined because the condensation facilitated by reconnection cools down from ∼0.9 MK, the characteristic temperature of the 171 Å channel, rather than from the higher temperatures.


There are several natural scenarios for the initial flare-caused impulsive perturbation of an active region to develop into a quasi-periodic response, which includes the effects of resonance in closed coronal plasma structures (acting as resonators), dispersion of a wave-guide, and non-linearity/self-organization (McLaughlin et al. 2018; Zimovets et al. 2021). The observed doubling of the QPP and shorter lifetime of shorter-period QPP modes strongly indicate in favour of resonant dynamics of magnetohydrodynamic waves in a coronal loop, for which the oscillation period is prescribed by the local plasma conditions (i.e. the Alfvén and sound speeds) and the loop length (Nakariakov et al. 2021; Wang et al. 2021). More specifically, fast- and slow-mode magnetoacoustic waves in coronal plasma structures are well-known to be subject to a frequency-dependent damping by e.g. resonant absorption and thermal conduction (e.g. Ofman & Aschwanden 2002; Ruderman & Roberts 2002; De Moortel & Hood 2003). Likewise, excitation of even and/or uneven parallel harmonics of fast- and slow-mode standing waves in a plasma loop is known to be highly sensitive to the location of the initial perturbation along the loop. For example, Tsiklauri et al. (2004) and Selwa, Murawski & Solanki (2005) theoretically demonstrated that the second parallel harmonic of a slow standing wave can be effectively excited if the impulsive energy release occurs near the apex of the loop. Observations of higher harmonics of fast-mode oscillations in coronal loops were also shown to be subject to the excitation mechanism and location of the initial displacement of the loop (e.g. De Moortel & Brady 2007; Srivastava et al. 2008; Yuan & Van Doorsselaere 2016; Pascoe et al. 2017; Duckenfield et al. 2019). Thus, taking cs = 600 km s−1 for the sound speed in a hot flaring loop, the Alfvén speed cA = 1200 km s−1 (e.g. Mathioudakis et al. 2006), and treating the observed QPP periods as characteristic acoustic or Alfvén transit times along the loop, we can estimate the corresponding loop lengths as 80–160 Mm for the 2018 flare and 50–100 Mm for the 2019 flare, i.e. 0.2–0.7 R⋆. These estimations agree with a typical length of solar coronal loops, and, are approximately an order of magnitude larger than those derived by Mathioudakis et al. (2006). However, the above authors ruled out these small loop lengths suggesting instead that they may be due to a fast-MHD wave, with the modulation of the emission being due to the magnetic field. The present observation in the doubling of the QPP in both YZ CMi flares presents rare and compelling evidence for the presence of compact plasma loops in a stellar corona.


A different approach is to count the amount of baryonic material within the proto-cluster bounds associated with the member galaxies and attempt to relate that back to the overall mass of the structure, an approach which has been employed successfully at low redshift when the galactic baryonic content of cluster member galaxies is dominated by stars (Andreon 2012). The approach we take here is similar to that of Lemaux et al. (2014a). Briefly, the total amount of stellar matter of the zspec members is counted and a completeness correction is made to this value for galaxies at stellar masses

$\log(\mathcal{M}_{\ast}/M_{\odot})\ge 9.5$log(M∗/M⊙)≥9.5
 (see Sect. 4.2.1 for the reasoning behind this cut) based on the number of zphot members and non-members without secure spectral redshifts within the bounds of the proto-cluster and the likelihood of their being true members. An additional correction is made to correct for galaxies in the stellar mass range

$8.0 < \log(\mathcal{M}_{\ast}/M_{\odot})< 9.5$8.0log(M∗/M⊙)9.5
 by integrating the stellar mass function of Davidzon et al. (2017) appropriate for this redshift. Here we additionally make the assumption that stellar mass comprises 50% of the baryonic content of galaxies by mass at these redshifts, a value broadly consistent with the few measurements made at or near these redshifts (e.g., Tacconi et al. 2010; Capak et al. 2011b; Schinnerer et al. 2016; Scoville et al. 2016). We assume for the purposes of this calculation that the proto-cluster is a closed system, with all gas being converted to stars by z = 0 and that the completeness-corrected galaxy population which lies within Rproj ≤ 3 Mpc at z ~ 4.57 comprises the entirety of the galaxy population which will eventually be contained within the cluster virial radius at z = 0. The latter assumption is broadly consistent with simulations (Muldrew et al. 2015) to ~10% accuracy, a factor which we account for in the calculation below. Any total to stellar mass conversion then provides a z = 0 total mass, which we de-evolve to z ~ 4.57 using the correction factors of Muldrew et al. (2015) appropriate for z ~ 4.57 (0.20 ± 0.03), a correctionwhich is appropriate for descendents of all masses. Into this formalism we input the resulting completeness-corrected baryonic content of

$\log(\mathrm{\Sigma}\mathcal{M}_{\ast}/M_{\odot})=12.39^{0.05}_{-0.07}$log(ΣM∗/M⊙)=12.39−0.07+0.05
 to the r200 stellar mass to M500 total mass relation of Andreon (2012) and scale the resulting M500 to the virial radius (Rvir = 0.33 Mpc) using the methods presented in Lemaux et al. (2014a) giving:

(2)

\begin{equation*}
\log(\mathcal{M}/\mathcal{M}_{\odot})_{z=4.57, \, \mathrm{\Sigma}\mathcal{M}_{\ast, corr}} = 13.31^{0.23}_{-0.27}.\end{equation*}log(M/M⊙)z=4.57, ΣM∗,corr=13.31−0.27+0.23.


Recently, rotationally supported disks have been found not only in Class I sources but also in some Class 0 sources (e.g., Murillo et al. 2013; Yen et al. 2013, 2017; Ohashi et al. 2014; Tobin et al. 2015, 2016b, 2016a; Seifried et al. 2016; Aso et al. 2017; Lee et al. 2017; Okoda et al. 2018). In spite of these extensive studies, there is still controversy regarding when and how a disk structure is formed around a newly born protostar. Moreover, the disk formation process has been revealed to be much more complicated for binary and multiple cases, both in observations (Dutrey et al. 2014; Tokuda et al. 2014; Takakuwa et al. 2014, 2017; Tobin et al. 2016b, 2016a; Boehler et al. 2017; Artur de la Villarmois et al. 2018; Alves et al. 2019) and in numerical simulations (e.g., Bate & Bonnell 1997; Kratter et al. 2008; Fateeva et al. 2011; Shi et al. 2012; Ragusa et al. 2017; Satsuka et al. 2017; Price et al. 2018; Matsumoto et al. 2019). For instance, circumbinary/circummultiple disk structures with a spiral structure as well as a circumstellar disk for each component are reported (e.g., Tobin et al. 2016a; Takakuwa et al. 2017; Artur de la Villarmois et al. 2018; Matsumoto et al. 2019; Alves et al. 2019). In addition, it is not clear how molecules are processed during the disk formation process and what kinds of molecules are finally inherited by protoplanetary disks and potentially by planets. Understanding these processes is crucial, as they will provide important constraints on the initial physical and chemical conditions for the planetary system formation study. In this context, physical and chemical structures and their mutual relation for disk-forming regions of low-mass protostellar sources have been investigated with the Atacama Large Millimeter/submillimeter Array (ALMA; e.g., Sakai et al. 2014b, 2014a; Oya et al. 2016, 2017, 2018, 2019; Imai et al. 2016, 2019; Jacobsen et al. 2019). These studies reveal that infalling envelopes and rotationally supported disks are not smoothly connected to each other either in physical structure or in chemical composition, unlike previous expectations.


NGC 4418 is one of the closest and best-studied galaxies hosting CONs. It is an LIRG with its 8–1000 μm infrared luminosity (LIR) of 1.4 × 1011 L (Sanders et al. 2003)4

4
With our assumed distance, the luminosity is larger than the threshold for the LIRG classification of LIR = 1 × 1011 L (Sanders & Mirabel 1996). We note, however, that NGC 4418 is sometimes classified as a non-LIRG if one adopts smaller distance to the galaxy. For example, with its recession velocity (cz) and an assumed Hubble constant of H0 = 75 km s−1 Mpc−1, the distance is estimated to be 28.32 Mpc and LIR = 9. 4 × 1010 L.
 at a distance of 34 Mpc (1″ = 165 pc; Sakamoto et al. 2013).5

5
Sakamoto et al. (2013) adopted the distance from Sanders et al. (2003), in which distance is calculated with cz using the cosmic attractor model outlined in Appendix A of Mould et al. 2000, using H0 = 75 km s−1 Mpc−1 and adopting a flat cosmology in which ΩM = 0.3 and Ωλ = 0.7. We adopt this distance for consistency with recent closely related studies of this galaxy (Aalto et al. 2012; Costagliola et al. 2013; Varenius et al. 2014).
 In spite of its huge infrared luminosity, the host galaxy is classified from the optical morphology as an ordinary Sa-type galaxy ([R’]SAB[s]a; de Vaucouleurs et al. 1991) with moderate inclination (i = 62°; taken from Sakamoto et al. 2013 for consistency; based on Jarrett et al. 2000). It has a neighbor galaxy about 32 kpc (32) away (VV 655 = MCG+00- 32-013 = SDSS J122704.47-005420.6;

 km s−1; Evans et al. 2003; Varenius et al. 2017). Varenius et al. (2017) found a bridge of H i 21 cm emission connecting these two galaxies and argued that their strong tidal interaction occurred about 190 Myr ago. The optical nuclear emission line spectrum of NGC 4418 is classified as LINER (Armus et al. 1989; Shi & Gu 2005) or Seyfert 2 (Baan et al. 1998), but no direct signature of AGNs such as very broad permitted lines is known (see also Lehnert & Heckman 1995). NGC 4418 is deficient of X-ray emission for its infrared luminosity, and its interpretation has been a matter of controversy. Maiolino et al. (2003) tentatively identified, with low statistics, a Compton-thick (reflection-dominated) AGN on the basis of its small photon index (or flat X-ray spectrum;

, where

, E is the photon energy, and N(E) is the photon number density). On the other hand, Lehmer et al. (2010) found the opposite (soft) spectral index (

), which is even softer than the one of Compton-thin AGNs (Γ ≃ 1.7; Mushotzky et al. 1993). We note that both analyses are based on the Chandra AICS-S data, and Lehmer et al. (2010) added ≃30% more integration onto the earlier data used by Maiolino et al. (2003).


There is a similarity between the ISM and the young stellar structures identified here. First, similar to the young stellar structures, the ISM also displays irregular morphologies and contains large amounts of substructures (clouds, clumps, cores, filaments, etc.) that are hierarchically organized (Rosolowsky et al. 2008). Second, the ISM substructures also follow a power-law size distribution, which indicates a scale-free behavior (e.g., Elmegreen & Falgarone 1996). The third aspect of their similarity comes from the fractal dimension. The projected fractal dimension of the ISM has been investigated based on the perimeter–area relation of its projected boundaries. Typical values are close to D2 = 1.4–1.5 (e.g., Beech 1987; Scalo 1990; Falgarone et al. 1991; Vogelaar & Wakker 1994; Lee 2004; Lee et al. 2016; although smaller values have also been reported by, e.g., Dickman et al. 1990; Hetem & Lepine 1993), which are consistent with the fractal dimension as derived for the young stellar structures. Using power-spectrum analysis, Stanimirovic et al. (1999, 2000) reported D2 = 1.4 or 1.5 for the ISM in the SMC, also close to that of the young stellar structures. On the other hand, it is possible to measure the volume fractal dimension of the ISM, since clouds along the line of sight can be distinguished by their velocities. For instance, Elmegreen & Falgarone (1996) reported D3 = 2.3 ± 0.3 based on the size distribution for a number of Galactic molecular clouds, and Roman-Duval et al. (2010) found D3 = 2.36 ± 0.04 using the mass–size relation. If the relation D3 = D2 + 1 holds for the ISM, these results would not be far from the fractal dimension of the young stellar structures. Unfortunately, there is no reported measurement of the fractal dimension of the ISM in the LMC bar region. However, it has been suggested that, despite a few exceptions, the fractal dimension is invariant from cloud to cloud, regardless of their nature as star-forming or quiescent, whether gravitationally bound or unbound (e.g., Williams et al. 2000).


The millimetre bump in M87 as recently observed by the Atacama Large Millimeter/submillimeter Array can be naturally modelled by the synchrotron emission of the thermal electrons in the ADAF, which is different from the prediction of the jet model. Therefore, it provides an opportunity to explore the accretion process near the BH horizon. In particular, Feng etal. (2016) and Li etal. (2016) both found that the rotation measure predicted from the ADAF is roughly consistent with the observational values. It is still difficult to constrain the BH spin parameter from the modelling of the SED of M87 due to some degeneracy in model parameters (wind parameter, s, magnetic parameter ; Feng etal. 2016). The spin parameter can be better constrained from the jet model if the relativistic jet is indeed powered by the rotating BHs as suggested by MHD simulations and some observations. We find that the dimensionless BH spin parameter should be larger than 0.96 for the lower limit of jet power derived from the X-ray cavities (e.g. Rafferty et al. 2006; Russell etal. 2013b). In this work, we adopt several typical values of parameters (e.g. 0.1, 0.3 and 0.5). The larger value of  will lead to a lower accretion rate near the horizon to explain the observed millimetre bump, and the BHs need to rotate faster to reproduce the observed jet power. The peak of synchrotron emission from the thermal electrons of ADAF will move to the submillimetre waveband if  is too small, which is different from the observed millimetre bump. We adopt the equipartition case of 0.5 in our calculations, where magnetic energy will become dominant if the BH is fast spinning, considering the possible amplification of the magnetic field by the frame dragging effect. For the weaker magnetic case (e.g. 0.5), the BH needs to rotate faster to explain the observed SED and jet power. We find that our results are not sensitive to the viscosity parameter . Therefore, we suggest that the BH should be fast rotating in M87 even after considering the possible uncertainties.


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


Traditionally, the Parker transport equation (Parker 1965) was used to model pickup ion acceleration at the SWTS when using a transport theory approach. However, interesting Voyager results, such as strongly fluctuating pitch-angle anisotropies upstream, the detection of highly anisotropic intensity spikes at the SWTS, the average upstream anisotropy peaking at a surprisingly high energy far above the upstream flow energy, and energetic particle spectra with multiple power-law slopes with breaking points in between that are highly variable upstream (Decker et al. 2005, 2008b; Cummings et al. 2006), suggest that transport modeling should be modified in at least two ways. First, the turbulent nature of the magnetic field conditions at the SWTS should be taken into account, and second, a transport theory that applies when particle distributions are highly anisotropic is needed, given that the Parker transport equation only holds for nearly isotropic particle distributions. In response, shock acceleration transport models were developed in recent years based on the numerical solutions of the focused transport equation (Kóta & Jokipii 2004; le Roux et al. 2007; Florinski et al. 2008a, 2008b; le Roux & Webb 2009) to take advantage of the fact that focused transport is not restricted to small pitch-angle anisotropies. This is especially advantageous at lower suprathermal particle energies upstream, where particle distributions can be sporadically strongly anisotropic (Decker et al. 2006), allowing one to model particle injection into diffusive shock acceleration (DSA) naturally at those energies. Furthermore, statistical variations in the observed magnetic field direction near the SWTS were included as a time series to model time variations in the injection and DSA of pickup ions to simulate the highly volatile nature of actual DSA at the SWTS (Florinski et al. 2008a, 2008b; le Roux & Webb 2009; Arthur & le Roux 2013). This focused transport approach should be seen as complementary to more sophisticated self-consistent shock acceleration models based on hybrid codes (Kucharek & Scholer 1995; Giacalone 2005) and particle-in-the-cell models (Scholer et al. 2003; Lembege et al. 2004), but it has the virtue of relative simplicity because different statistical plasma parameters can easily be studied separately and in combination at the SWTS to gain a more clear conceptional understanding of the role of such statistics on pickup acceleration at the SWTS.


In the previous sections, we have shown the difficulty in balancing follow-up time with large numbers of unconfirmed candidate companions from single-epoch photometry. This follow-up dilemma was the motivation for designing the K-peak filter: can we optimize the observing time required to determine the nature of a target? One answer is to use a carefully chosen combination of photometric filters. Using only photometry, we can calculate colours that contain information about the type of object being observed, allowing approximate characterization with single-epoch photometry. Past works (e.g. Najita, Tiede & Carr 2000; Allers & Liu 2020) have shown that custom photometric filters can be used to greatly improve the confirmation rate of photometrically selected candidate low-mass brown dwarfs. In previous work (Allers & Liu 2020; Jose et al. 2020; Dubber et al. 2021), we used a custom filter centred on the deep 1.45 µm feature present in YPMOs to distinguish between them and background sources. In the 2–5 µm range covered by NIX, such water features are far less dominant, and there are strong telluric features across some of this range that would make a similar ‘water’ technique difficult to use. Instead, we use the differing spectral shape in K-band of very low mass brown dwarfs when compared to earlier spectral type stars. This can be seen in the sample of spectra shown in Fig. 3. By locating filters at key spectral points for defining the overall shape of the spectra, the extracted colour information can be used for direct characterization. Also shown in Fig. 3 are spectra of well-studied brown dwarfs and exoplanets, discovered via direct imaging: 51 Eri b (Macintosh et al. 2015), β Pictoris b (Lagrange et al. 2010), PSOJ-318 (Liu et al. 2013), G196-3B (Rebolo et al. 1998), and HR 8799d and e (Marois et al. 2008, 2010). References for the spectral data plotted are detailed in the caption of Fig. 3. These spectra demonstrate the general variety in the spectral shapes of objects that have been detected via direct imaging previously, but also the similar features in the highlighted filter windows.


Cosmological hydro dynamical N-body simulations offer another possibility to investigate the origin of the bimodality in the ([Fe/H], [α/Fe]) plane. Earlier simulations, e.g. full N-body simulations by Loebman et al. (2011), Brook et al. (2012) or hybrid simulations in which a semi-analytic chemical evolution was added on top of a cosmological simulation (Minchev, Chiappini & Martig 2013, 2014), were able to show that the thin and thick discs lie along different tracks in the ([Fe/H], [α/Fe]) plane, with the thick disc being old metal poor and rich in [α/Fe] and the thin disc being young, metal-rich and poor in [α/Fe]. They also showed that migration was important to generate the two discs. However, a clear bimodality in the ([Fe/H], [α/Fe]) plane was not seen. In the past few years good progress has been made to improve the spatial resolution as well as the chemical enrichment prescriptions. The bimodality has now been observed in some simulations (Grand et al. 2018; Mackereth et al. 2018; Clarke et al. 2019), and some of the simulations, in addition to the bimodality, also reproduce the basic trends of the ([Fe/H], [α/Fe]) distribution with radius R (Buck 2020; Vincenzo & Kobayashi 2020). Unlike analytical models, such simulations cannot be fine tuned to reproduce the Milky Way data, hence, the focus of these simulations is to qualitatively reproduce the abundance trends seen in the Milky Way, to understand how frequently do we get the bimodality and what is the mechanism for it. However, there is a lack of consensus between the different studies. Clarke et al. (2019) and Buck (2020) suggest that bimodality should be common in disc galaxies, whereas Mackereth et al. (2018) suggest that it is rare. Each simulation suggests slightly different mechanisms for the existence of the bimodality. Clarke et al. (2019) attribute bimodality to vigorous star formation in clumps at high redshift. Grand et al. (2018) suggest two distinct pathways, a centralized starbust pathway induced by mergers and a shrinking gas disc pathway. Buck (2020) suggest that after the formation of the high-[α/Fe] sequence a gas-rich merger dilutes the metallicity of the ISM leading to the formation of the low-[α/Fe] sequence. Mackereth et al. (2018) attribute the bimodality to unusually rapid gas accretion at earlier times, which is also characterized by a short time-scale to convert gas to stars. While some simulations clearly identify migration as key process to shape the sequences, others do not. In spite of the differences, it seems that some of the simulations (e.g. Mackereth et al. 2018; Buck 2020; Vincenzo & Kobayashi 2020) are not inconsistent with the Schönrich & Binney (2009a) paradigm.


The multiwavelength spectral data of 13 SNRs with hard γ-ray spectra. The γ-ray spectra are fitted with a hadronic model with the normalization of the individual spectrum as free parameters. The model assumes that protons have a single power-law energy distribution with an exponential high-energy cutoff. Note that the TeV spectra of G78.2+2.1 (HAWC) and N132D (HESS) cut off at relatively lower energies, and the soft spectral component of GeV of HESS 1912+101 may be from other contributors and are not considered in SED fitting. The best-fit model parameters are indicated in the figure. References for the observational data are as follows: RX J0852.0−4622: radio (Duncan & Green 2000), GeV (Tanaka et al. 2011), X-ray (Aharonian et al. 2007), TeV (H.E.S.S. Collaboration et al. 2018c); RX J1713.7−3946: radio (Lazendic et al. 2004), X-ray (Tanaka et al. 2008), GeV and TeV (H.E.S.S. Collaboration et al. 2018a); HESS J1731−347: radio (Tian et al. 2008), GeV (Condon et al. 2017; Guo et al. 2018), X-ray (Doroshenko et al. 2017), TeV (H.E.S.S. Collaboration et al. 2011); RCW 86: radio (Clark et al. 1975; Lemoine-Goumard et al. 2012), X-ray (Lemoine-Goumard et al. 2012), GeV (Ajello et al. 2016), TeV (H.E.S.S. Collaboration et al. 2018d); SN 1006: radio Dyer et al. 2009, X-ray (Bamba et al. 2008), GeV (Condon et al. 2017), TeV (Acero et al. 2010); G150.3+4.5: radio (Gerbrandt et al. 2014), X-ray and GeV (Devin et al. 2020); G296.5 + 10.0: radio (Milne & Haynes 1994), GeV (this work), HESS J1534−571: radio (Maxted et al. 2018), GeV (Araya 2017), X-ray and TeV (H.E.S.S. Collaboration et al. 2018b); RCW 103: radio (Dickel et al. 1996), GeV (Xing et al. 2014); G78.2+2.1: radio (Wendker et al. 1991; Zhang et al. 1997; Kothes et al. 2006; Gao et al. 2011), X-ray (Leahy et al. 2013), GeV (Abeysekara et al. 2018) and TeV (Fleischhack 2019); G279.0+1.1: radio (Woermann & Jonas 1988; Duncan et al. 1995), GeV Araya (2020); N132D: radio (Dickel & Milne 1995), X-ray (Hughes et al. 1998; Bamba et al. 2018), GeV (Y. L. Xin et al. 2020, in preparation), and TeV (H.E.S.S. Collaboration et al. 2015).


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.


Being a benchmark system H + H2, H + HD, and their isotopic counterparts have received much attention over the last several decades (Marinero et al. 1984; Zhang & Miller 1989; D’Mello et al. 1991; Harich et al. 2002; Gao et al. 2015; Yuan et al. 2018a, b, 2020). Most early experimental and theoretical investigations were centered around benchmarking theory against experiments and providing improved descriptions of the H3 potential energy surfaces (PES; Boothroyd et al. 1996; Mielke, Garrett & Peterson 2002; Yuan et al. 2018a, b). Among the available PESs for the H3 system, the one by Boothroyd et al. (1996) referred to as the BKMP2 PES and by Mielke et al. (2002) referred to as the CCI PES, nearly equally well account for most experimental data for H + H2, H + HD, and D + HD collisions. These PESs have also been able to account for even subtle effects such as the GP (Kendrick et al. 2015; Hazra et al. 2016; Croft et al. 2017; Kendrick 2018, 2019). The GP effect, while not significant at temperatures relevant to astrophysics, is important below 1 K as illustrated in a series of calculations on H + HD (v, j) collisions for vibrational levels v = 4 − 9 (Kendrick et al. 2015; Hazra et al. 2016; Croft et al. 2017; Kendrick 2018, 2019). Though several prior studies of Flower and co-workers  (Flower 1999, 2000; Flower & Roueff 1999; Wrathmall et al. 2007) have reported rate coefficients for H + HD collisions, due to the approximations involved in the scattering calculations (e.g. neglect of hydrogen atom-exchange), the reliability of the available rate coefficients has been a source of debate (Desrousseaux et al. 2018). Recently, Desrousseaux et al. (2018) reported rate coefficients for pure rotational transitions for j ≤ 10 within the v = 0 vibrational level using accurate quantum calculations that include the exchange channel. In this paper, we report rate coefficients for state-to-state rovibrational transitions in HD induced by H atoms between and within the v = 0 and 1 vibrational levels and for temperatures ranging from T = 1–1000 K.


However, we note that the quoted eccentricity for the inner planet in HD 155358 is 0.17 ± 0.03 (Robertson et al. 2012a). The mean value is exceeded for the standard run at 4000 orbits after going into resonance with the implication that the planets could not have been in resonance longer than this time. If this is the case, the above discussion would have to be modified to allow the planets to migrate independently from larger radii before converging on to resonance close to their final locations. This is likely to need to be considered for different possible exterior disc models and in addition the planets may have built up their masses as they went (see e.g. Tadeu dos Santos et al. 2015). These considerations are beyond the scope of this paper. None the less, because the migration rates for single planets and the resonantly coupled planets are in general similar, the estimated starting radii would also be similar for disc models that are similar to those we considered. But note that the attained eccentricities depend on the eccentricity damping rates which depend on the details of the disc model (see Crida et al. 2008). For example, we found that for the same amount of relative resonant migration, the entirely inactive disc model led to smaller eccentricities while the 3D layered model led to larger eccentricities. Thus, it is important to note that there is uncertainty as to how long the planets could have been in resonance. In the same context, we comment that migration in the completely active disc model was slower by a factor of ∼1.6 compared to the standard case on account of its lower mass, that being determined so as to maintain the same steady-state accretion rate as in the standard case. Furthermore, the potential importance of a residual inner gaseous disc for damping the eccentricity of the inner planet and so preventing the eccentricities of both planets from continuing to increase in the later stages of the orbital evolution has been stressed by Crida et al. (2008). In addition, Murray, Paskowitz & Holman (2002) indicate that a residual disc of planetesimals could produce a similar effect.


According to general relativity, in the limit in which the wavelength of gravitational waves is small compared to the radius of curvature of the background spacetime, the waves propagate with the velocity of light, i.e., c (see Will 1998, and references therein). In other theories, the speed

 could differ from c. Let us define the parameter
4

If the gravitational wave velocity is subluminal (i.e.,

), then cosmic rays lose their energy via gravitational Cerenkov radiation significantly. The detection of ultrahigh-energy cosmic rays thus imposes a stringent constraint

 (i.e., the “subluminal constraint”), depending on the Galactic or extragalactic origin of such particles (Caves 1980; Moore & Nelson 2001). However, there is no theoretical argument (or pathology) against GWs propagating faster than light (see Nishizawa & Nakamura 2014; Blas et al. 2016, and references therein) and the weak bounds from radiation damping in binary systems are

 (Yagi et al. 2014). The time lag of arrival times between the GW and the simultaneously radiated photons is
5

where

 is the differential distance the photons have traveled. Note that in this work we take the flat cosmological model (i.e.,

),

, and

 is Hubble’s constant (Riess et al. 2011; Ade et al. 2014). In general, ς may be a function of the GW frequency (f) and especially when graviton mass is non-zero (i.e.,

), which gives

, where h is Planck’s constant. For simplicity we assume a constant ς and focus on the association of GWs with electromagnetic counterparts at redshifts

. Hence Equation (5) yields (see also Will 1998; Nishizawa & Nakamura 2014)
6

In reality the photons and the coalescence are not usually simultaneous and we have

, where

 and

 are the differences in arrival time and emission time, respectively, of the GW and the photons. In most cases, it is rather hard to get an a priori value for

. Assuming

 (i.e., the GW and the electromagnetic counterparts were emitted simultaneously; see Nishizawa (2016) for a more general discussion), we constrain the absolute amplitude of ς as
7

We call the above process the “canonical approach” to measuring the GW velocity directly, in which the graviton and photon are assumed to make the same journey (i.e., EEP is guaranteed). The advantage is that as long as a GW/GRB association is established one can constrain

 directly. In Section 4.2 we outline an approach to measure the GW velocity with a simultaneous test of EEP.

Nishizawa & Nakamura 2014
Nishizawa & Nakamura 2014