From analytical and semi-analytical work (see for example Lovelace & Romanova 2014) we know that the local conditions where the RWI grows are what trigger the growth of one mode over another and in turn the strengths of each mode directly impacts the PDS. In the following section we focus on only one spin (a = 0.995) and position (rc = 2.7rg) where the RWI is triggered but look at different local conditions (see Eq. 3 for the parametrization), meaning the (unstable) zone where the RWI is active will be different. We can then see how the local condition affect the PDS, especially focusing on which modes are selected and how they relate to one another when present. We saw in previous studies of the RWI (Tagger & Varnière 2006; Vincent et al. 2013; Casse et al. 2017; Casse & Varniere 2018) that every simulation triggers a lot of modes, with up to m = 19 being detectable in Fourier space; though lower modes tend to be a lot stronger, especially once the instability reaches saturation. Because of the timescale near the last stable orbit of a black-hole of ten solar masses, we mostly observe the saturated state of the instability in a standard observation. We have therefore first performed several simulations with the same aforementioned corotation radius rc = 2.7rg but with various ε and δ parameters leading to different geometries of the unstable zone. A typical GRHD simulation example and the related ray-tracing synthetic observation can be found in Fig. 1. Once a simulation has reached the saturation stage, namely when the amplitude of the fluctuations remains approximately constant, we stop the simulation and proceed to use GYOTO in order to compute the light curve of the simulation as perceived by a remote observer. We stress here that the combination of the GR-AMRVAC code and the GYOTO code encompasses all general relativistic effects at work upon both the disc and its radiative emission, here providing reliable synthetic observations.


Substantial effort has been made by research groups in this field to improve the fibre link performance by employing non-circular fibres, double scramblers, fibre shakers, and fibre stretchers (Pepe et al. 2000; Chazelas et al. 2010; Perruchot et al. 2011; Avila 2012; Chazelas, Pepe & Wildi 2012; Bouchy et al. 2013; Reynolds & Kost 2014; Halverson et al. 2015a; Spronck et al. 2015; Ishizuka et al. 2016; Sutherland et al. 2016). Recent test results on the performance of MM optical fibres with non-circular cores show improved scrambling performance over that of standard circular MM fibres (Chazelas et al. 2012; Feger et al. 2012; Sturmer et al. 2016). However, a native non-circular fibre has also been shown to fail to provide the high level of stability and homogeneity in both the near-field and far-field of the fibre that is required for the next generation of PRV instruments operating below the 1 m s−1 radial velocity precision level. Much work has been done to improve the degree of stability and homogeneity that the fibre link can deliver by investigating and testing various combinations of fibre core geometries combined with a double scrambler. Optical double scramblers placed in the fibre link act to exchange the near and far-field light distributions of the fibre by means of a lens rely (Barnes & MacQueen 2010). This method has been shown to improve the level of scrambling in both the near and far-fields of the fibre output (Halverson et al. 2015a; Seifahrt, Sturmer & Bean 2016). Although these methods improve the fibre scrambling they do not necessarily reduce modal noise. Modal noise mitigation/suppression requires a time variable correction which is typically achieved by means of shaking and/or stretching the fibre (Reynolds & Kost 2014; Roy et al. 2014; Halverson et al. 2015a). In this paper, we present a new fibre technology (multicore fibre and photonic lanterns) that has the possibility to provide improved fibre scrambling and modal noise characteristics.


We initiated the H0LiCOW (H0 Lenses in COSMOGRAIL's Wellspring) program with the aim of measuring the Hubble constant with better than 3.5 per cent precision and accuracy (in most background cosmological models), through a sample of five time-delay lenses. We obtain the key ingredients to each of the lenses through observational follow-ups and novel analysis techniques. In particular, we have high-quality lensed quasar light curves, primarily obtained via optical monitoring by the COSMOGRAIL (COSmological MOnitoring of GRAvItational Lenses; e.g. Courbin et al. 2005; Vuissoz et al. 2008; Courbin et al. 2011; Tewes et al. 2013b) and Kochanek et al. (2006) teams but also via radio-wavelength monitoring (Fassnacht et al. 2002). COSMOGRAIL has been monitoring more than 20 lensed quasars for more than a decade. The unprecedented quality of the light curves combined with new curve-shifting algorithms (Tewes, Courbin & Meylan 2013a) lead to time delays with typically ∼3 per cent accuracy (Fassnacht et al. 2002; Courbin et al. 2011; Tewes et al. 2013b). In addition, we obtain HST imaging that reveal the ‘Einstein ring’ of the lens systems in high resolution, and develop state-of-the-art lens modelling techniques (Suyu et al. 2009; Suyu & Halkola 2010; Suyu et al. 2012b) and kinematic modelling methods (Auger et al. 2010; Sonnenfeld et al. 2012) to obtain the lens mass distribution with a few percent uncertainty (e.g. Suyu et al. 2013, 2014). We further obtain wide-field imaging and spectroscopy to characterize the environment of the field, as well as the spectroscopy of the lens galaxy to obtain the stellar velocity dispersion. The exquisite follow-up data set that we have acquired allow us not only to constrain cosmology but also to study lens galaxy and source properties for understanding galaxy evolution, including the dark matter distribution in galaxies, the stellar initial mass function of galaxies and the co-evolution between supermassive black holes and their host galaxies.


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

10.2

−
1.6

+
2.2

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

30.39

−
0.14

+
0.17

 keV and

29.42

−
0.24

+
0.27

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


The diffusion time-scale of the field lines in the disc is comparable to the viscous time-scale which is much longer than the interaction time-scale of the field lines and the inner disc, tint = |ΩK − Ω*|−1 (Fromang & Stone 2009), where Ω* is the angular velocity of the neutron star. The field lines cannot slip through the disc. Theoretical studies and numerical simulations show that the field lines interacting with the inner disc in a narrow boundary inflate and open up within the interaction time-scale (Aly 1985; Lovelace, Romanova & Bisnovatyi-Kogan 1995; Hayashi, Shibata & Matsumoto 1996; Miller & Stone 1997; Uzdensky, Königl & Litwin 2002; Uzdensky 2004). If the system is in the SP phase, the matter flowing in to the boundary at the innermost region of the disc is expelled from the system along the open field lines. The open lines reconnect on the dynamical time-scale, $\Omega _{\mathrm{K}}^{-1}$, and continue to apply torque on the matter until they open up again (Lovelace, Romanova & Bisnovatyi-Kogan 1999; Ustyugova et al. 2006). The simulations show that the field lines outside the interaction boundary are decoupled from the disc. The magnetosphere inside the boundary is the region where the closed field lines and the plasma can rotate together at radius rm ≃ rin. These results indicate that a strong-propeller mechanism could be sustained if the field lines expel the matter from the inner boundary at the same rate as that of the mass-flow from the outer disc. Furthermore, for this strong-propeller phase to be steady, the matter should be accelerated to speeds greater than the escape speed, υesc, within tint. Ertan (2017) showed that the maximum radius at which the strong-propeller condition is satisfied is much smaller than rA, while the accretion rates estimated for the WP/SP transition in this model seem to be in agreement with the transition properties of tMSPs (Ertan 2017, 2018). The inner boundary in the spin-up phase is also continuously evacuated, as in the case of strong-propeller, but now due to accretion on to the star. At rin the field lines decelerate and bring the matter into co-rotation within tint in the spin-up phase. In other words, the same equation could determine the inner disc radius in both the strong propeller phase (for rin > rco) and the spin-up phase (for rin rco). However, this is not the whole story, since the conditions in the spin-up (SU) phase are rather different, in particular rA enters the picture (Sections 2.1–2.4).


We note that there has recently been some debate about potential observational effects (beam-smearing effect) on the dynamical state of (field) high-z galaxies (e.g., Di Teodoro et al. 2016; Kohandel et al. 2020). More specifically, when studying the gas kinematics with low spectral and spatial resolution data, the unresolved rotations within the PSF can artificially increase the value of σ0 and decrease the value of Vmax, leading to a severe systematic underestimation of the Vmax/σ0 ratio. The beam-smearing effect has been widely explored in local galaxies (e.g., see Fig. 6 in Di Teodoro & Fraternali 2015) and high-z simulated galaxies (e.g., Kohandel et al. 2020). Subsequently, given the high spatial and spectral resolution of ALMA observations, which have been able to reach subkpc spatial resolution in high-z galaxies, the beam-smearing effect is less significant. Compared to previous data, ALMA allows for a more robust way to measure intrinsic velocity dispersions. However, in our case, comparing two cluster SBs (with a spatial resolution of ∼0.3″ and a channel width of 30 km s−1) with other field SBs at similar redshifts and similar resolutions (with spatial resolutions of 0.1″–0.7″ and channel widths of 20–50 km s−1, except for one with a channel width of ∼100 km s−1), the σ0 values of the two cluster SBs are about three times lower than that of those field SBs (blue triangles in Fig. 6; Calistro Rivera et al. 2018; Barro et al. 2017; Swinbank et al. 2011; Tadaki et al. 2017). In addition, even at the same spatial and spectroscopical resolution, the σ0 values of the two cluster SBs are still more than three times lower than those of the two cluster MSs (green stars in Fig. 6). Furthermore, the simulations have confirmed the robustness of σ0 and Vmax for the two SBs and two MSs in our measurements (see Sect. 3.6). Therefore, we argue that the higher Vmax/σ0 and lower σ0 of the two cluster SBs with respect to field galaxies is a real physical difference, rather than being driven by observational effects.


In the present work, we neglect the processes that generate the halo, but this topic deserves some review. Notably, the apparent growth of the halo at the expense of the anti-sunward suprathermal ‘strahl’ population may imply that the halo is locally formed in the inner heliosphere by scattered strahl electrons (e.g. Maksimovic et al. 2005; Štverák et al. 2009). This has led to significant theoretical development, focused on the resonant interaction of electrons with the whistler and fast-magnetosonic whistler (FM/W) modes (e.g. Vocks et al. 2005; Saito & Gary 2007; Vasko et al. 2019; Verscharen et al. 2019b; Micera et al. 2021; Zenteno-Quinteros, Viñas & Moya 2021; Tang, Zank & Kolobov 2022; Vo, Lysak & Cattell 2022). Observations have struggled to confirm these theories. Notably, whistlers are practically absent (occurrence rate 0.1 per cent) during PSP perihelion passes (Cattell et al. 2022). Additionally, the eVDFs sampled by Helios and PSP are stable with respect to the oblique FM/W mode (Jeong et al. 2022a). Theoretical calculations show that at r ≲ 1 AU, the strahl is stable to whistler fluctuations (Horaites et al. 2018b; Schroeder et al. 2021) and should be unaffected by whistler turbulence in the inner heliosphere (Boldyrev & Horaites 2019). High-resolution measurements of the strahl at 1 AU confirm that ‘anomalous diffusion’, e.g. from whistler waves, is not required to explain the strahl angular widths at resolvable energies ≲300 eV Horaites et al. (2018a), Horaites, Boldyrev & Medvedev (2019). Similar results were found from simulations at distances r ≲ 20RS (Jeong et al. 2022b), which showed that near the corona the strahl is adequately described by a combination of Coulomb collisions and expansion effects. This all suggests that a mechanism besides local wave particle scattering may account for the halo’s presence in the inner heliosphere. Such theories have been proposed (e.g. Leubner 2004; Lichko et al. 2017; Che et al. 2019; Horaites et al. 2019; Scudder 2019), though no consensus has emerged.


In this paper we extend previous work based on cosmological simulations by analysing the general magnetic field properties and the diffuse radio halo emission in galaxy clusters in the IllustrisTNG project, a set of cosmological magnetohydrodynamics simulations run with the moving-mesh code arepo (Springel 2010) that include a comprehensive module for galaxy formation physics. The main and novel aspect of our work is the analysis of the diffuse radio emission resulting from radio haloes in galaxy clusters (Feretti & Giovannini 1996; Murgia et al. 2009; Vacca et al. 2011; Feretti et al. 2012). We investigate radio emission from clusters by a detailed comparison with observations, trying to match the current observational constraints and to make predictions for the upcoming radio surveys that will be performed with the new generation of radio instruments such as SKA and LOFAR. The analysis of simulated radio haloes gives us a complementary view on the spatial extent and energy content of magnetic fields in galaxy clusters, since the radio emission is proportional to their strength. As such, the study of radio halo scaling relations (Giovannini et al. 2009; Cassano et al. 2013; Zandanel, Pfrommer & Prada 2014) with the total X-ray power and halo mass may yield important information about the amplification mechanisms of magnetic fields in clusters and the level of turbulence in the ICM. The modelling of radio emission makes it also possible to study the transport of charged particles and their re-acceleration to relativistic speeds, and it constrains the probability of detecting extended radio-emitting structures in a statistical sample of realistic simulated clusters. The comparison of the simulated radio emission with actual observations might also be employed as a useful check for the implementation of the galaxy formation physics modules used to perform the simulations, although our modelling of relativistic particles is rather preliminary and might have a non-negligible impact on the results.


The choice of these initial abundances is motivated by the following two scenarios about the history of the midplane material. The first scenario is that the material going into protostellar systems is inherited from the cloud out of which the protoplanetary disk collapsed and formed. This scenario is denoted “inheritance”, and it implies that the material has the same composition as found in dark clouds, especially their ices (see Marboeuf et al. 2014; Mumma & Charnley 2011). The second scenario is the case where the material coming from the dark cloud experiences heating events from the protostar (i.e., accretion bursts or regular stellar irradiation). These heating events are assumed to alter the chemistry in disks significantly (see, e.g., Visser et al. 2015). In the extreme case, the chemistry is reset, meaning that the molecules are assumed to be dissociated into atoms out to R = 30 AU, which can then reform molecules and solids in a condensation sequence, as traditionally assumed for the inner solar nebula (e.g. Grossman 1972). Hence, the scenario considering atomic initial abundances is denoted “reset”. Early chemical models of protoplanetary disks often assumed a set atomic initial abundances (e.g., Willacy et al. 1998; Aikawa et al. 1999; Semenov et al. 2004; Vasyunin et al. 2008; Walsh et al. 2010); however, these early models also did not typically include a comprehensive grain-surface network and focussed solely on the gas-phase chemistry. Some recent physico-chemical models do include surface formation of e.g., H2O ice, via the Eley-Rideal mechanism (e.g., Kamp et al. 2013; Bruderer et al. 2014; Helling et al. 2014). Early models that did include grain-surface chemistry (e.g. Willacy 2007; Walsh et al. 2010) were limited to simple atom-addition stemming from Tielens & Hagen (1982) and Hasegawa & Herbst (1993). Here, a more comprehensive grain-surface network is used which includes radical-radical recombination, atom addition, and also ice processing (Garrod et al. 2008). This work differs from earlier protoplanetary disk models in that we directly compare and quantify the effects of the inheritance versus reset scenarios for a single disk model using a comprehensive gas-grain chemical network.


A pragmatic solution to these problems is to generate and analyse synthetic Milky Way catalogues cast in the observational frame of the survey (Bahcall & Soneira 1980; Robin & Creze 1986; Bienayme, Robin & Creze 1987). ‘Mock catalogues’ of this general type were first used in cosmology in the 2000s (e.g. Cole et al. 2005) and have now become an essential tool for the design and analysis of large galaxy and quasar surveys. Realistic mock catalogues provide assessments of an instrument’s capabilities and biases, tests of statistical modelling techniques applied to realistic representations of observational data, and detailed comparisons between theoretical predictions and observations. Perhaps one of the best known recent attempts is the Besançon model (Robin et al. 2003), which provides a disc (or set of discs) with a set of coeval and isothermal (single velocity dispersion) stellar populations assumed to be in equilibrium, with analytically specified distributions of density, metallicity, and age. This has been the basis of the Gaia Universe Model (GUMS; Robin et al. 2012). However, these models are not dynamically consistent and oversimplify the structure of the Galaxy, particularly the stellar halo that is modelled as a smooth component. An important advance was made by Sharma et al. (2011), who developed the galaxia code for creating mock stellar catalogues either analytically or from phase-space sampling of hybrid semi-analytic-N-body simulations to represent stellar haloes in a cosmological context (Bullock & Johnston 2005; Cooper et al. 2010). Rybizki et al. (2018) have developed a mock catalogue designed specifically for Gaia DR2 based on galaxia. Building on the method of Sharma et al. (2011), Lowing et al. (2015) developed a technique to distribute synthetic stars sampled from a cosmological N-body simulation in such a way as to preserve the phase-space properties of their parent stellar populations. In a separate method, Hunt et al. (2015) introduced the snapdragons code that generates a mock catalogue taking into account Gaia errors and extinction and demonstrated the resulting observable kinematics of stars around a spiral arm in an idealized smoothed particle hydrodynamic simulation set-up in isolation.


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

(40)

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

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


The SFR surface densities of ΣSFR = (750 ± 440) and (1800 ± 700) M⊙ yr−1 kpc−2 found above for GN10 and the central region of AzTEC-3 are even higher than the values found for some other compact starbursts like ADFS-27 (z = 5.66; 430 ± 90 M⊙ yr−1 kpc−2) and HFLS3 (z = 6.34; 480 ± 30 M⊙ yr−1 kpc−2; Riechers et al. 2013, 2017). The source-averaged value of >(500 ± 160) M⊙ yr−1 kpc−2 for AzTEC-3 is comparable to these sources. Like these systems, GN10 and AzTEC-3 thus show the properties expected for so-called “maximum starbursts”. At face value, the peak ΣSFR in AzTEC-3 may slightly exceed the expected Eddington limit for starburst disks that are supported by radiation pressure (e.g., Thompson et al. 2005; Andrews & Thompson 2011), but it is potentially consistent under the assumption of a more complex source geometry. On the other hand, the high ΣSFR value of GN10 could be boosted by an obscured AGN contribution to the dust heating. GN10 exhibits strong 0.5–8 keV X-ray emission.43

43
AzTEC-3 is not detected at X-ray wavelengths.
 Using Equation (15) of Ranalli et al. (2003), its observed (absorption-corrected)44

44
From fitting a Galactic absorption plus power-law model, an effective photon index Γ =

 was found for GN10, but it was not possible to simultaneously fit the absorbing column NH and Γ due to the limited photon counts. The data are consistent with no intrinsic absorption within the uncertainties, such that the absorption-corrected LX could be considered an upper limit (Laird et al. 2010) or, alternatively, a lower limit, in the case that it is heavily absorbed.
 rest-frame 2–10 keV X-ray luminosity of LX = 5.6(12.5) × 1042 erg s−1 (Laird et al. 2010) corresponds to an SFRX of 1100(2500) M⊙ yr−1. Given its SFRIR =

 M⊙ yr−1, its LX remains consistent with intense star formation, but a contribution from a modestly luminous obscured AGN cannot be ruled out, depending on the (relatively uncertain) absorption correction required. This would also be consistent with a possible excess mid-infrared emission due to an obscured AGN, which may be favored by some of the SED fits.


The atmospheric parameters of white dwarfs, the effective temperature (Teff) and surface gravity (log g), play a fundamental role in the study of post-main-sequence stellar evolution (see e.g., Kalirai, Marigo & Tremblay 2014; Rolland, Bergeron & Fontaine 2018), evolved planetary systems (Koester, Gänsicke & Farihi 2014), Galactic formation history (Tremblay et al. 2014), and the calibration of instruments (Bohlin, Gordon & Tremblay 2014). For decades, the most precise method to determine Teff and log g has been the spectroscopic fitting of the Balmer lines in hydrogen-atmosphere DA white dwarfs (Bergeron, Saffer & Liebert 1992; Finley, Koester & Basri 1997), and the He i lines in helium-dominated DB stars (Beauchamp et al. 1999; Voss et al. 2007; Bergeron et al. 2011). In contrast, trigonometric parallax measurements of stellar remnants or their companions can also be used to characterize Teff and stellar radii from photometric analyses (Koester, Schulz & Weidemann 1979; Bergeron, Leggett & Ruiz 2001). The surface gravity can then be inferred by using the white dwarf mass–radius relation (see e.g., Fontaine, Brassard & Bergeron 2001), with a small dependence on the assumed internal stratification (Romero et al. 2012). The main advantage of the photometric technique is that it can be used to fit cool DC white dwarfs with no optical transitions as well as metal- or carbon-rich remnants where spectroscopic log g determinations are difficult (Dufour, Bergeron & Fontaine 2005; Dufour et al. 2007b). One shortcoming is that for $T_{\rm eff} \gtrapprox 12\, 000$ K, optical colours of all stellar remnants get rather insensitive to the temperature, requiring very precise photometry for that determination (Carrasco et al. 2014). Until now, the main limitation of the photometric analyses has been that precise parallax measurements were available for only hundreds of white dwarfs (Bédard, Bergeron & Fontaine 2017), compared to the ≈ 30 000 objects (Kleinman et al. 2013; Kepler et al. 2015, 2016; Gentile Fusillo et al. 2018) with spectroscopy from the Sloan Digital Sky Survey (SDSS; Abazajian et al. 2009).


Pulsar timing experiments (Sazhin 1978; Detweiler 1979) allow us to explore the low-frequency (∼1–100 nHz) part of the gravitational-wave (GW) spectrum. By measuring deviations from the expected arrival times of radio pulses from an array of millisecond pulsars, we can search for a variety of GW signals and their sources. The most promising sources in the nanohertz part of the GW spectrum are supermassive binary black holes (SMBHBs) that form via the mergers of massive galaxies. Orbiting SMBHBs produce a stochastic GW background (GWB; Lommen & Backer 2001; Jaffe & Backer 2003; Volonteri et al. 2003; Wyithe & Loeb 2003; Enoki et al. 2004; Sesana et al. 2008; McWilliams et al. 2012; Sesana 2013; Ravi et al. 2015; Rosado et al. 2015; Kelley et al. 2016; Sesana et al. 2016; Dvorkin & Barausse 2017; Kelley et al. 2017; Bonetti et al. 2018; Ryu et al. 2018), individual periodic signals or continuous waves (CWs; Sesana et al. 2009; Sesana & Vecchio 2010; Mingarelli et al. 2012; Roedig & Sesana 2012; Ravi et al. 2012, 2015; Rosado et al. 2015; Schutz & Ma 2016; Mingarelli et al. 2017; Kelley et al. 2018), and transient GW bursts (van Haasteren & Levin 2010; Cordes & Jenet 2012; Ravi et al. 2015; Madison et al. 2017; Islo et al. 2019; Bécsy & Cornish 2021). We expect to detect the GWB first, followed by detection of individual SMBHBs (Siemens et al. 2013; Rosado et al. 2015; Taylor et al. 2016; Mingarelli et al. 2017) that stand out above the GWB. Detection of GWs from SMBHBs will yield insights into galaxy mergers and evolution not possible through any other means. Other potential sources in the nanohertz band include cosmic strings (Damour & Vilenkin 2000, 2001; Berezinsky et al. 2004; Damour & Vilenkin 2005; Siemens et al. 2006, 2007; Ölmez et al. 2010; Sanidas et al. 2013; Blanco-Pillado et al. 2018; Chang & Cui 2021; Ghayour et al. 2021; Gorghetto et al. 2021; Wu et al. 2021a; Blanco-Pillado et al. 2021; Lin 2021; Chiang & Lu 2021; Lazarides et al. 2021; Chakrabortty et al. 2021; Ellis & Lewicki 2021), phase transitions in the early universe (Witten 1984; Caprini et al. 2010; Addazi et al. 2021; Arzoumanian et al. 2021; Di Bari et al.2021; Borah et al. 2021; Nakai et al. 2021; Brandenburg et al.2021; Neronov et al. 2021), and relic GWs from inflation (Starobinskiǐ 1979; Allen 1988; Lazarides et al. 2021; Ashoorioon et al. 2021; Yi & Zhu 2021; Li et al. 2021; Poletti 2021; Vagnozzi 2021; Sharma 2021), all of which would provide unique insights into high-energy and early-universe physics.


Compact objects, such as, neutron stars and black holes (BHs) are the end products of massive stars. The gravitational pull of BHs is so high that no particle or radiation can escape from them. They both can be detected only by the electromagnetic radiation emitted by the accreted matter falling on them. Most of the black hole candidates (BHCs) in our Galaxy are in close binaries with companion stars which act as donors. Wind material from the companion star or matter accreting via Roche lobe overflow falls towards the black hole due to its intense gravitational pull and starts swirling around it to form accretion disc due to the presence of angular momentum. The observed electromagnetic radiation from a black hole binary is from the accretion flow itself. Some of the black hole candidates in low-mass X-ray binaries are transients in nature, which occasionally undergo outbursts. The increased X-ray flux in these transient X-ray binaries shows variability in the temporal and spectral states. Several works have already been done on this and many papers are available in the literature (see e.g. Tomsick et al. 2000; McClintock & Remillard 2006; Debnath et al. 2008; Nandi et al. 2012; Debnath, Chakrabarti & Nandi 2013; Rao 2013) to explain the variation of spectral and temporal properties of these objects during their active X-ray outburst phases. It is also reported by some authors that these objects transit through several spectral states (e.g. hard state (HS), hard-intermediate state (HIMS), soft-intermediate state (SIMS), soft state (SS)) during their active outburst phases (see Debnath et al. 2013 and references therein). Depending upon the observed spectral states, Debnath et al. (2017) classified these transient BH binaries into two types: classical or type-I (all four states are observable) and harder or type-II (softer states are missing). Low- and high-frequency quasi-periodic oscillations (QPOs) are generally observable in the power density spectra (PDS) of these sources (see Remillard & McClintock 2006 for a review). Low-frequency QPOs are commonly observed in hard and intermediate spectral states. Generally, it has been observed that during the rising HS and HIMS, frequency of these QPOs monotonically increases with time (day) and during the declining phase, the opposite nature is observed. In SIMS, these QPOs are observed sporadically.


Critical luminosity (Lcrit) is the luminosity above which a state transition from subcritical to supercritical takes place. The subcritical state (LX Lcrit) is known to be the low luminosity state whereas the supercritical state is high luminosity state (LX > Lcrit) (Becker et al. 2012). The critical luminosity is crucial to determine whether the radiation pressure of the emitting plasma is capable of decelerating the accretion flow (Basko & Sunyaev 1976; Becker et al. 2012). The luminosity during the 2020 giant outburst reached a record high, which was significantly higher than the critical luminosity (Reig & Nespoli 2013). The source entered a supercritical regime from a subcritical regime during the outburst. In the supercritical regime, radiation pressure is high enough to stop the accreting matter at a distance above the neutron star, forming a radiation-dominated shock (Basko & Sunyaev 1976; Becker et al. 2012). For the subcritical regime, accreted material reaches the neutron star surface through nuclear collisions with atmospheric protons or through Coulomb collision with thermal electrons (Harding 1994). These accretion regimes can also be probed by noting changes in the cyclotron line energies, pulse profiles, and changes in the spectral shape (Parmar, White, & Stella 1989; Reig & Nespoli 2013). During the transition from the subcritical to the supercritical regime, sources show two different branches in their hardness–intensity diagram (HID) which are known as horizontal branch (HB) and diagonal branch (DB) (Reig & Nespoli 2013). The HB implies the low-luminosity state of the source, which is represented by spectral changes and high X-ray variability. The DB corresponds to the high-luminosity state that appears when the X-ray luminosity is above the critical limit. The classification HB and DB depends on HID patterns that the source follows. The HB pattern is generally observed in the subcritical regime and the DB pattern is observed in the supercritical regime (Reig & Nespoli 2013).


With this study, our group continues the effort to investigate the optical properties of cosmic dust analogues in the mid infrared (MIR) to the millimeter domain as a function of temperature, undertaken 20 years ago by different groups (we refer to Demyk et al. 2013, for the details of the studied samples). Briefly, Agladze et al. (1996) were the first to study relevant interstellar silicate dust analogues in the temperature range from 1.2 K to 30 K and in the wavelength range from 700 μm to 2.9 mm. Mennella et al. (1998) studied amorphous carbon samples and silicate samples in the 24 μm−2 mm spectral domain and 24−300 K temperature range. Boudet et al. (2005) investigated silica and silicate samples in the 10−300 K temperature range and in the spectral region 100−1000 μm. The work by Coupeaud et al. (2011) was focussed on pure sol-gel Mg-rich silicates, of composition close to enstatite (MgSiO3) and forsterite (Mg2SiO4), amorphous and crystalline, whose spectra were recorded in the 100−1000 μm spectral range and from 10 K to 300 K. These studies have brought important results about the spectroscopic characteristics and behavior of interstellar dust analogues in the FIR at varying temperature. They show that the MAC of the amorphous analogues (silicates and carbonaceous matter) increases with the grain temperature and that its spectral shape cannot be approximated with a single power law in the form λ− β. The dependence of the MAC on the temperature, which is not observed in crystalline samples, is related to the amorphous nature and to the amount of defects in the structure of the material (Coupeaud et al. 2011). A physical model was proposed by Meny et al. (2007) to explain these experimental results. This model, named the TLS model, is based on a description of the amorphous structure of the material in terms of a temperature independent disordered charge distribution and of a collection of atomic configurations modeled as two-level systems and sensitive to the temperature.


Although most galaxies have an implied SFR that scatters within a factor two around the MS, some do show a significantly higher SFR. Those objects also exhibit a higher gas content, shorter gas depletion times (e.g., Genzel et al. 2015; Schinnerer et al. 2016; Tacconi et al. 2013, 2018), and higher dust temperatures (e.g., Magnelli et al. 2014). Likewise, the stellar-light radial distribution is different in these two galaxy populations; while MS galaxies are closely approximated by exponential disks (e.g., Bremer et al. 2018), those above (and below) it exhibit a higher central mass concentration (e.g., Wuyts et al. 2011). Based on this dichotomy and the parametrization of the MS over cosmic time, a scenario has been proposed to explain the evolutionary path of galaxies along the MS. Since the normalization of the MS, the gas fraction of galaxies, and cosmic molecular gas density decrease from z ∼ 2.5 to 0 at a similar pace (e.g., Speagle et al. 2014; Decarli et al. 2016; Tacconi et al. 2018), it is thought that MS galaxies evolved through a steady mode of star formation, possibly regulated by the accretion of cool gas from the intergalactic medium (e.g., Dekel et al. 2009; Kereš et al. 2009; Davé et al. 2010; Hodge et al. 2012; Romano-Díaz et al. 2014, 2017; Feng et al. 2015; Anglés-Alcázar et al. 2017). From theoretical predictions, the scatter of the MS could thus be explained as the result of a fluctuating gas inflow rate that is different in each galaxy (e.g., Tacchella et al. 2016; Mitra et al. 2017). In this context, a galaxy enhances its SFR and moves towards the upper envelope of the MS due to gas compaction. As the gas is depleted, the SFR decreases and the galaxy falls below the MS. As long as a SFG is replenished with fresh gas within a timescale shorter than its depletion time, it will be confined within the MS (Tacchella et al. 2016). On the other hand, the enhanced star formation efficiency of galaxies above the MS has been linked to mergers (e.g., Walter et al. 2009; Narayanan et al. 2010; Hayward et al. 2011; Alaghband-Zadeh et al. 2012; Riechers et al. 2013, 2014) and instability episodes in gas-rich disks (particularly at high redshift; e.g., Davé et al. 2010; Hodge et al. 2012; Wang et al. 2019).


Other important components of the X-ray sky are X-ray binaries, the hot gas present in our own Galaxy and the extragalactic hot gas. Amongst these X-ray sources, the large hot gas reservoir (Tvir ∼ 107 K) filling the space between the galaxies in the clusters, known as the ICM, has been observed in its X-ray emission for a long time (Reichert et al. 1981; Jones & Forman 1984; Branduardi-Raymont et al. 1985; Oukbir, Bartlett & Blanchard 1997; Diego et al. 2003a; Diego, Silk & Sliwa 2003b; Cavagnolo et al. 2009; Hurier et al. 2015). However, the hot gas (Tvir > 106 K) present in the form of circumgalactic medium (CGM) in massive galaxies (Mh ∼ 1012–1013 h−1 M⊙; Birnboim & Dekel 2003; Kereš et al. 2005; Singh et al. 2015) is less explored in X-rays due to its fainter X-ray emission. Some of the recent observations and studies (Grcevich & Putman 2009; Anderson & Bregman 2011; Dai et al. 2012; Putman, Peek & Joung 2012; Anderson, Bregman & Dai 2013; Bogdán et al. 2013a,b; Gatto et al. 2013) indicate that the CGM can account for a good fraction of the baryons in these galaxies. The X-ray emission from the CGM, therefore, is a promising tool to put strong constraints on the distribution and energetics of the gas (Singh et al. 2016) with eROSITA. At energies above 2 keV, the extragalactic point sources like AGN completely dominate the X-ray sky (Lehmann et al. 2001; Kim et al. 2007). Even below 2 keV, where the X-ray emission from the hot gas in the ICM and CGM is significant, the major contribution to the observed X-ray sky comes from AGNs (Sołtan 2007). Therefore, studying the X-ray emission from the AGN is crucial to understand the origin and evolution of the AGN as well as to extract the X-ray signal from the subdominant components. We thus also compute the angular power spectrum of the unresolved AGNs that are expected to contribute to the diffuse X-ray background of eROSITA and contaminate the angular power spectrum due the ICM/CGM in the 0.5–2 keV X-ray band.


For the first time, we detected [C ii] 158-μm emission from a GRB host galaxy at z > 2. This is the second detection of [C ii] 158-μm emission among known GRB host galaxies, following GRB 980425 (Michałowski et al. 2016). The [C ii] 158-μm fine structure line is the dominant cooling line of the cool interstellar medium, arising from photodissociation regions (PDR) on molecular cloud surfaces. It is one of the brightest emission lines from star-forming galaxies from FIR to metre wavelengths, almost unaffected by dust extinction. [C ii] 158-μm luminosity, L[C II], has been discussed as an indicator of SFR (e.g. Stacey et al. 2010). If L[C II] scales linearly with SFR, the ratio to FIR luminosity, L[C II]/LFIR, is expected to be constant, since LFIR is a linear function of SFR (e.g. Kennicutt 1998a). However, LC II/LFIR is not constant, but declines with increasing LFIR, known as the ‘[C ii] deficit’ (e.g. Luhman et al. 1998, 2003; Malhotra et al. 2001; Sargsyan et al. 2012; Díaz-Santos et al. 2013, 2017; Spilker et al. 2016). The [C ii] deficit persists when including high-z galaxies (e.g. Stacey et al. 2010; Wang et al. 2013; Rawle et al. 2014). In Fig. 5, we compare the [C ii] deficit in the GRB 080207 host and other star-forming galaxies. Two GRB hosts are shown by stars: GRB 080207 (orange star) and 980425 (blue star). The comparison sample is compiled from the literature up to z ∼ 3 (Malhotra et al. 2001; Cormier et al. 2010, 2014; Ivison et al. 2010; Stacey et al. 2010; Sargsyan et al. 2012; Farrah et al. 2013; Magdis et al. 2014; Brisbin et al. 2015; Gullberg et al. 2015; Schaerer et al. 2015). Active galactic nuclei are separated from star-forming galaxies based on either (i) the explicit description in the literature or (ii) EWPAH 6.2μm  0.1 (Sargsyan et al. 2012). As reported by previous studies (e.g. Maiolino et al. 2009; Stacey et al. 2010), high-z galaxies are located at a different place from local galaxies in the L[C II]/LFIR–LFIR plane.


The detailed kinematic reconstruction of the Sgr tidal debris by Law & Majewski (2010) used an initial total mass of

 M⊙ for the Sgr satellite. However, several studies point to a Sgr remnant mass significantly exceeding that value. Ibata et al. (1997) and Ibata & Lewis (1998) estimate lower bounds of 109 M⊙ for the mass of the dwarf today. With the discovery of previously unseen branches of the stream, the total luminosity budget of the progenitor galaxy is now believed to be on the order of 108 L⊙ (Niederste-Ostholt et al. 2010). As a result, recent studies have shifted to using dark-matter halo masses as large as 1011 M⊙ (Purcell et al. 2011; Gòmez et al. 2015) based on halo abundance matching arguments. Such high values are comparable to the mass of the LMC progenitor (see e.g., Jethwa et al. 2016; Peñarrubia et al. 2016) and imply a mass ratio relative to the MW on the order of 1:10. However, unlike the Magellanic Clouds, which may be on their first passage near the MW (Besla et al. 2007), Sgr is known to have experienced multiple close passages in the past. If true, such high Sgr progenitor masses would have important implications for the formation and evolution of the MW disk (e.g., Purcell et al. 2011; Gòmez et al. 2013; D’Onghia et al. 2016). Because the dynamical friction force is proportional to the square of the satellite mass, we expect drag to play a much more important role in slowing down the Sgr satellite and bringing it to closer galactocentric distances. Here, we perform an exploration across orbital angular momentum parameter space analogous to Section 3.1, this time using a Sgr progenitor mass of 6×1010 M⊙ according to the recent estimates of Gibbons et al. (2017). We consider two possibilities: a “slow sinking” scenario in which, as in Section 3, Sgr crosses the MW virial radius at

 (approximately 8 Gyr ago), and a “rapid sinking” scenario, in which we examine a first infall around

, about 4 Gyr ago.


For many hot channel eruption events, their exact origin and initiation process still remain under debate. Some observations supported that before the hot channel eruption, a corresponding MFR may already exist (e.g., Liu et al. 2016; Wang et al. 2016; Yang et al. 2019) and slow photospheric flows might be important for its gradual formation (e.g., Hou et al. 2018; Yan et al. 2018; Vasantharaju et al. 2019); while others argued that they can also be newly built up via rapid coronal reconnection during the eruption (Cheng et al. 2011; Song et al. 2014; Palacios et al. 2015). For their loss-of-equilibrium, some researchers found that the loss-of-equilibrium of the hot channel is initially facilitated by the breakout type (e.g., Shen et al. 2012; Chen et al. 2016; Mitra et al. 2018) or tether-cutting type (e.g., Chen et al. 2014, 2018; Joshi et al. 2015; Dudík et al. 2016) preflare reconnection, but others believed the loss-of-equilibrium of the hot channel may be directly triggered by the ideal MHD instabilities (e.g., Liu et al. 2007; Bi et al. 2015; Vemareddy et al. 2017). Note that Duan et al. (2019) recently carried out a survey on the initiation mechanism of all the major solar flares, either eruptive or confined, from 2011 to 2017. Statistically, their study results indicate that magnetic reconnection and ideal MHD instabilities seemingly play an equal role in the triggering of major flares and eruptions. In the present study, our NLFFF extrapolation and topology analysis shows that a seed MFR existed within an HFT configuration prior to the later solar eruption. Near the HFT, two sets of sheared arcades serve as an enveloping field holding the seed MFR, and have rooted their opposite footpoints at canceling fluxes. Combining these results with imaging observations, we suggest that the preflare 3D reconnection is most likely first triggered at the HFT in the precursor phase due to the preceding flux cancellation (Savcheva et al. 2012a), and the newborn hot channel should originate from the preexisting seed MFR. Through preflare 3D reconnection, the seed MFR was rapidly heated up to 10 Mk manifesting as a newborn hot channel, and its spatial size also underwent an enlarging process at the same time (as revealed by Figures 2 and 5). As a result, the enlarged hot channel may readily lift into the abovementioned torus-unstable domain (around 12 Mm above the photosphere), and soon enter its exponential accelerated eruption.


As in Flowers et al. (2019), to compare our model transmission spectra directly against the Ehrenreich et al. (2020) results, we must calculate the transmission spectra as a function of orbital phase throughout the duration of transit. To account for orbital phase dependencies, we apply the following procedure:1.Account for phase-dependent backlighting of the planet (i.e., stellar limb-darkening effects). At different points of its transit, the planet will occult regions of its host star of varying brightness. Furthermore, at a fixed orbital phase, different regions of the planet’s limb will be backlit by varying intensities of stellar light. Similar to Flowers et al. (2019), we calculate the normalized stellar intensity at the center of each cell of the 2D projected planetary grid produced by our GCM at each modeled orbital phase of the planet. We use the quadratic limb-darkening coefficients reported by Ehrenreich et al. (2020) to establish the stellar center-to-limb intensity profile, and we take into account the 89.°623 orbital inclination of WASP-76b (Ehrenreich et al. 2020) to determine where the planet resides on the stellar disk as a function of its orbital phase. We make the assumption of constant impact parameter b over the course of transit.
9

9
In reality, a planet on an inclined orbit will not have a constant b over the entire duration of transit; rather, the planet’s distance from the stellar equator will be decreased at ingress and egress, reaching its maximum at center of transit. Our tests reveal that, for WASP-76b, the relative error induced by the constant b assumption is on the order of 4% in distance, which results in a change on the order of 1 m s−1 at the blueshift level (see Section 3.1). Hence, our b treatment is justified. This procedure allows us to calculate a backlighting factor f, which ranges from 0 to 1, effectively replacing the constant I

λ,0 from Equation (3) with a variable

Iλ,0×f(θ′,z,φ)

, for a given orbital phase φ and 2D projected polar angle

θ′

.2.Account for the decreasing of the continuum by interpolating a light curve produced by the batman code (Kreidberg 2015). Step 1 ensures that less light is transmitted through the planet’s atmosphere than a uniform stellar disk would emit. Step 2 further enforces that the inner, optically thick core of the planet is simulated crossing a limb-darkened star, as opposed to a star of uniform brightness.3.Account for the planet’s rotation over the course of transit. Because the planet is continually rotating as it travels across the face of its host star, we must transform the GCM coordinate system so that the correct observer-facing hemisphere is modeled at each instance during transit. For simplicity, we assume zero obliquity, which allows us to calculate the coordinate transform simply by assigning a linear offset to each planetary longitude; i.e., ϕ
rotated = ϕ + φ.


The origin of ultra-high energy cosmic rays (UHECR) is uncertain, and many possible sources have been proposed. Radio galaxies have long been considered a likely source of UHECR because of their high power, large size, and longevity (e.g. Hardcastle et al. 2009; O’Sullivan, Reville & Taylor 2009; Wykes et al. 2013; Eichmann et al. 2018). In Matthews et al. (2018, 2019), we made the case from observations and theory that UHECR may be accelerated by shocks in the lobes of radio galaxies. Our numerical simulations demonstrated the presence of shocks in concentrated, approximately annular, flows centred on the jet axis, which we refer to as hydromagnetic flux tubes, or more simply as ‘flux tubes’, that emerge from the high pressure hot-spots at the end of relativistic jets. Back-flows in radio lobes have been discussed by many authors (for example Norman et al. 1982; Falle 1991; Scheuer 1995; Saxton et al. 2002, Krause 2005; Keppens et al. 2008; Mignone et al. 2010; Cielo et al. 2014; Tchekhovskoy & Bromberg 2016). The flow expands into the lobes where the pressure is lower. As discussed in Matthews et al. (2019), from application of the Bernoulli equation, the flow becomes supersonic before being slowed down in one or more shocks as it progresses deeper into the lobe as depicted in an idealized model in Fig. 1. Our simulations of radio jets support this picture by demonstrating the presence of a succession of shocks in flux tubes with Mach numbers of a few and flow velocities of the order of c/4. With these velocities, shocks are well suited to UHECR acceleration since fully relativistic shocks pose severe problems for acceleration to the highest energies (Kirk & Reville 2010; Lemoine & Pelletier 2010; Reville & Bell 2014; Bell et al. 2018). Further discussion of our model and the observational context can be found in Matthews et al. (2018, 2019). Simulations show that flux tubes are usually more contorted than the idealized flux tubes in Fig. 1. However, the flux tube need only be long enough to contain the CR diffusion scaleheights upstream and downstream of a shock, and curvature should not invalidate the model since magnetic field lines threading the tube should cause CR to diffuse predominantly parallel to the tube. Cosmic ray (CR) acceleration by diffusive shock acceleration (Krymskii 1977; Axford, Leer & Skadron 1977; Bell 1978a,b, Blandford & Ostriker 1978) has been studied at length, both theoretically and observationally, in the context of supernova remnants (SNR). The maximum energy of CR accelerated by SNR is constrained by various factors. The most general constraint is set by the physical size R of the shock, leading to a maximum CR energy of ZuBR (Hillas 1984), where u is the flow velocity, B is the magnetic field, and the CR has charge Ze. ZuBR is the characteristic maximum CR energy in eV if u, B & R are in SI units. A related constraint is set by the need for the shock to persist for a time longer than the time taken for CR to be accelerated (Lagage & Cesarsky 1983a,b). For a quasi-parallel shock (magnetic field parallel to or at an angle significantly smaller than π/2 to the shock normal) the Lagage & Cesarsky limit is equivalent to the Hillas limit if the shock persists for a flow time R/u. For perpendicular shocks, the acceleration is very rapid and the maximum CR energy is set by the Hillas limit (Jokipii 1982, 1987). In this work, we assume that the hydrodynamic flow through a flux tube is in steady state on the scale of the time taken for CR acceleration, in which case the limit on the maximum CR energy is better understood through the spatial limit of Hillas than the time-scale analysis of Lagage & Cesarsky.


The physical parameters governing the MS are still being investigated, although some basic inferences have been made. The main parameters that describe quasars as accreting black holes are the black hole mass (MBH, ranging from 106$\rm M_{\rm \odot }$ to 109.5$\rm M_{\rm \odot }$; Kormendy & Richstone 1995), the accretion luminosity, Eddington ratio (LBol/LEdd, Boroson & Green 1992; Sulentic et al. 2000b; Marziani et al. 2001, 2003b), and the black hole spin (e.g. Wang et al. 2014). The MBH can be estimated by assuming that the gas motions are predominantly Keplerian around the black hole, and by applying the virial theorem for a system whose mass is entirely concentrated in the center of gravity. Reverberation mapping provides a measurement of the radial distance rBLR of the line emitting gas from the central black hole (Peterson 1993, 2004). The so-called ‘virial mass’ have been computed for large samples of quasars employing several different emission lines, various measures of line width, and exploiting correlation between the emitting region radius and luminosity (see Marziani & Sulentic 2012; Shen 2013; Popović 2020, for reviews). An independent method relies on the scaling law between MBH and the stellar velocity dispersion of the galaxy bulge (σ⋆; Kormendy & Ho 2013). Recently, spectropolarimetric observations of the Hydrogen Balmer lines have allowed to measure the intrinsic line FWHM due to a Keplerian velocity field and to compute the black hole mass independently from orientation (Afanasiev & Popović 2015; Afanasiev, Popović & Shapovalova 2019, and references therein). All methods to compute black hole mass in active galactic nucleus (AGN) are subject to caveats and suffer considerable uncertainties (e.g. Dalla Bontà et al. 2020, and references therein). None the less, the LBol/LEdd, which is proportional to the luminosity-to-black hole mass ratio (L/MBH), has been revealed to be a fundamental driver of the E1 MS, closely related to several observational parameters (Marziani et al. 2001, 2003b; Kuraszkiewicz et al. 2004; Shen & Ho 2014; Panda et al. 2018; Panda, Marziani & Czerny 2019). With decreasing Eddington ratio, source properties change from the ones of Pop. A to the ones of Pop. B, which tend to show broader Balmer emission lines, weaker RFeII,1 and more asymmetric Balmer line profiles (Sulentic et al. 2000b; Marziani et al. 2003b; Shen & Ho 2014).


SN 2011fe, discovered a mere ≈11 h after explosion (Nugent et al. 2011) by the Palomar Transient Facility (PTF; Law et al. 2009), is the brightest SN Ia since the advent of modern astronomical detectors. Located at just $d_L \approx 6.5~\rm {Mpc}$ (e.g. Shappee & Stanek 2011; Beaton et al. 2019), SN 2011fe exploded in a region of M101 uncontaminated by intervening dust (Patat et al. 2013) providing an ideal location for testing SN Ia progenitor and explosion models. The early detection allowed extensive follow-up observations across the electromagnetic spectrum (e.g. Matheson et al. 2012; Parrent et al. 2012; Pereira et al. 2013; Hsiao et al. 2013; Johansson, Amanullah & Goobar 2013; Tsvetkov et al. 2013; Munari et al. 2013; Mazzali et al. 2014; Zhang et al. 2016) and provided direct constraints on the radius of the exploding star (Nugent et al. 2011; Bloom et al. 2012). Stringent non-detections in radio (Chomiuk et al. 2012; Horesh et al. 2012; Kundu et al. 2017) and X-ray (Horesh et al. 2012; Margutti et al. 2012) observations exclude nearby CSM at high significance. Early ultraviolet (UV) photometry did not show any evidence for the ejecta encountering a nearby companion star (Brown et al. 2012) and nebular spectra lacked the Balmer emission lines from material ablated off the donor star by the ejecta impact (Shappee et al. 2013b; Lundqvist et al. 2015; Tucker et al. 2022). Pre-explosion imaging excludes the presence of a RG or He donor star (Li et al. 2011) and disfavor an accreting WD in the ∼105 yr prior to explosion (Graur, Maoz & Shara 2014). Multi-epoch spectropolarimetry reveal consistently-low continuum polarization suggestive of a symmetric ejecta distribution with evidence for minor oblateness (Milne et al. 2017). Finally, nebular-phase observations at ≳ 1 year after maximum light allows a direct view to the inner ejecta and provides unique constraints on the explosion conditions (McClelland et al. 2013; Kerzendorf et al. 2014, 2017; Mazzali et al. 2015; Graham et al. 2015; Taubenberger et al. 2015; Dimitriadis et al. 2017; Friesen et al. 2017; Shappee et al. 2017; Tucker et al. 2022). SN 2011fe is one of the best-studied astronomical objects in the past decade and remains a key benchmark for any SN Ia theory or model.


A star having highly eccentric and compact orbit around a black hole experiences tidal distortion. The tidal radii of the black hole–star system are expressed as (Shiokawa et al. 2015; Coughlin et al. 2017)
(7)$$\begin{eqnarray*}
r_t = (\frac{M_{\rm BH}}{M})^{1/3} R,
\end{eqnarray*}$$where MBH is the mass of the black hole, M is the mass of the star, and R is the radius of the star. Stars orbiting at a distance smaller than the tidal radius are disrupted by tidal force of the black hole. The additional contribution to perihelion shift arising from tidal effect in terms of pericentre distance is given by (Will 2008)
(8)$$\begin{eqnarray*}
\delta \phi _{\rm prec}^{\rm tidal} = \frac{30 \pi }{(1+e)^5} k_2 (1+ \frac{3e^2}{2} + \frac{e^4}{8})(\frac{M_{\rm BH}}{M}) (\frac{{R}^5}{ r_{\rm p}^5}),
\end{eqnarray*}$$k2 in equations (8) is the Love number of a star that measures its deformability and susceptibility of its shape to change in response to a tidal potential (Poisson & Will 2014). The tidal Love number (kl) of degree l for polytropic stars has been studied by Yip & Leung (2017) through perturbative expansion of kl around the polytropic indices n = 0 and n  = 1. These are obtained for Newtonian stars whose stiffness is governed by polytropic index (n). In the general framework of Yip & Leung (2017), the Lane Emden equation is solved perturbatively by applying Scaled Delta Expansion method to develop perturbation series of the multipolar tidal Love number about two exactly solvable polytropic indices (n = 0, n  = 1). These perturbative expansions are then used to make a two-point Pade approximation of the Love number for n ϵ [0, 3] which is given as
(9)$$\begin{eqnarray*}
k_l({\it n}) = (5 - {\it n})^3 \frac{a_1 + {\it n}a_2 + {\it n}^2 a_3 + {\it n}^3 a_4}{1000 + {\it n}a_5 + {\it n}^2 a_6}.
\end{eqnarray*}$$The factor (5 − n) is empirically inserted to ensure that the Love number reduces to zero for n  = 5 that corresponds to infinite configuration. Here, ais are analytically determined coefficients of the perturbation series and these are taken from table 1 of Yip & Leung (2017). We consider polytropic models, n = 1 and n  = 3, for evaluating the Love number and obtain k2 (n = 1)  = 0.26 k2 (n = 3)  = 0.014. These values are then used to evaluate tidal contribution to the periastron shift. For the tidal effect, we also have to take into account the mass and radii of the stars. Structure of the nuclear star cluster in the vicinity of Sgr A* was reported by Do et al. (2010). A general consensus is that the cluster has preponderance of young main sequence stars (∼ 4 – 8Myr) over late-type stars (∼1 – 10Gyr). Presence of OB main-sequence stars was also reported by Allen, David & Hyland (2010), Ghez et al. (2003a), and Do et al. (2013). Here, we consider only the main-sequence stars for the mass–radius relation that is required for calculation of tidal contribution to periastron shift (see equation 8). Study of empirical mass–radius relation (MRR) of stars began to appear in literature after late twentieth century (Gimenez & Zamorano 1985; Harmanec 1988; Demircan & Kahraman 1991; Malkov 2007). The stellar radii are related to luminosity through Stefan–Boltzmann law which in turn is dependent on stellar masses. Unfortunately, there was no final consensus on what functions properly represent mass–luminosity relation (MLR) and MRR. It had been challenging to have a single MRR for main-sequence stars till the publication of Eker et al. (2015) in which the MLR and MRR for Galactic nearby main-sequence stars were reported. The MLR was revised with the help of power law L ∝ Mα for a sample of galactic main-sequence stars with mass and radii accurate up to ≤3 per cent and luminosities accurate up to ≤30  per cent. But there was no derivation of MRR to estimate radii for a given stellar mass. It was found that for LMSs (M  1M⊙) stellar radii have narrow distribution with mass but for massive stars (M > 1M⊙) the distribution was quite wide. Thus, there was no unique function to represent MRR. Eker et al. (2018) updated the data of 509 main-sequence stars in the solar neighbourhood and obtained interrelated MLR, MRR, and mass-effective temperature relation (MTR) in the mass range 0.179 ≤ (M/M⊙) ≤ 31. A single MRR was found for the LMSs with 0.179 ≤ (M/M⊙) ≤ 1.5. An MTR function was found for massive stars with 1.5 ≤ (M/M⊙) ≤ 31. The MLR was established for six mass ranges encompassing ultra-low-mass (0.179 ≤ (M/M⊙) ≤ 0.45) and very high-mass (7 ≤ (M/M⊙) ≤ 31) stars. Thus, by using Stefan–Boltzmann law (L  = 4$\pi R^2 \sigma T_{\rm eff}^4$), the MRR can be obtained for the massive stars with 1.5 ≤ (M/M⊙) ≤ 31. It is true that there are effects of metallicities of the stars on the MLR and hence finally on MRR (Eker et al. 2018). But due to absence of detailed model of stellar evolution and stellar atmosphere of the GC stars with different metallicities, we have assumed that the young GC stars have nearly the solar metallicities (see Lu et al. 2013 and references therein) and hence obey the interrelated MLR, MTR, and MRR functions of the main-sequence stars in the solar neighbourhood. The MRR for the LMSs [0.179 ≤ (M/M⊙) ≤ 1.5] is (Eker et al. 2018)
(10)$$\begin{eqnarray*}
\frac{R}{{\rm R}_{\odot }} \cong [0.438(\frac{M}{{\rm M}_{\odot }})^2 + 0.479 (\frac{M}{{\rm M}_{\odot }}) + 0.075].
\end{eqnarray*}$$For massive stars (1.5 ≤ (M/M⊙) ≤ 31), we use the interconnection between MLR, MTR, and MRR presented by Eker et al. (2018) as follows. The Stefan–Boltzmann law
(11)$$\begin{eqnarray*}
{\rm log}(\frac{L}{{\rm L}_{\odot }}) = 2 {\rm log}(\frac{R}{{\rm R}_{\odot })} + 4{\rm log}(\frac{T_{\rm eff}}{T_{{\rm eff}(\odot)}})
\end{eqnarray*}$$is used in conjunction with the M–Teff relation (MTR) for 1.5 ≤ (M/M⊙) ≤ 31
(12)$$\begin{eqnarray*}
{\rm log}(\frac{T_{\rm eff}}{1K})\simeq - 0.170({\rm log}(\frac{M}{{\rm M}_{\odot }}))^2 + 0.888 {\rm log}(\frac{M}{M_{\odot }}) + 3.671
\end{eqnarray*}$$and the MLR for the mass range 7 ≤ (M/M⊙) ≤ 31,
(13)$$\begin{eqnarray*}
{{\rm log}(\frac{L}{{\rm L}_{\odot }})\simeq 2.865 {\rm log}(\frac{M}{{\rm M}_{\odot }}) + 1.105}.
\end{eqnarray*}$$The result is the following MRR for massive stars,
(14)$$\begin{eqnarray*}
{\rm log}\Big (\frac{R}{{\rm R}_{\odot }}\Big) \cong [-0.3435 {\rm log}\Big (\frac{M}{{\rm M}_{\odot }}\Big) + 0.34 {{\rm log}\Big (\frac{M}{{\rm M}_{\odot }}\Big) }^2 + 0.7365]. \nonumber \\
\end{eqnarray*}$$We study the tidal contribution to periastron shift for both the low-mass (0.179 ≤ (M/M⊙) ≤ 1.5) and high-mass (7 ≤ (M/M⊙) ≤ 31) categories of young main-sequence stars near Sgr A*. For low-mass category, the contribution is studied for M/M⊙ = 0.18, 1.0, and 1.5, whereas for high-mass category it is estimated for M/M⊙ = 10, 20, and 30. Equation (8) can be written as
(15)$$\begin{eqnarray*}
\delta \phi _{\rm prec}^{\rm tidal} = \frac{30 \pi }{(1+e)^5} k_2 (1+ \frac{3e^2}{2} + \frac{e^4}{8})(\frac{M_{\rm BH}}{M}) (\frac{{{\rm R}_{\odot }}}{ r_p})^5 (\frac{R}{{\rm R}_{\odot }})^5.
\end{eqnarray*}$$Equations (10) and (14) have been used in equation (15) to estimate the tidal contributions to periastron shift arising from LMS and HMS. The actual astrometric size of the perihelion shift at periapsis is given by θ  = ($\delta \phi ^{\rm total}_{\rm prec}$) ($\frac{ r_{p} \sin i}{D}$), where D is the distance to the GC and i is the inclination of the orbital plane of the star with respect to the observer. Therefore, the actual rate of periastron shift is expressed as
(16)$$\begin{eqnarray*}
\dot{\theta }_{\rm prec} = \frac{(\delta \phi)^{\rm total}_{\rm prec} r_{p} \sin i}{\rm PD}.
\end{eqnarray*}$$Here, P is the orbital period for the stars, P  = ${ 2\pi a^{\frac{3}{2}}}/{\sqrt{GM_{\rm BH}}}$  = ${2\pi r_p^{\frac{3}{2}}}/{\sqrt{GM_{\rm BH}}(1-e)^{\frac{3}{2}}}$.


Information about fundamental parameters of stars – like their mass, luminosity, surface temperature and chemical composition – comes primarily from matching observations to synthetic spectra computed using models of stellar atmospheres. For massive stars with hot surfaces, scattering and absorption in spectral lines further transfer momentum from the star’s intense radiation field to the plasma, and so provides a force that overcomes gravity and drives a wind-outflow directly from the stellar surface (Castor et al. 1975). These starlight-powered winds are very strong and fast, and can dramatically affect the star’s atmospheric structure (review by Puls et al. 2008) as well as the evolution of its mass and luminosity, chemical surface abundances, rotational velocity, and nuclear burning life-times (review by Smith 2014). Atmospheric models of such hot, massive stars must thus generally be constructed using a unified, or global, approach, wherein the basic structural equations for the quasi-static photosphere and the outflowing stellar wind are solved simultaneously (Gabler et al. 1989). In addition, the expanding atmospheres of these stars are characterized by their large departures from local thermodynamic equilibrium (LTE), meaning the full number density rate equations (typically reduced to statistical equilibrium, and often simply called non-LTE or NLTE) must be solved to obtain the atmospheric radiation field and the excitation and ionization balance. As such, quite intricate numerical solution techniques are normally required to compute synthetic observables, like spectral lines and energy distributions, for these objects (for details, see book by Hubeny & Mihalas 2014). Over the past decades, much effort has been devoted toward constructing such global NLTE, steady-state model atmospheres of hot stars with winds; several numerical computer codes meanwhile exist on the market, for example CMFGEN (Hillier & Miller 1998), POWR (Gräfener et al. 2002; Sander et al. 2015), PHOENIX (Hauschildt 1992), WM-BASIC (Pauldrach et al. 2001), and the subject of this paper, FASTWIND (Santolaya-Rey et al. 1997; Puls et al. 2005; Rivero González et al. 2011; Carneiro et al. 2016). FASTWIND is routinely applied for both photospheric and wind analyses of hot stars, and used for detailed studies of individual objects as well as in large spectroscopic surveys (like within the recent VLT-FLAMES survey of massive stars in the Tarantula giant star-forming region in the Large Magellanic Cloud, Evans et al. 2011). A critical component of all these codes regards their practical treatment of the stellar wind; traditionally this has been to assume a parametrized steady-state and smooth outflow, without any clumps or shocks. However, it has been known for quite many years now, that these line-radiation driven winds are in fact inhomogeneous and highly structured on small spatial scales (see overviews in Puls et al. 2008, 2015; Hamann et al. 2008; Sundqvist et al. 2012b). Such wind clumping arises naturally from the strong line-deshadowing instability, the LDI, a fundamental and inherent property of line driving (e.g., Owocki & Rybicki 1984, 1985). Radiation-hydrodynamic, time-dependent wind models (Owocki et al. 1988; Feldmeier et al. 1997; Owocki & Puls 1999; Dessart & Owocki 2003; Sundqvist & Owocki 2013, 2015; Sundqvist et al. 2018) following the non-linear evolution of this LDI show a characteristic two-component-like structure consisting of spatially small and dense clumps separated by large regions of very rarified material, accompanied by strong thermal shocks and a highly non-monotonic velocity field. Such clumpy winds then affect both the atmospheric structure and the radiative transfer needed to derive synthetic observables; as just one example of this, neglecting clumping typically leads to observationally inferred mass-loss rates that might differ by more than an order of magnitude for the same star, depending on which spectral diagnostic is used to estimate this mass loss (Fullerton et al. 2006). Global model atmospheres nowadays normally account for such wind inhomogeneities by simply assuming a two-component medium consisting of overdense, optically thin clumps of a certain volume filling factor, following a smooth, parametrized velocity law, and an inter-clump medium that is effectively void (e.g., Hillier 1991; Puls et al. 2006). However, if clumps become optically thick, it leads to an additional leakage of light – not accounted for in the filling factor approach – through porous channels in between the clumps. Such porosity can occur either spatially (e.g., Feldmeier et al. 2003; Owocki et al. 2004; Sundqvist et al. 2012a), or for spectral lines in velocity-space due to Doppler shifts in the rapidly accelerating wind (sometimes thus called velocity-porosity, or “vorosity”, Owocki 2008). Regarding spatial porosity, several studies over the past years have focused on examining potential effects on the bound-free absorption of X-ray photons by the bulk wind (e.g., Oskinova et al. 2006; Owocki & Cohen 2006; Sundqvist et al. 2012a; Leutenegger et al. 2013; Hervé et al. 2013). Regarding velocity-space porosity, similar studies (Oskinova et al. 2007; Hillier 2008; Sundqvist et al. 2010, 2011, 2014; Šurlan et al. 2012, 2013) have shown that clumps indeed very easily become optically thick in especially the strong UV wind-lines of hot stars (the so-called P-Cygni lines), and that the associated additional leakage of line-photons leads to weaker line profiles than predicted by smooth or volume filling factor models1. But constructing realistic, multi-dimensional ab-initio radiation-hydrodynamic wind simulations that account naturally for (time-dependent) spatial and velocity-field porosity is an extremely challenging and time-consuming task (Sundqvist et al. 2018). Thus there has also been a big need for developing simplified, parameterized models that can be more routinely applied to diagnostic work on samples of hot stars with winds. Building on their prior studies Sundqvist et al. (2010; 2011; 2012a; 2014, hereafter SPO14) developed and benchmarked such a method, using effective quantities to simulate the reduction in opacity associated with optically thick clumps. In contrast to some other models mentioned above, this “effective opacity” approach has the great advantage that it can be quite readily implemented into the already existing (time-independent) global NLTE atmosphere models discussed above.


Various studies have investigated the color-magnitude relation at high redshifts (z ≳ 2), and the results are inconclusive. Reddy et al. (2008) found weak-to-no correlation between dust or UV color (related as shown in Fig. 4) and R mag for UV-selected galaxies at 1.5 ≲ z ≲ 2.6. Similarly, Heinis et al. (2013) through their investigation of far-infrared/dust properties of UV selected galaxies at z ~ 1.5 found that the average UV slope is mostly independent of the UV luminosity. On the other hand, Bouwens et al. (2009) studied the relation between the UV slope and MUV for a sample of U-band dropout galaxies at z ≃ 2.5 and found a positive color-magnitude correlation. At higher redshifts (z > 3), similar disagreements have been observed for samples based on the Lyman break color selection, in the sense that, some studies find no (or very weak) trends between β and UV magnitude (e.g., Ono et al. 2010; Finkelstein et al. 2012; Dunlop et al. 2012; Castellano et al. 2012), while other studies find a strong color-magnitude relation (e.g., Wilkins et al. 2011; Bouwens et al. 2012; Rogers et al. 2014; Bouwens et al. 2014). Bouwens et al. (2014) also argue that this relation could be described by a double power-law with a different slope for fainter magnitudes. The differences in these various studies could be because of many systematic and/or physical reasons, such as selection of galaxy samples (especially at lower redshifts), UV magnitude and/or β measurements, intrinsic scatter in β, dynamic range in UV luminosity. Our study relies on a UV selected sample with spectroscopic redshifts but it lacks a significant dynamic range in UV luminosity as seen in Fig. 5. A detailed study of a uniformly selected spectroscopic sample covering a wider range in UV luminosity is needed to understand the true nature of the color-magnitude relation at high redshifts. At least for ~L∗ (~0.5L∗ – 3.0L∗) galaxies in a uniformly selected VUDS sample at 2  z  2.5 there appears to be no correlation between β and M1500.


Radio searches for single pulses and average pulse emission by folding the data based on the ephemeris derived from the X-ray observations (e.g. Israel et al. 2016) were carried out using the NC, GMRT (Surnis et al. 2016), and Arecibo (Younes et al. 2017b), on time-scales of days to a few weeks after the outbursts in 2014–2016. Neither telescope reported a detection, and the GMRT quotes upper limits of 0.4 and 0.2 mJy at 326.5 and 610 MHz, respectively, assuming a 10 per cent duty cycle and an 8σ detection threshold. The Arecibo observations were at 6.7 and 1.4 GHz and they report upper limits of 14 and 7 μJy, respectively, having used a 10σ threshold and a 20 per cent duty cycle. However, regular monitoring is supported by the most recent detection of just three pulses with CHIME (Good & CHIME/FRB Collaboration 2020) and the subsequent detection of single pulses and average pulse emission with FAST (Zhu, Wang & Zhou 2020), which also appears to have been transient in nature. It is also unclear how long it takes before the radio emission turns on in these systems. Sometimes it is relatively rapid (e.g. Levin et al. 2019) and other times it can be quite some time after the X-ray outbursts (see Kaspi & Beloborodov 2017, for more details) and can apparently also vary for a given source too. Usually, when a magnetar turns on in the radio, it emits radio pulses during most rotations and stays on, with some significant variability in flux density and pulse shape, over a time-scale of months to years. In the case of SGR J1935+2154, the Kirsten et al. (2020a) campaign lasted for 2 months with a total observing time of 522 h, while our campaign lasted for 1.5 months for a total integration time of ∼110 h. Between these two overlapping campaigns, only two radio pulses were seen by Kirsten et al. (2020a). These results along with the the very recent detection of bright radio single pulses and pulsed radio emission from the magnetar (Good & CHIME/FRB Collaboration 2020; Zhu et al. 2020) suggest that the change in the magnetosphere configuration in SGR J1935+2154 to enable pulsed radio emission might be more gradual or sporadic than other magnetars like XTE J1810–197 and Swift J1818.0–1607 where bright radio pulses were seen in the immediate aftermath of the X-ray bursting behaviour. A possible change in the magnetosphere is also supported by X-ray pulsar variations (Younes et al. 2020b). This diversity of emission characteristics emphasizes the need to regularly monitor magnetars in their active states.


Two additional interesting sources for a comparison are the radio galaxies M 87 (z = 0.0044) and 3C 84 (also called NGC 1275, z = 0.0176). Both sources have a viewing angle similar to NGC 3894: 15°  θ   25° (Mertens et al. 2016) and θ   18° (Giovannini et al. 2018), respectively. The velocities of the jet components are about 0.2c in 3C 84 (Suzuki et al. 2012) and in the inner part of M 87 (Mertens et al. 2016), similar to what we find for NGC 3894. The three sources have a comparable photon index (Γ ∼ 2.1). Although it is less distant and more extended (∼100 kpc), M 87 shows a γ-ray luminosity of 6−7 × 1041 erg s−1, similar to NGC 3894. Different is the case of 3C 84, which has two-sided compact (parsec scale) jets and a distance similar to NGC 3894, but it presents a γ-ray luminosity more than 200 times higher (2 × 1044 erg s−1). Unlike NGC 3894, for which no observations with Cherenkov telescopes have been performed, M 87 and 3C 84 are also detected at very high energy (VHE, E > 100 GeV; Aharonian et al. 2006; Aleksić et al. 2012). In particular, at VHE, M 87 displayed strong variability on timescales as short as one day, but no unique signature of the region responsible for the VHE flares has been identified (Abramowski et al. 2012). Despite the long-term monitoring of M 87 during 2012−2015 in a low-activity state, the production site of γ-rays remains unclear (MAGIC Collaboration 2020). However, the correlation observed between the radio and X-ray activities is a strong indication that most often the emitting region is close to the core in this source. In the case of 3C 84, several works on radio, X-ray, and γ-ray variability suggest that short-term and long-term variability may be produced in different regions of the source. In particular, short-term variability seems related to the injection of fresh particles that are accelerated in a shock in the core region, whereas long-term variability is more likely connected with the jet structure (e.g., Fukazawa et al. 2016; Hodgson et al. 2018). Similarly to M 87 and 3C 84, long-term radio and X-ray monitoring of NGC 3894 may provide important information about the origin of the γ-ray emission.


In comparison with studies focused on other T Tauri systems, the period analysis of the Hα lines for this target often do not exhibit a single and highly significant peak. As the Hα line is expected to form not only at the accretion spot, but also in the accretion funnel and in the stellar winds, the variability of this line is also influenced by the variations of the circumstellar environment. However, the rotation period might appear with varying strengths in the periodograms. It is instructive to compare our findings with similar analyses of individual targets. In the LkCa 15 system, the strength of the emission at the line center is modulated by stellar rotation, and this effect is clearly displayed in the periodogram (Alencar et al. 2018). On the other hand, the inverse P Cygni profile of the Hα line of the HQ Tau system displays modulation on the timescale of the stellar rotation not only in the line center, but all the way to the red wing (Pouilly et al. 2020). Another interesting system to mention is V2129 Oph. When analyzing this target, Sousa et al. (2021) compared their results with the periodograms for the same system as was analyzed by Alencar et al. (2012), and they found some differences on timescales of a decade, similarly to our results. Sousa et al. (2021) discussed a few possible explanations for the observed phenomena, such as variations in the magnetic field strength, which would result in variations in the magnetospheric truncation radius, or latitudinal differential rotation, or a more complex magnetic structure with two major funnel flows originating at different radii in the inner disk. However, in the case of V2129 Oph, a periodicity longer than the stellar rotation period is present at the line center for a time of almost a decade. The likely cause of the periodicity is a structure that is present beyond the corotation radius that is stable for almost a decade. In the case of CR Cha, the rotation period has been stable for decades, but the line profiles (and the photometry as well) also vary with longer periods, likely because of variations in the circumstellar environment.


Observations of the polarized dust emission of nine low-mass protostars at 0.87 mm were obtained using the SMA (Projects 2013A-S034 and 2013B-S027, PI: A. Maury) in the compact and subcompact configuration. To increase our statistics, we also included SMA observations from three additional sources from Perseus (NGC 1333 IRAS4A and IRAS4B) and Ophiuchus (IRAS16293) observed in 2004 and 2006 (Projects 2004-142 and 2006-09-A026, PI: R. Rao; Project 2005-09-S061, PI: D.P. Marrone). The observations of NGC 1333 IRAS4A and IRAS16293 are presented in Girart et al. (2006) and Rao et al. (2009), respectively. Marrone (2006) and Marrone & Rao (2008) provide a detailed description of the SMA polarimeter system, but we provide a few details on the SMA and the polarization design below. The SMA has eight antennas. Each optical path is equipped with a quarter-wave plate (QWP), an optical element that adds a 90° phase delay between orthogonal linear polarizations and is used to convert the linear into circular polarization. The antennas are switched between polarizations (QWP are rotated at various angles) in a coordinated temporal sequence to sample the various combinations of circular polarizations on each baseline. The 230, 345, and 400 band receivers are installed in all eight SMA antennas. Polarization can be measured in single-receiver polarization mode and in dual-receiver mode when two receivers with orthogonal linear polarizations are tuned simultaneously. In this dual-receiver mode, all correlations (the parallel-polarized RR and LL and the cross-polarized RL and LR; with R and L for right circular and left circular, respectively) are measured at the same time. Both polarization modes were used in our observations. This campaign was used to partly commission the dual-receiver full polarization mode for the SMA. A fraction of the data was lost during this period owing to issues with the correlator software. Frequent observations of various calibrators were interspersed to ensure that such issues were detected as early as possible to minimize data loss.


Since the 1960s, Venus has been investigated by various flyby missions (Mariner 2, 5 and 10, Galileo, and Cassini), landers (Venera 11–14), atmospheric probes, and orbiter missions (Pioneer Venus, Venus Express, and Akatsuki), out of these, Mariner 10 had the most similar flyby trajectory to Solar Orbiter and could study magnetic field fluctuations far downtail (Lepping & Behannon 1978). Nevertheless, the nature of the high frequency plasma waves at Venus has been mainly studied by the Pioneer Venus Orbiter (PVO), as it was the only orbiter that carried a plasma wave instrument, the Orbiter Electric Field Detector (OEFD; Scarf et al. 1980b). Various types of propagation modes have been identified in different regions around the planet: 30 kHz Langmuir oscillations were present in the foreshock, 5.4 kHz Doppler-shifted electrostatic ion-acoustic waves were observed in the bow shock and appeared to be a prominent feature of the magnetotail boundary, and electromagnetic 100 Hz whistler waves were thought to be generated at the bow shock, propagating through the magnetosheath and eventually absorbed within the ionosphere (Scarf et al. 1979, 1980a; Strangeway 1991). However, the identification of these waves was not well determined as they were also suspected to be lower hybrid waves (Szegö et al. 1991), or ion acoustic waves (Strangeway & Crawford 1993; Huba 1993). This ambiguity was a direct consequence of the absence of a wave magnetic field sensor on-board PVO and the limited frequency coverage of the OEFD instrument, that had only a 4 channel electric field receiver (E field wave power at 100 Hz, 730 Hz, 5.4 kHz, 30 kHz). Furthermore, after more than forty years long search for lightning on Venus, results obtained by the different spacecraft missions are still inconclusive. The most compelling indications of some kind of atmospheric electrical activity at Venus appear to be the Venera landers’ detections of electromagnetic pulses at frequencies from 10 to 80 kHz (Ksanfomaliti 1980). Their origin is questionable (Lorenz 2018); they might be assigned to interferences similarly as electric pulses found by Galileo (Gurnett et al. 1991). No lightning related signals were found during the Cassini Venus flyby in spite of the fact that the same instrument detected up to 70 sferics per second during the Earth flyby in 1999 (Gurnett et al. 2001). The whistler-mode waves at frequencies near 100 Hz recorded by Pioneer Venus and Venus Express were attributed to lightening (Russell et al. 2008). Nevertheless, a variety of other explanations were offered for these electromagnetic observations (Lorenz 2018). Up to now, not a single image from any spacecraft has been able to confirm the existence of lightning including an extensive a 5-years long search for lightning by the Akatsuki Venus orbiter (Takahashi et al. 2018). However, the modeling did not exclude electrical breakdown in the Venusian atmosphere and transient luminous events were forecasted to occur on Venus (Riousset et al. 2020).


The high temperatures of these filaments result in the matter being highly ionised so that it absorbs and emits far-UV and soft X-ray photons. However, these WHIM filaments are of low column density and, therefore, produce a low signal intensity which makes them difficult to detect with the current instrumentation. In spite of this, the search for the missing baryons has continued and detections of extragalactic O VII and O VIII have been claimed (Nicastro et al. 2005) but they are often disputed (Kaastra et al. 2006; Williams et al. 2006; Rasmussen et al. 2007), of a single-line or low statistical significance (Nicastro et al. 2010; Bonamente et al. 2016), misidentifications of the WHIM (Nicastro et al. 2016), or they are local to the background source (Johnson et al. 2019). More recently, Nicastro et al. (2018), later updated by Nicastro (2018), reported the detection of two O VII absorption features at redshifts z = 0.3551 and z = 0.4339 along the sight-line towards blazar 1ES 1553+113 after a 1.75 Ms observation with the XMM-Newton reflection grating spectrometer. Johnson et al. (2019) conducted additional studies towards 1ES 1553+113, suggesting that the feature located at z = 0.4339 may not originate from the WHIM and is associated, rather, with the local environment of the blazar. A study by Kovács et al. (2019) quotes a 3.3σ detection of O VII towards H1821+643 from a stacked spectrum of Chandra observations with an 8 Ms total exposure. Ahoranta et al. (2020) performed spectral analysis of Chandra and XMM-Newtown observations at previously determined FUV redshifts, yielding two X-ray line candidates of Ne IX[[Inline38]He and O VIII Lyα at a combined significance of 3.9σ. In spite of the large observational efforts, only these few marginal detections have been achieved so far. The small equivalent widths of ≈0.07−0.42 eV (Branchini et al. 2009; Nicastro et al. 2018) from WHIM absorption features mean that high signal-to-noise ratio observations are required for their detection. This calls for an observatory with a large effective area, high energy resolution, and a low energy threshold in the soft X-ray energy band.


Mid-infrared and millimeter polarimetric observation has so far been considered as the best method to probe the magnetic field. This is because if aspherical grains in disks become aligned with the magnetic field as is the case in the interstellar medium (ISM), the polarization vector arising from thermal emission of the aligned grains becomes perpendicular to the local magnetic field line (Cho & Lazarian 2007, henceforth CL07, Matsakos et al. 2016; Yang et al. 2016b; Bertrang et al. 2017). At mid-infrared wavelengths, Li et al. (2016) performed a polarimetric imaging observation of AB Aur using CanariCam. As a result, they detected a centrosymmetric polarization pattern, and the degree of polarization was as high as 1.5% at large radii. At millimeter wavelengths, polarimetric observations of disks have been performed (e.g., Hughes et al. 2009, 2013; Rao et al. 2014; Stephens et al. 2014; Cox et al. 2015; Kataoka et al. 2016b). Polarized emission from a circumstellar disk has been detected in the Class 0 phase (Rao et al. 2014; Cox et al. 2015). More evolved disks do not show a degree of linear polarization larger than 0.5% (Hughes et al. 2009, 2013). It should be mentioned that Stephens et al. (2014) detected polarized flux from HL Tau, which is classified as a Class I-II, with an average degree of linear polarization of 0.9%. More recently, Kataoka et al. (2016b) reported the first submillimeter polarization observation of a disk obtained with ALMA, and they clearly detected polarized flux from HD 142527. The polarization fraction at a peak position of polarized intensity was 3.26%, and the maximum polarization fraction was as high as 13.9%. The disk reveals radial polarization vectors; however, they flip by 90° in its northeast and northwest regions. In addition, the detected polarization fraction is much larger than the stringent limit set by Hughes et al. (2009, 2013), and further polarimetric observations by ALMA will reconcile this discrepancy.


With our joint analysis of stellar mass fraction and source size, we find a larger stellar mass fraction than earlier statistical studies. In FigureÂ 2, we compare our determination of the stellar surface density fraction to a simple theoretical model and to the best fit of a sample of lens galaxies by Oguri etÂ al. (2014). The simple theoretical model is the early-type galaxy equivalent of a maximal disk model for spirals. We follow the rotation curve of a de Vaucouleurs component for the stars outward in radius until it reaches its maximum and then simply extend it as a flat rotation curve to become a singular isothermal sphere (SIS) at large radius (see details in the Appendix). The ratio of the surface mass density of the de Vaucouleurs component to the total surface mass density is shown as a dashed curve in FigureÂ 2. We also show as a gray band the best fit for the stellar fraction in the form of stars determined by Oguri et al (2014) in a study of a large sample of lens galaxies using strong lensing and photometry, as well as the best model using a Hernquist component for the stars and an NFW halo for the dark matter with and without adiabatic contraction, also from Oguri etÂ al. (2014). We have used the average and dispersion estimates for the Einstein and effective radii available for 13 of the objects in our sample from Oguri etÂ al. (2014), Sluse etÂ al. (2012), Fadely etÂ al. (2010), and LehÃ¡r etÂ al. (2000; see TableÂ 1) as an estimate of RE/Reff in FigureÂ 2. The average value and dispersion of the sample is RE/Reff = 1.8 Â± 0.8. This also averages over the different radii of the lensed images. The agreement of our estimates with the expectations of the simple theoretical model and with estimates from other studies (Oguri etÂ al. 2014) is quite good. For comparison, the estimate of Pooley etÂ al. (2012; using the Einstein and effective radii estimates for 10 out of 14 of their objects from Schechter etÂ al. 2014) seems somewhat lower than expected at those radii. The range of stellar mass fractions from MED09 for source sizes in the range 0.3â15.6 light days is also shown in FigureÂ 2. In this case, the discrepancy between our estimate and their reported value of Î± = 0.05 is completely due to the effect of the source size. Although accretion disk sizes are known to be smaller in X-rays, recent estimates are in the range of 0.1â1 light-days, depending on the mass of the black hole (see Mosquera etÂ al. 2013), and these finite sizes will increase the stellar surface densities implied by the X-ray data. Another possible origin for this discrepancy is that Pooley etÂ al. (2012) use the macro model as an unmicrolensed baseline for their analysis. It is well known that simple macro models are good at reproducing the positions of images, but have difficulty reproducing the flux ratios of images due to a range of effects beyond microlensing. Recently, Schechter etÂ al. (2014) found that the fundamental plane stellar mass densities have to be scaled up by a factor 1.23 in order to be compatible with microlensing in X-rays in a sample of lenses with a large overlap with that analyzed by Pooley etÂ al. (2012). It is unclear how this need for more mass in stars at the position of the images found by Schechter etÂ al. (2014) can be reconciled with the apparently low estimate of mass in stars at those radii by Pooley etÂ al. (2012). Our estimate of the stellar mass fraction agrees better with the results of microlensing studies of individual lenses (Keeton etÂ al. 2006; Kochanek etÂ al. 2006; Morgan etÂ al. 2008, 2012; Chartas etÂ al. 2009; Pooley etÂ al. 2009; Dai etÂ al. 2010) that reported values in the range 8%â25%, and with the estimates from strong lensing studies (see for example Jiang & Kochanek 2007; Gavazzi etÂ al. 2007; Treu 2010; Auger etÂ al. 2010; Treu etÂ al. 2010; Leier etÂ al. 2011; Oguri etÂ al. 2014) which produced stellar mass fractions in the range 30%â70% integrated inside the Einstein radius of the lenses.