The other significant source of scatter in the size–mass plane is the uncertainty in measuring the total stellar mass of galaxies from the integrated stellar mass density profile of the objects. As explained in Section 5.4, we measure our total stellar mass by integrating the stellar mass density profiles. To quantify how the uncertainty in the total stellar mass affects our results, we have assumed the following uncertainties in measuring the stellar mass: δmass = 0.24 ± 0.01 dex (for the entire sample), δmass = 0.19 ± 0.01 dex (for the E0-S0 + subsample), δmass = 0.24 ± 0.01 dex (for the S0/a-Sm subsample) and δmass  = 0.25 ± 0.03 dex (for the Dwarfs subsample). These values were computed by an analysis of the differences between the Portsmouth stellar masses of our galaxies (Maraston et al. 2013) and those we measured using the g–r colour profile (Roediger & Courteau 2015, see Appendix D for further details). To model the effect of the mass uncertainty ($\sigma _{\rm R_{mass}}$) on the scatter of the scaling relationship, all the observed stellar mass profiles were either scaled up or down in mass to place the galaxies on the best-fitting line through the observed stellar mass plane. This has been performed self-consistently, i.e. taking into account the change in the location of R1 due to the scaling of the profile. Once all the galaxies are located exactly on top of the best fitting stellar mass–size relation (i.e. with zero scatter), we randomly scale the stellar mass density profiles up or down again, this time by a quantity compatible with a Gaussian distribution whose standard deviation is given by the above δmass values. We repeat this procedure 1000 times and on each occasion we measure the scatter of the stellar mass–size plane produced by the uncertainty in measuring the stellar mass. We show an illustration of the scatter of the stellar mass–size relation caused by the uncertainty in stellar mass in Fig. D2. The scatter in the stellar mass–size plane generated by the uncertainty in mass is shown in Table 3. Interestingly, for R1, RH, and R23.5, i, we find that the dwarfs are the most affected by the uncertainty due to our mass determination. This is once again expected as the star formation activity of dwarf galaxies is, on average, more stochastic (Kauffmann 2014) and complicated to model than that of massive spirals and ellipticals. Therefore, a single colour is not a good proxy for the M/L ratio of dwarfs as it is in the case for more gentle star formation histories.


In light of this, the allowed structure of gamma-ray burst (GRB) jets and the efficiency at which it produces gamma-rays at large angles remains a topic of major importance, and it is useful to consider what types of jet structures are consistent with GRB observations (see also Beniamini et al. 2018b). Previous studies have considered the implications of structure models on the true energetics and rates of GRBs (Frail et al. 2001; Lipunov, Postnov & Prokhorov 2001; Rossi, Lazzati & Rees 2002; Zhang & Mészáros 2002; Eichler & Levinson 2004; van Eerten & MacFadyen 2012; Pescalli et al. 2015), on the shape of the afterglow light curve (Granot & Kumar 2003; Kumar & Granot 2003; Salmonson 2003) or on detectability of orphan afterglows (Lamb & Kobayashi 2017). Here, we propose a novel way to test the allowed structure of GRBs (in terms of both the energy and Lorentz factor angular distributions), by applying three independent techniques. We focus on long GRBs for which more detailed observations are available. First, we compare the predictions of these models regarding the EX/Eγ distribution (i.e. the isotropic equivalent early X-ray afterglow to prompt gamma-ray energy ratio) to the observations. We show that a variety of structure models predict large variations in this quantity, in contrast with results from GRB observations. Secondly, we reconsider the effect of the structure on the observed luminosity function and show that a large family of models can be ruled out as they lead to an overproduction of bursts with gamma-ray luminosities below the peak of the observed luminosity function. Both these considerations imply that while the energy angular profile may be steep, the Lorentz factor of GRBs must remain large at any region that produces gamma-rays efficiently. However, even such models typically lead to very peculiar light curves that can be ruled out by observations. The most likely implication is that efficient gamma-ray emission must be confined to a narrow opening angle around the jet’s core, where the isotropic equivalent energy is not much lower than that of the core. This will naturally resolve all the problems mentioned above.


Besides the Patchy and the LN mocks, we also model the multipoles of the BOSS CMASS two-point correlation function using an analytic approach, which is required to run the Monte Carlo analysis (see Section 5). The 2PCF can be obtained from the Fourier transform of the matter power spectrum, P(k), for which we assume the template from Padmanabhan & White (2008):
(10)$$\begin{eqnarray*}
P(k)=\left[P_{\rm {lin}}(k)-P_{\rm {dw}}(k)\right]e^{-k^2\Sigma _{\rm {nl}}^2/2}+P_{\rm {dw}}(k) .
\end{eqnarray*}$$In the equation above, Plin(k) is the linear matter power spectrum computed using the Boltzmann code CLASS (Lesgourgues 2011), assuming the Planck 2015 (Ade et al. 2016) fiducial cosmology. The Pdw(k) term is the de-wiggled power spectrum (Eisenstein & Hu 1998), while the Σnl parameter encodes the smoothing of the BAO peak due to non-linear effects (Crocce & Scoccimarro 2006). The multipoles of the analytic 2PCF are defined as
(11)$$\begin{eqnarray*}
\xi _l(s) = \frac{i^l}{2\pi ^2}\int _0^{\infty } P_l(k)j_l(ks)k^2{\rm d}k ,
\end{eqnarray*}$$from which we recover the monopole (l = 0) and the quadrupole (l = 2). In equation (11), jl(x) represents the spherical Bessel function of first kind and order l, while Pl(k) are the multipoles of the power spectrum defined as
(12)$$\begin{eqnarray*}
P_l(k)=\frac{2l+1}{2}\int ^1_{-1}\left(1+f\mu ^2\right)^2P(k)L_l(\mu){\rm d}\mu ,
\end{eqnarray*}$$where Ll(x) is the Legendre polynomial of order l and P(k) is the template given in equation (10). By replacing equation (12) in equation (11), the analytic expressions for monopole (l = 0) and quadrupole (l = 2) are respectively (Xu et al. 2012):
(13)$$\begin{eqnarray*}
\xi _{\rm {model}}^{(0)}(s) = B_0\xi _0(\alpha s)+a_0^{(0)}+\frac{a_1^{(0)}}{s}+\frac{a_2^{(0)}}{s^2} ,
\end{eqnarray*}$$(14)$$\begin{eqnarray*}
\xi _{\rm {model}}^{(2)}(s) = B_2\xi _2(\alpha s)+a_0^{(2)}+\frac{a_1^{(2)}}{s}+\frac{a_2^{(2)}}{s^2} ,
\end{eqnarray*}$$where α is the shift parameter, while $(a_1^{(i)},a_2^{(i)},a_3^{(i)})$ are linear nuisance parameters.


When energy flows from the interior of the Sun outward into the solar atmosphere, why is the Sun’s outer atmosphere, the corona, much hotter than the inner atmosphere, the underlying chromosphere and photosphere? This is the long-standing problem of the coronal heating, which is one of the eight key mysteries in modern astronomy (Kerr 2012). For about 80 yr since the discovery of the extremely hot corona around the late 1930s (Grotian 1939; Edlen 1945), people have worked hard on addressing this issue, and great advances have been made in observation and theoretical studies (Parnell & De Moortel 2012; Amari et al. 2015; Arregui 2015; Cargill et al. 2015; De Moortel & Browning 2015; Jess et al. 2015; Klimchuk 2015; Longcope & Tarr 2015; Peter 2015; Schmelz & Winebarger 2015; Velli et al. 2015; Wilmot-Smith 2015). Especially during recent decades, high-resolution observations of solar super-fine structures indicate that small spicules, minor hot jets along small-scale magnetic channels from the low atmosphere upwards to the corona, petty tornados and cyclones, and small explosive phenomena such as mini-filament eruptions and micro- and nano-flares—all of these small-scale magnetic activities contribute greatly to coronal heating (De Pontieu et al. 2011; 2018; Zhang & Liu 2011; Parnell & De Moortel 2012; Klimchuk 2015; Peter 2015; Schmelz & Winebarger 2015; Henriques et al. 2016; Li et al. 2018a). Additionally, contributions of MHD waves to heating the corona have been observationally illustrated (van Ballegooijen et al. 2011; Jess et al. 2015; Kubo et al. 2016; Morton et al. 2016; Soler et al. 2017; Morgan & Hutton 2018). Meanwhile, with the progress of observational studies, two groups of theoretical models, magnetic reconnection models and magnetohydrodynamic wave models, have traditionally attempted to explain coronal heating, but so far no models can address the key mystery perfectly (van Ballegooijen et al. 2011; Arregui 2015; Cargill et al. 2015; Peter 2015; Velli et al. 2015; Wilmot-Smith 2015). Maybe we do not need to intentionally take to heart such the classical dichotomy, because waves and reconnections may interact with each other (De Moortel & Browning 2015; Velli et al. 2015). Additionally, statistical studies may look at coronal heating from a comprehensive perspective. Li et al. (2018b) found that the long-term variation of the heated corona, which is represented by coronal spectral irradiances, and that of small-scale magnetic activity are in lockstep, indicating that the corona should statistically be effectively heated by small-scale magnetic activity. Observational and theoretical model studies through heating channels and modes, and statistical studies by means of heating effect (performance of the heated corona), both suggest that coronal heating originates from small-scale magnetic activity.


From ∼17:07 UT onward, especially during 17:12–17:14 UT, we detected multiple blobs in the bright, inverted-V-shaped structure below the flux rope, along with the fast rise of the filament (Figure 3). In Figure 12(b), boxes U and D encompass the upward- and downward-moving blobs, whose projected speeds are ∼135 and 55 km s−1, respectively. Some blobs also appear to coalesce during their propagation. We attribute the growing linear features beneath the rising flux rope to plasma emission associated with a current sheet, analogous to the flare current sheet in CME/eruptive flare models (e.g., Karpen et al. 2012). In this case, the multiple bright blobs are plasmoids formed by bursty reconnection in this current sheet, another phenomenon commonly found in high-Lundquist-number reconnection simulations (e.g., Daughton et al. 2006, 2014; Drake et al. 2006; Fermo et al. 2010; Uzdensky et al. 2010; Huang & Bhattacharjee 2012; Karpen et al. 2012; Mei et al. 2012; Cassak & Drake 2013; Guo et al. 2013; Wyper & Pontin 2014a, 2014b; Guidoni et al. 2016; Lynch et al. 2016). Multiple plasmoids moving bidirectionally were previously detected below flux ropes in active-region eruptive flares (Takasao et al. 2012; Kumar & Cho 2013; Kumar et al. 2015). If we assume a minimum base field strength of 50 G and an Alfvén speed of ∼135 km s−1 for an upward-moving plasmoid, we obtain an estimated minimum density of 4.5 × 1010 cm−3 for the flare current sheet. The curious appearance of the bright inverted-V-shaped structure diverging beneath the flux rope (see Figure 3 red and white arrows, Column 3, and the accompanying movie) underscores the 3D geometry of the flare current sheet. Here the right-hand bright line (marked by white arrows) appeared first (∼17:05 UT), followed by the left one (marked by a green arrow) at ∼17:13 UT. The right-hand line disappeared by ∼17:15 UT, while the left faded gradually through the rest of the observing period. A large downward-moving blob is visible during ∼17:17–17:18 UT. Because current sheets are very thin, they become visible only if the line of sight passes through multiple folds or through regions of enhanced density. We speculate that the appearance of two plasmoid-generating regions could be a sign of patchy reconnection in a rippled current sheet, with reconnection sites appearing at different locations along the sheet.


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.


Investigations of the turbulent nature of solar wind fluctuations have been ongoing for more than half a century (see, e.g., Bruno & Carbone 2016). Advances have been made consistently thanks to the increasingly accurate measurements of several dedicated space mission as well as to the enormous improvement of numerical calculation, new detailed models and theoretical frameworks, and the development of specific data analysis techniques. Nevertheless, the extremely complex nature of the system and the coexistence of multiple actors, scales, and dynamical regimes have led to a number of questions that remain open (Viall & Borovsky 2020). Among these, the very nature of the turbulent cascade of the solar wind flow and its relationship with the small-scale processes still need to be described in full (Tu & Marsch 1995; Bruno & Carbone 2013; Matthaeus & Velli 2011; Chen 2016). Magnetic field fluctuations have been characterized with great detail at magnetohydrodynamic and kinetic scales, for example, through spectral and high-order moments analysis (Tu & Marsch 1995; Bruno & Carbone 2013). The anisotropic nature of magnetic turbulence has also been addressed, and is still being debated, due to the limited access to three-dimensional measurements in space (see, e.g., Horbury et al. 2008, 2012; Sorriso-Valvo et al. 2010; Yordanova et al. 2015; Verdini et al. 2018; Telloni et al. 2019a; Oughton & Matthaeus 2020). Velocity fluctuations have been studied thoroughly (see, e.g., Sorriso-Valvo et al. 1999; Bruno & Carbone 2013), although the kinetic scales still remain quite unexplored for instrumental limitations, most notably in the sampling time resolution. Both the velocity and magnetic field show highly variable turbulence properties, with well developed spectra, strong intermittency (Sorriso-Valvo et al. 1999), anisotropy, and linear third-order moments scaling (Sorriso-Valvo et al. 2007; Carbone et al. 2011). The level of Alfvénic fluctuations (mostly but not exclusively found in fast streams, see e.g., D’Amicis et al. 2011; Bruno et al. 2019) are believed to be associated with the state of the turbulence. In particular, solar wind samples containing more Alfvénic fluctuations are typically associated with less developed turbulence, as inferred from both shallower spectra and reduced intermittency (see Bruno & Carbone 2013, and references therein). This is consistent with the expectation that uncorrelated Alfvénic fluctuations contribute to reduce the nonlinear cascade by sweeping away the interacting structures (Dobrowolny et al. 1980), as also confirmed by the observed anticorrelation between the turbulent energy cascade rate and the cross-helicity (Smith et al. 2009; Marino et al. 2011a,b).


In the context of AGN models, for SAD-dominated sources the ratio Lradio/$L_{\rm X} \propto \eta _{\rm jet} \, \bar{a}^{2}$ (Yi & Boughn 1999) is expected to be constant and limited to a narrow range of values, as we find for our Seyferts, if the $\bar{a}$ range is finite. Conversely, for LINERs, that are powered by RIAF discs, the relation between bolometric AGN and jet power is difficult to model because jet emission can dominate their entire SED (Körding, Jester & Fender 2008) and [O iii]-line contamination from jet photoionizing shocks can overpredict the bolometric AGN power (Capetti, Verdoes Kleijn & Chiaberge 2005; Netzer 2009). However, in a simplistic scenario of a disc origin of the radio emission, ADAF discs would predict much shallower relations ($L_{\rm core} \propto L_{\rm X}^{\alpha }$ with α 0.6 depending on bremsstrahlung-dominated and multiple Compton scattering regimes, Yi & Boughn 1998) than the observed slopes for LINERs (1.2–1.3). Furthermore, the observed radio-[O iii] relation found for LINERs is even steeper (despite the large scatter) than any previous relations between the kinetic jet power and the bolometric AGN luminosities found for LINER-like RL AGN (slopes 1, e.g. Capetti & Balmaverde 2006; Merloni & Heinz 2007; Baldi et al. 2019b). Therefore, assuming that RL LINERs are the scaled-down version of RGs and normalizing the Lradio/LX comparison with previous studies based on this assumption, the steeper slopes might be the consequence of a closer view of jet-launching mechanism even in RQ LINERs. The high sensitivity and sub-arcsec resolution (crucially intermediate between VLA and VLBI) provided by our survey allowed us to probe the parsec-scale region near the core where the jet is launched and reveal the relevant role of Γjet and BH spin/mass in the jet production. These parameters could eventually induce much steeper relations than those established with shallower radio observations.


After the recombination epoch, the CMB hardly interacts with the neutral intervening medium. This restricts the CMB from probing the evolution of the structures till the end of EoR. The 21-cm radiation, which is involved in the hyperfine transition of H i, is a promising probe to study the high-redshift universe including EoR (e.g. Sunyaev & Zeldovich 1972; Hogan & Rees 1979). There are existing and the upcoming radio interferometers aiming to observe the brightness temperature fluctuations of the redshifted 21-cm signal from EoR that we coin as the ‘EoR 21-cm signal’. However, the detection of the signal is not yet possible due to the foreground contamination from galactic and extra-galactic source. The foregrounds are ∼104−105 times stronger (e.g. Ali, Bharadwaj & Chengalur 2008; Bernardi et al. 2009, 2010; Ghosh et al. 2012; Paciga et al. 2013; Beardsley et al. 2016) compared to the signal. The foregrounds, system noise, and calibration errors together keep the current observations at bay from directly detecting the EoR 21-cm signal. As a consequence, the first detection is likely to be statistical in nature. These observations plan to measure the power spectrum (PS) of the EoR 21-cm signal (e.g. Bharadwaj & Sethi 2001; Bharadwaj & Ali 2004, 2005). Several radio interferometers such as the GMRT1 (Swarup et al. 1991), LOFAR2 (van Haarlem et al. 2013), MWA3 (Tingay et al. 2013), and PAPER4 (Parsons et al. 2010) have carried out observations to measure the EoR 21-cm PS. However, only few weak upper limits on the PS amplitudes have been reported in the literature to date (e.g. GMRT: Paciga et al. 2011, Paciga et al. 2013; LOFAR: Yatawatta et al. 2013; Patil et al. 2017; Gehlot et al. 2019; Mertens et al. 2020; MWA: Dillon et al. 2014; Jacobs et al. 2016; Barry et al. 2019; Li et al. 2019; Trott et al. 2020; PAPER: Cheng et al. 2018; Kolopanis et al. 2019). A few more upcoming telescopes with improved sensitivity such as HERA5 (DeBoer et al. 2017) and SKA6 (Koopmans et al. 2014) also aim to measure the EoR 21-cm PS. Apart from PS, several other estimators such as the variance (Patil et al. 2014), bispectrum (Bharadwaj & Pandey 2005; Yoshiura et al. 2015; Shimabukuro et al. 2017; Majumdar et al. 2018), and Minkowski functional (Bag et al. 2018, 2019; Kapahtia et al. 2018; Kapahtia, Chingangbam & Appleby 2019) are being used to quantify the EoR 21-cm signal. These estimators are supposed to be rich in information about the underlying physical processes during EoR.


The data presented here comprise quasi-simultaneous observations during secondary eclipse of WASP-33 b around the V and Y bands. The predicted planet-star flux ratio in the V-band is 0.2 ppt, four times lower than the accuracy of our measurements. Therefore, we can neglect the planet imprint and use this band to measure the stellar pulsations, and most specifically to tune their current phases (see phase shifts in von Essen et al. 2014). Particularly, our model for the light contribution of the stellar pulsations consists of eight sinusoidal pulsation frequencies with corresponding amplitudes and phases. Hence, to reduce the number of 24 free parameters and the values they can take, we use prior knowledge about the pulsation spectrum of the star that was acquired during von Essen et al. (2014). As the frequency resolution is 1/ΔT (Kurtz 1983), 3.5 h of data are not sufficient to determine the pulsations frequencies. Therefore, during our fitting procedure we use the frequencies determined in von Essen et al. (2014) as starting values plus their derived errors as Gaussian priors. As pointed out in von Essen et al. (2014), we found clear evidences of pulsation phase variability with a maximum change of 2 × 10-3 c/d. In other words, as an example after one year time a phase-constant model would appear to have the correct shape with respect to the pulsation pattern of the star, but shifted several minutes in time. To account for this, the eight phases were considered as fitting parameters. The von Essen et al. (2014) photometric follow-up started in August, 2010, and ended in October, 2012, coinciding with these LBT data. We then used the phases determined in von Essen et al. (2014) during our last observing season as starting values, and we restricted them to the limiting cases derived in Sect. 3.5 of von Essen et al. (2014), rather than allowing them to take arbitrary values. The pulsation amplitudes in δ Scuti stars are expected to be wavelength-dependent (see e.g. Daszyńska-Daszkiewicz 2008). Our follow-up campaign and these data were acquired in the blue wavelength range. Therefore the amplitudes estimated in von Essen et al. (2014), listed in Table 1, are used in this work as fixed values. This approach would be incorrect if the pulsation amplitudes would be significantly variable (see e.g., Breger et al. 2005). Nonetheless, the short time span of LBT data, and the achieved photometric precision compared to the intrinsically low values of WASP-33’s amplitudes, make the detection of any amplitude variability impossible.


An independent approach to constrain the strength of magnetic fields in accretion flow models in binary systems is by measuring how much angular momentum is lost from the system via magnetized outflows and estimating the corresponding orbital decay in the system due to magnetic braking. The orbital decay in A0620-00 is rapid, with orbital-period derivative $\dot{P} =-0.6 \, {\rm [ms \, yr^{-1}]}$ (González Hernández, Rebolo & Casares 2014), and it cannot be explained by the emission of gravitational waves alone. Magnetic braking of the system is a possible explanation for the measured $\dot{P}$, but other explanations, such as resonant interactions between the binary and the possible circumbinary disc, have been proposed (Chen & Podsiadlowski 2017). Here we can estimate the magnitude of the magnetic braking of the system using a first-principles approach. The orbital angular momentum of a binary system is $J_{\rm orb}= M_{\rm BH}M_*/(M_{\rm BH}+M_*) \sqrt{G(M_{\rm BH}+M_*) d}$, where d is the separation between the star and the black hole. In GRMHD simulations, the loss of total angular momentum through the outer boundary is defined as $\dot{J}(r_{\rm out},t)=\int _\theta \int _\phi T^r_\phi \,\mathrm{ d}A_{\theta \phi }$, where $T^r_\phi \equiv (\rho + \gamma u + b^2) u^r u_\phi -b^r b_\phi$ is the stress–energy tensor describing the radial flux of angular momentum. The quantity u is the internal energy of the gas, γ = 4/3 is the adiabatic index, uμ is the four-velocity of the gas and bμ is a four-vector that describes the magnetic field in a frame comoving with the gas. We integrate the above formula at rout = 50GM/c2 over θ ∈ (0, π) and ϕ ∈ (0, 2π). In our best-fitting model, the ratio of angular momentum flux through the outer boundary to the orbital angular momentum is extremely low: $\dot{J}/J_{\rm orb} \approx 10^{-22}$ [s−1], which could account for an orbital period derivative of $\dot{P} = 2 \times 10^{-8} {\rm [ms \, yr^{-1}]}$ only. Our calculations confirm that the inner highly magnetized, rotating accretion flow (with current $\dot{M}$) alone cannot be responsible for the rapid orbital decay observed in the system and this favours the idea of a circumbinary disc.


The evolution of colour or the spectral index, α, (F(ν) ∝ ν−α where ν is the radiation frequency and F(ν) is the flux density provides an insight into the particle distribution giving rise to the observed flux density and its variability. In particular, at the synchrotron frequencies, within the simplest scenario of single-zone emission models with homogeneous magnetic field distributions, clear patterns between the spectral index and the total intensity are predicted, i.e. a ‘spectral hysteresis’, depending on the relative lengths of the radiative cooling time-scale and the escape time-scale of the accelerated particles from the emission zone (e.g. Kirk, Rieger & Mastichiadis 1998). A significant fraction of long-term multiband flux monitoring studies have revealed bluer-when-brighter trends for BL Lac objects but frequently redder-when-brighter trends for FSRQs (Gu et al. 2006; Osterman Meyer et al. 2009; Hao et al. 2010; Rani et al. 2010; Ikejiri et al. 2011; Bonning et al. 2012; Sandrinelli, Covino & Treves 2014; Li et al. 2018; Meng et al. 2018; Gupta et al. 2019) while ‘achromatic’ flux variability (no colour evolution, Stalin et al. 2006; Bonning et al. 2012; Gaur et al. 2019), and erratic patterns (Wierzcholska et al. 2015) have also been reported. It has been argued that particles accelerated to higher energies are injected at the emission zone before being cooled radiatively in BL Lac sources leading to their overall SEDs being bluer-when-brighter; however, the ‘redder’ and more variable jet-component can overwhelm the ‘bluer’ contribution from the accretion disc, leading to redder-when-brighter trends for FSRQ type sources (Gu et al. 2006). Achromatic variability is often ascribed to changes in the Doppler boosting factor (δ) as each frequency notes the same special relativistic multiplication of flux (Gaur et al. 2012). However, erratic colour trends together with the opposite behaviours, i.e. redder-when-brighter changes for BL Lacs (Gu & Ai 2011) and bluer-when-brighter trends for FSRQs (Wu et al. 2011), indicate that more complex scenarios, presumably involving the dominance of the relative contributions of the Doppler boosted jet emission component and the accretion disc component, respectively, are particularly relevant for blazars with peak synchrotron frequencies in the range of 1013–15 Hz (low-frequency peaked blazars; Isler et al. 2017; Gopal-Krishna, Britzen & Wiita 2019).


Comptonisation Monte Carlo code (MoCA; see Tamborra et al. 2018 for a detailed description of the code) is based on a single photon approach, working in a fully special relativistic scenario. MoCA allows for various and different physical and geometrical conditions of the accretion disc and of the Comptonising corona. In this paper, the corona is assumed to have either a spherical or a slab-like geometry, and to be as extended as the disc, whose radii have been set to be Rout = 500 rg and Rin = 6 rg, respectively. Even though arguments (e.g. variability, Uttley et al. 2014, and references therein, microlensing Chartas et al. 2009; Morgan et al. 2012 and timing Kara et al. 2016; De Marco et al. 2013) exist that favour a compact corona, we used extended coronae. In fact, as discussed by Marinucci et al. (2019), Comptonised spectra emerging from compact corona (Rout = 100 rg–Rin = 6) do not deviate significantly from those produced in more extended corona; see their Fig. 3. The adoption of even more compact coronae (Rout = 20 rg, Rin = 6) results only in the need for higher optical depths to recover the same spectral shape for a given temperature. However, in such cases, general relativity (GR) effects are not negligible (see Tamborra et al. 2018, for a detailed discussion on this topic), and the present version of MoCA does not include GR. For the slab-like geometry case, MoCA allows the user to set up the corona height above the accretion disc (set to 10 rg in our simulations). We use synthetic spectra computed assuming the source BH mass and accretion rate to be the same as those of Ark 120 (e.g. Marinucci et al. 2019, and references therein), namely MBH = 1.5 × 108 M⊙ and ṁ = Lbol/LEdd = 0.1. For both the slab and spherical hot electron configurations, we simulated the Comptonised spectra using a wide range of values for electron temperature and optical depth: 0.1   τ   7 and 20  kT  200 keV, and in Fig. 1 we show a sample of spectra obtained by MoCA. Moreover, spectra are computed from 0.01 keV up to 700 keV using 1000 logarithmic energy bins, and a Poissonian error accompanies each spectral point. The obtained spectra are averaged over the inclination angle and in Fig. 1 we show some exemplificative spectra normalised at 1 keV accounting for the two geometries considered in this work.


The detection of LSBGs is usually carried out by a sequence of tasks. The first step is a broad detection of LSBG candidates. Both the depth of the data and the efficiency of this detection in the low-surface-brightness regime will define the completeness of the sample, and so a high efficiency in the detection of diffuse sources in this first step is a key point in the process. Given the importance of this primary detection, it is common to use specialized software or procedures (e.g., Akhlaghi & Ichikawa 2015; Prole et al. 2018; Haigh et al. 2021). After a first detection of potential objects, a characterization of their structural and morphological properties is necessary in order to accurately define the sample, typically with certain criteria in surface brightness and radius. To obtain the structural parameters of the LSBG candidates, the detected sources are usually fitted with a Sérsic model (Sérsic 1968). Specific procedures such as GALFIT (Peng et al. 2010) or IMFIT (Erwin 2015) are used to obtain accurate morphological and structural parameters. However, the computational cost of these is very high, becoming a bottleneck in LSBG analysis pipelines. For this reason, it is advisable to minimize the number of LSBG candidates prior to their Sérsic fitting to save computational time. This is not trivial because structural parameters from automated segmentation catalogs are much less accurate than Sérsic fit modeling, making correct screening of the sample challenging. As a last step, a “supervision” of all the objects matching the criteria of the sample is necessary in order to discard the frequent presence of false positives. These are sources that, although meeting the imposed criteria, are clearly not LSBGs. Examples of false positives are clumped sources that have been considered as a single source, faint reflections due to the optics of the instrumentation, or artifacts present in the images. Depending on the data volume analyzed, the number of objects to be supervised can become very high. For this reason, it is increasingly common to use deep learning techniques to screen objects in order to eliminate these false-positive detections (e.g., Tuccillo et al. 2018; Burke et al. 2019; Tanoglidis et al. 2021a). However, unsupervised or automated detections can not yet reach the accuracy that human visual inspection is capable of obtaining, reaching almost 100%. Therefore, human supervision is desirable, when possible, in order to minimize the presence of false positives in samples of reasonably limited volume, such as that used here.

Compare/Contrast Compare/Contrast Compare/Contrast Compare/Contrast


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


The PN IC 5148 (PN G002.7-52.4) is a nebula which is to date not well investigated in detail. First listed in the Second Index Catalogue of Nebulae and Clusters of Stars (Dreyer 1910) with two independent entries as numbers IC 5148 and IC 5150 discovered by Swift (1899) and Gale (1897) independently, it was finally discovered to be the same object by Hoffmeister (1961). Morphologically it is declared as a round nebula in all catalogs and Chu et al. (1987) classified it as a multiple shell planetary nebula (MSPN) due to a small step in the H α image with a radius ratio of only 1:1.2 between the two structures. In addition, the intensity decrease was found smaller than that for typical MSPNe. A few years later the authors searched with a larger field systematically around many nebulae for extended emission features without detecting the very low surface brightness halo we investigate here (Hua et al. 1998). While earlier spectroscopic studies took only a small fraction of one or two spectral lines to obtain radial velocity and expansion of the nebula (e.g. Meatheringham et al. 1988), to our knowledge up to now the only, more extended spectroscopic analysis were performed by Kaler et al. (1990) and by Kingsburgh & Barlow (1994) within two surveys of 75 and 80 southern PNe, respectively. Both studies used pre-CCD electronic spectral scanning devices, taking a very small aperture region of the nebula and detected only a hand full of lines. They end up coinciding in the result that the nebula has about galactic disk abundance or only slight underabundance despite its large galactic latitude (b approximately −52°). Further, thesurvey spectra used in the PN catalog of Acker et al. (1992) gives intensities of only four lines. The inspection of the original data file of this survey, provided now at the Hong Kong/AAO/Strasbourg PN data base (thereafter HASH2; Parker et al. 2016; Bojičić et al. 2017), does not recover more usable lines above the noise level.


In this Letter, we directly test the relationship between proton kinetic instabilities and plasma turbulence in the solar wind using a hybrid expanding box model that allows us to study self-consistently physical processes at ion scales. In the hybrid expanding box model, a constant solar wind radial velocity vsw is assumed. The radial distance R is then

, where R0 is the initial position and

 is the initial value of the characteristic expansion time

 Transverse scales (with respect to the radial direction) of a small portion of plasma, comoving with the solar wind velocity, increase ∝ R. The expanding box uses these comoving coordinates, approximating the spherical coordinates by the Cartesian ones (Liewer et al. 2001; Hellinger & Trávníček 2005). The model uses the hybrid approximation where electrons are considered as a massless, charge-neutralizing fluid and ions are described by a particle-in-cell model (Matthews 1994). Here, we use the two-dimensional (2D) version of the code, fields and moments are defined on a 2D x–y grid 2048 × 2048, and periodic boundary conditions are assumed. The spatial resolution is Δx = Δy = 0.25dp0, where

 is the initial proton inertial length (vA0: the initial Alfvén velocity, Ωp0: the initial proton gyrofrequency). There are 1024 macroparticles per cell for protons that are advanced with a time step

, while the magnetic field is advanced with a smaller time step

 The initial ambient magnetic field is directed along the radial z-direction, perpendicular to the simulation plane

, and we impose a continuous expansion in the x- and y-directions. Due to the expansion, the ambient density and the magnitude of the ambient magnetic field decrease as

 (the proton inertial length dp increases ∝ R; the ratio between the transverse sizes and dp remains constant; the proton gyrofrequency Ωp decreases as ∝R−2). A small resistivity η is used to avoid accumulation of cascading energy at grid scales; initially, we set

 (μ0 being the magnetic permittivity of vacuum) and η is assumed to be

 The simulation is initialized with an isotropic 2D spectrum of modes with random phases, linear Alfvén polarization (

), and vanishing correlation between magnetic and velocity fluctuation. These modes are in the range 0.02 ≤ kdp ≤ 0.2 and have a flat one-dimensional (1D) power spectrum with rms fluctuations = 0.24 B0. For noninteracting zero-frequency Alfvén waves, the linear approximation predicts

 (Dong et al. 2014). Protons initially have the parallel proton beta

 and the parallel temperature anisotropy

 as typical proton parameters in the solar wind in the vicinity of 1 AU (Hellinger et al. 2006; Marsch et al. 2006). Electrons are assumed to be isotropic and isothermal with βe = 0.5 at t = 0.


One of our main long-term goals is to work towards a full forward modelling pipeline for multiwavelength galaxy surveys. Over the next decade, wide area surveys from DESI, VRO, Euclid, the Nancy Grace Roman Space Telescope, 4MOST, and other facilities will be carried out. We can use the legacy observations from surveys such as CANDELS, to build a foundation for interpreting these new surveys. What we have shown here is that the current generation of SAMs produce decent broad agreement with key properties of galaxy evolution as represented by CANDELS over the redshift range 0.5 ≲ z ≲ 3. It has been shown elsewhere that these models produce similar results to those of numerical cosmological simulations and other SAMs (Somerville & Davé 2015), and that they are also in agreement with higher redshift observations of galaxy populations (Yung et al. 2019a, b), the reionization history (Yung et al. 2020), and observational probes of the cold gas phase in galaxies (Popping, Somerville & Trager 2014; Popping et al. 2019). While there are certainly remaining tensions with observations, as seen here and also in, e.g. Popping et al. (2019), there is promising ongoing work to continue to improve the realism of the treatment of physical processes in SAMs (e.g. Pandya et al. 2020). In work in progress, we are using this framework to create similar mock observations for future planned surveys with the James Webb Space Telescope and the Nancy Grace Roman Space Telescope (L.Y.A., Yung et al., in preparation). SAMs coupled with light-cones extracted from large volume N-body simulations have recently been used to create a 2 deg2 light-cone from 0  z  10 (Yang et al. 2020; Yung et al., in preparation). In order to create mock surveys for even larger areas – tens to hundreds of square degrees – that will be probed by the projects mentioned above, it is likely that new, even more computationally efficient techniques will need to be developed, perhaps enabled by machine-learning-based tools.


Given this correlation between dust luminosity and SFR, it is reasonable to expect the dust mass to scale with SFR as well. In the top panel of Figure 10 we show this relation for our data with the additional parameter of the dust temperature indicated by color. This dust temperature is a weighted average of the temperatures of the two components of the dust model, namely the ISM and birth clouds. Using MAGPHYS, da Cunha et al. (2010) found a tight correlation between dust mass and SFR in a local sample derived from the Sloan Digital Sky Survey, which we show as a black line. The da Cunha et al. (2010) sample is selected to be star-forming by emission line diagnostics and lies at z ≤ 0.2. It is also important to note that the SFRs for their sample lie mostly below ∼20 M⊙ yr−1. The solid portion of the line represents the extent of their data. We also show the Spitzer Infrared Nearby Galaxy Sample (Kennicutt et al. 2003) analyzed in da Cunha et al. (2008) as purple stars for comparison. At first, our data do not appear to follow any trend, with only our highest measured dust masses falling near the da Cunha et al. (2010) relation. Given that MAGPHYS allows a range of dust temperatures when fitting for the dust mass, we investigate the effects of dust temperature in this diagram. When we examine the temperature of the dust (which MAGPHYS allows to vary from 20 to 80 K) as indicated by color in the figure, we see that sources with lower dust temperature actually lie on the published relation. If we consider bands of constant dust temperature in the diagram we see that the slope of the Mdust–SFR relation for our sources actually closely matches the slope of the da Cunha et al. (2010) relation. As shown in Figures 6 and 7, we observe a slight increase in average dust temperature with redshift for our sample, so it may be tempting to interpret the variation in this diagram as a redshift dependence. We checked the relation between dust temperature and redshift for our sample and found the scatter in temperature at a given redshift to be much larger than the evolution between redshift bins. This suggests that the local calibration between dust mass and SFR can be extended to higher redshift samples through the incorporation of the additional parameter of dust temperature. Given our particular sample selection, the application of these results to a more general star-forming population would have to be done with caution.


The most prominent metallicity structure in the Milky Way disk is the decrease of metallicity with increasing Galactic radius—the radial metallicity gradient. All of the major tracers reveal radial gradients, typically with slopes between −0.03 and −0.09

. The radial metallicity gradient can be explained by an inside-out galaxy formation where the disk grows via a radially dependent gas infall rate and star formation rate (e.g., Matteucci & Françoi 1989). But why is there such a wide range of radial gradient slopes measured? There are several possibilities. (1) Measurement uncertainty. Measurement errors will cause some variations, but it is unlikely to produce a factor of 3 difference in slope. Homogeneity in observing procedures and data analysis may be more important given the variations in abundance that can be derived for the same source (for further discussion see Rudolph et al. 2006; Henry et al. 2010; Balser et al. 2011). (2) Dynamical evolution. Radial gradients calculated with stellar tracers may be affected by radial migration, where stars are scattered into different orbits (Sellwood & Binney 2002). Radial migration should flatten the radial metallicity gradient, but there is some evidence that this may not be a large factor for stars in the Milky Way (Di Matteo et al. 2013; Kubryk et al. 2013; Bovy et al. 2014). (3) Temporal evolution. Many tracers have a wide range of age and therefore are probing the Milky Way disk at different times. For example, the radial gradient has been observed to flatten with time when using Open clusters (e.g., Friel et al. 2002). But accurate ages are crucial to separate out these temporal effects. PN studies indicate a flattening of the radial gradient with time (Maciel et al. 2003), a steepening with time (Stanghellini & Haywood 2010), or no temporal variation (Henry et al. 2010). These vastly different conclusions reveal the difficulty in deriving accurate PN ages and distances. (4) Sample Evolution. Hayden et al. (2013) measure a flattening of the radial gradient away from the Galactic mid-plane. Therefore, including sources out of the Galactic plane, which may be from an older population, may alter the derived radial gradient slope (see Minchev et al. 2014). Azimuthal abundance variations have been reported (e.g., Pedicelli et al. 2009; Balser et al. 2011, Section 3.3). If real, these will complicate any analysis of radial gradients. Here we detect metallicity gradient slopes over different azimuth ranges that span the values observed in the literature. The usual assumption is that the disk is well mixed at a given radius but this may not be true.


There are two possibilities resulting in the different magnetic field strengths inferred from the polarimetric and molecular-line observations: (1) the rotational-to-gravitational energy βrot is overestimated, and (2) there are additional contributions in the polarized intensity from other mechanisms, such as dust scattering. In our MHD simulations, βrot is adopted to be 0.4% based on the observational estimates of the core mass of ∼1 M and the angular speed of the core rotation of 4 × 10−14 s−1. The angular speed was estimated based on the global velocity gradient along the major axis of the dense core observed with single-dish telescopes (Saito et al. 1999; Yen et al. 2011; Kurono et al. 2013). Numerical simulations of dense cores including synthetic observations show that the specific angular momentum derived from the synthetic images of the dense cores can be a factor of 8–10 higher than their actual specific angular momentum computed by the sum of the angular momenta contributed by the individual gas parcels in the dense cores (Dib et al. 2010). In addition, if there are filamentary structures in the dense core in B335, which could not be resolved with the single-dish observations, infalling motions along the filamentary structures could also contribute to the observed velocity gradient, leading to an overestimated angular speed of the core rotation (Tobin et al. 2012). We have also performed our simulations with a lower βrot, and we find that the rotational velocity on a 100 au scale in the simulations decreases with decreasing βrot. Thus, the discrepancy in the magnetic field strengths inferred from the field structures and the gas kinematics can be reconciled, if the core rotation in B335 is overestimated by a factor of a few in the observations, and these results would suggest a weak magnetic field of initial λ of 9.6 in B335. Further observations combining single dishes and interferometers to have a high spatial dynamical range and to map the velocity structures of the entire dense core in B335 at a high angular resolution are needed to study coherent velocity features and provide a better estimate of the core rotation.


The difference in iron abundance between the two XO-2 stellar components poses an interesting question. They belong to a visual binary and, as normally assumed for such systems, they should share the same origin and initial bulk metallicity. A relevant characteristic of this system is that both of the stars host planets. Thus, for components of wide binaries where at least one star has a planet, a reasonable hypothesis to explain any measured and significant difference in their present-day elemental abundances is that the planet formation process had played a relevant role. The higher iron abundance of XO-2N when compared to XO-2S might be due to past ingestion of dust-rich or rocky material that came from the inner part of the proto-planetary disk and that was pushed into the host star by the hot Jupiter XO-2N as it migrated inward to its current orbit. A second mechanism, which acts on a different time scale and after the pre-main-sequence stage, is presented by Fabrycky & Tremaine (2007), who discuss the pollution of the stellar photosphere with metals produced by mass loss of inward migrating hot Jupiters. In addition, Kaib et al. (2013) showed with their simulations that very distant binary companions may severely affect planetary evolution and influence the orbits of any planet around the other component of the system, perhaps favouring the ingestion of material by the host star. Following the results shown in Fig. 2 of Pinsonneault et al. (2001), we roughly estimated that XO-2N could have ingested an amount of iron slightly higher than 5 M⊕ to increase its photospheric iron content by ~0.05 dex, given its Teff ~ 5300 K. The difference in the iron abundance of the two XO-2 stellar components is similar to that found by Ramírez et al. (2011) for the solar twins 16 Cyg A and 16 Cyg B (Δ [Fe/H] = 0.042  ±  0.016 dex). These stars have masses close to those of the XO-2 companions and, together with a third companion 16 Cyg C, are members of a hierarchical triple system, where the A and C components form a close binary with a projected separation ~70 AU. The component B is known to host a giant planet in a long-period and highly eccentric orbit (P ~ 800 days and e ~ 0.69)5, but unlike the case of XO-2 it is the star with a lower iron content. To explain this deficiency, Ramírez et al. (2011) suggest that an early depletion of metals happened during the formation phase of the 16 Cyg Bb planet. An alternative and suggestive possibility is that 16 Cyg A may have ingested a massive planet that enriched the star with iron, while the large orbit of 16 Cyg Bb (with semi-major axis of 1.68 AU) very likely prevented any mass loss from the planet. We note that, although Δ[Fe/H] is similar to that found for XO-2, the amount of iron involved should be different. The XO-2 stars are cooler than 16 Cygni A and B and therefore have more massive convective envelopes, implying that more iron should be [is?] necessary to pollute the XO-2N photosphere and produce almost the same Δ[Fe/H]. Laws & Gonzalez (2001) also found the primary of the 16-Cyg system enhanced in Fe relative to the secondary. Similar studies conducted in binary stars hosting planets (see e.g. Gratton et al. 2001; Desidera et al. 2004, 2006; Schuler et al. 2011a; Teske et al. 2013; Liu et al. 2014; Mack et al. 2014) did not find relevant differences in elemental abundance among the components. All these results imply that the presence of giant planets does not necessarily imply differences in the chemical composition of the host star.


The LCs analyses were made using the phoebe v.0.29d software (Prša & Zwitter 2005) that is based on the 2003 version of the Wilson-Devinney (W-D) code (Wilson & Devinney 1971; Wilson 1979, 1990). In the absence of spectroscopic mass ratios, the “q-search” method (for details see Liakos & Niarchos 2012) was applied in modes 2 (detached system), 4 (semi-detached system with the primary component filling its Roche lobe) and 5 (conventional semi-detached binary) to find feasible (“photometric”) estimates of the mass ratio. The step of q change during the search was 0.05–0.1 starting from q = 0.05−0.1. The effective temperatures of the primaries (T1) were given the values derived from the spectral classification (see Sect. 2) and were kept fixed during the analysis, while the temperatures of the secondaries T2 were adjusted. The Albedos, A1 and A2, and gravity darkening coefficients, g1 and g2, were set to generally adopted values for the given spectral types of the components (Rucinski 1969; von Zeipel 1924; Lucy 1967). The (linear) limb darkening coefficients, x1 and x2, were taken from the tables of van Hamme (1993). The dimensionless potentials Ω1 and Ω2, the fractional luminosity of the primary component L1, and the orbital inclination of the system i were set as adjustable parameters. At this point it should to be noted that since the Kepler’s photometer has a spectral response range between approximately 410–910 nm with a peak at ~ 588 nm, the R filter (Bessell photometric system-range between 550–870 nm and with a transmittance peak at 597 nm) was selected as the best representative for the filter depended parameters (i.e. x and L). Moreover, there is evidence of maxima brightness changes in all of the systems, therefore parameters of photospheric spots on the surface of the secondary were also adjusted. The selection of the magnetically active component was based on the effective temperatures of the members of the systems. In all cases the secondaries are clearly cooler than the primaries (i.e. large minima difference), therefore, they host a convective envelope that better suits a magnetically active star. In addition, the hotter stars are candidates for δ Sct type pulsations and it is rather rare to present magnetic activity also. For all EBs, except for KIC 111, the third light parameter (l3) was also adjusted because the systems are candidates for triplicity (see Sect. 1). However, during the iterations it resulted in unrealistic values, therefore, it was omitted in the final analysis. Finally, all systems were found to have the minimum ∑ res2 in mode 5. KIC 066 and KIC 111 have a minimum at q = 0.3, while KIC 105 and KIC 106 at q = 0.15. In Fig. 7 the respective q-search plots are shown.


The binarity or binary fraction, f, is defined as the ratio of the number of binary or higher-order systems, Nbin, to the total number of systems, Nsys. Here, the term system includes multiple systems and singles (their number being noted as Nsng) as well. Then
6For the star-like population, we apply the binary DPS method developed by Marks etÂ al. (2011) and Marks & Kroupa (2011), hereafter referred to as dynamical or DPS pairing. In DPS the binary stars are formed in a population of embedded clusters, within which they are dynamically processed to yield the Galactic disk stellar single-plus-binary population. An attractive feature of this theory is its underlying assumption of the universality of binary properties of late-type stars being consistent with observational data (Marks & Kroupa 2012; Leigh etÂ al. 2014). For initial binaries with intermediate to large separations, the DPS pairing method applies random pairing11M. Marks etÂ al. (2014, in preparation) show that random pairing with subsequent dynamical processing does indeed reproduce at least the observed low-mass stellar population (see also Kroupa 1995).
below a primary mass of 5âM and ordered pairing (such that q â©¾ 0.9) above. Here, q = mcomp/mprim â©½ 1, where mcomp is the companion mass and mprim is the mass of the primary star. This initial binary population is then altered by dynamical evolution. Close binaries with orbital periods below about 10Â days undergo eigenevolution (Kroupa 1995) and tend to equalize the companion masses. Note that this eigenevolution term alters the very-low-mass end of the star-like IMF. For the purpose of this work, however, these effects only play a negligible role. Here, the initial or primordial binary fraction is 100%; that is, it is assumed that all stars form in binaries. The final (after dynamical processing in the embedded cluster) overall binary fraction is about 40% (i.e., f = 0.4) but varies as a function of the primary-star mass. For M dwarfs, in particular, it is as low as 25%, whereas G dwarfs show about 56% binarity. The binary fraction approaches 90% for O stars. For the BD-like population, we chose an overall binary fraction of 20% (i.e., f = 0.20), in accordance with TK07 and TK08. About half of the members of observed average stellar populations are binaries, most of them remaining unresolved in typical star-cluster surveys. However, very young and likely dynamically unevolved populations like the TaurusâAuriga association exhibit almost 100% binarity (Kroupa etÂ al. 2013; DuchÃªne & Kraus 2013; Reipurth etÂ al. 2014). The number of systems must not be confused with the number of individual bodies: Nbod = Nsng + 2Nbin. Because higher-order multiples are relatively rare (Goodwin & Kroupa 2005), they are summarized within the binary population in this work, so the total number of bodies is
7The CMRD describes the relative number of binaries as a function of the companion-to-primary mass ratio. Observations reveal a continuous decline of f as a function of the primary-object mass, which has been interpreted as a continuous transition from the stellar to the substellar regime (Joergens 2008; Kraus & Hillenbrand 2012; but see Thies & Kroupa 2008). There is also a shift toward more equal-mass binaries (q = 1) for VLMSs and BDs (Dieterich etÂ al. 2012). These properties of the stellar population are well reproduced by DPS such that the origin and properties of binary populations are well understood.


Here, for the first time, we have identified highly dynamic non-potential activity on QS-like supergranular network scales. These events overlie mixed polarity network flux elements near the spatial resolution of HMI, and are the first non-potential structures to be unassociated with strong concentrations of bipolar magnetic flux. One event (2011b August 05) shows eruptive activity in the form of jets, which is similar to larger-scale micro-sigmoids (Raouafi et al. 2010) and even QS bright point sigmoids (Chesny et al. 2015). The existence of flaring non-potential fields in the QS-like mixed network immediately shows that supergranular-scale magnetic fields can support processes similar to sigmoid formation (Chesny et al. 2013). Strong non-potential field arcades have been observed in hot X-ray sigmoids on scales of hundreds of arseconds (Moore et al. 2001; Gibson et al. 2002; Liu et al. 2010), micro-sigmoids in soft X-ray imaging on scales of ∼50″ (Mandrini et al. 2005; Raouafi et al. 2010) and small-scale AR EUV (Zheng et al. 2012, 2013), and now at EUV temperatures in QS-like mixed network fields with lengths down to ∼10″. This range of lengths over a range of temperatures and magnetic field topologies points directly to self-similar mechanisms influencing plasma and magnetic field dynamics at a range of scales. Our findings suggest that the processes driving some large-scale eruptions (i.e., flux emergence, helicity build-up, and flux cancellation leading to non-potential field heating (Chen et al. 2014)), can also manifest in a range of configurations on sub-network size scales in QS-like magnetic field configurations. These QS flaring non-potential fields are similar to their large-scale counterparts, but not as strict in their evolution. The diversity in the observed topologies may scale with the diversity of magnetic configurations that exist in the supergranulation network. QS non-potential fields evolve in multi-polar environments, and are not restricted to strongly bipolar dominated regions as in larger-scale, higher temperature events. Despite this, one of the presented events (2011a August 05) results in a post-flare potential loop arcade, which is similar to some observed AR sigmoid fields (Moore et al. 2001).


Subpulse drifting has been a topic of intensive research with the phenomenon expected to be present in 40–50 per cent of the pulsar population. There are around 120 pulsars known at present to exhibit some form of periodic modulations in their single-pulse sequence (Weltevrede et al. 2006, 2007; Basu et al. 2016). The drifting effects are very diverse and associations are seen with other phenomena like mode changing and nulling in some cases (Wright & Fowler 1981; Deich et al. 1986; Hankins & Wolszczan 1987; Vivekanand & Joshi 1997; Redman et al. 2005; Basu & Mitra 2018b). However, to gain a deeper understanding of the phenomenon at large, more comprehensive studies involving classification of the drifting population and identification of underlying traits are essential. The first such attempt was undertaken by Rankin (1986) who estimated the drifting behaviour within the empirical core–cone model of the emission beam. The pulsar profile, which is formed after averaging several thousand single pulses, has a highly stable structure and is made up of one or more (typically 5) components. The components can be classified into two distinct categories: the central core component and the adjacent conal components. A number of detailed studies suggest that the radio emission beam consists of a central core emission surrounded by conal emission arranged in nested rings (Rankin 1990, 1993; Mitra & Deshpande 1999). The differences in the observed profiles are a result of the different line of sight (LOS) traverses across the emission beam. Rankin (1986) suggested subpulse drifting to be primarily a conal phenomenon, and the drifting to arise due to the circulation of the conal emission around the magnetic axis. This would result in an association between the drifting properties (particularly the phase variation of the drifting feature across the pulse) and the profile classification. The most prominent drifting with clear drift bands and large phase variations was associated with the conal single (Sd) and barely resolved conal double (D) profile classes. This corresponded to the LOS traversing the emission beam towards the outer edge. Progressively more interior LOS traverses of the emission beam result in well-resolved conal double (D), conal Triple (cT), and conal Quadruple (cQ) profile shapes. In the above classification scheme, such profile classes were expected to show primarily longitude stationary drift with very little phase variations. The core-dominated profiles were associated with central LOS traverses of the emission beam. The principal profile classes were categorized as core single (St), Triple (T) with a central core component and pair of conal outriders, and Multiple (M) with central core and two pairs of conal components. Subpulse drifting was expected to be phase stationary and only seen in the conal components of the T and M class profiles. However, the core components sometimes show longer periodic structures that were not classified as subpulse drifting.


Surveys of radio bursts in decimetric wavelengths is presented in papers by Isliker & Benz (1994) and Jirička et al. (2001), within 1–3 GHz and 0.8–2.0 GHz frequency ranges, respectively. Some of these bursts are still not well understood. This is a case of the slowly positively drifting bursts (SPDBs). They appear in groups or as single bursts, with a duration of an individual burst from 1 to several seconds and their frequency drift is lower than about 100 MHz s−1 (Jirička et al. 2001). The SPDBs seem to be similar to the reverse type III bursts (Aschwanden 2002) but their frequency drift is much smaller. The majority of observed SPDBs are connected to solar flares (Jirička et al. 2001), and they appear many times at the very beginning of the flares (Benz & Simnett 1986; Kotrč et al. 1999; Kaltman et al. 2000; Karlický et al. 2018). Kaltman et al. (2000) reported on several SPDBs observed during three solar flares in the 0.8–2 GHz frequency range. They found frequency drifts of the observed SPDBs to be within the 20–180 MHz s−1 range. Kotrč et al. (1999) studied one of those flares. By combining the radio and spectral plus imaging Hα observations, they explained the observed SPDBs as radio emission generated by downwards propagating shock waves. Based on numerical simulations of the formation of thermal fronts in solar flares, Karlický (2015) proposed that SPDBs observed in the 1–2 GHz range could be a signature of a thermal front. Furthermore, Karlický et al. (2018) reported the observation of an SPDB (1.3–2.0 GHz) observed during the impulsive phase of an eruptive flare. They found time coincidence between the SPDB occurrence, an appearance of an ultraviolet (UV)/EUV multithermal plasma blob moving down along the dark Hα loop at approximately 280 km s−1, and the observed change of Hα profile at the footpoint of that dark loop. Combining these observations they concluded that observed SPDB was likely generated by the thermal front formed in front of the falling EUV blob.


Forbush decreases (FD) are the results of influence of solar wind (SW) large-scale disturbances on the background cosmic ray (CR) flux. They often demonstrate relatively fast CR intensity decrease, accompanied by large and extremely variable CR anisotropy, which is followed by a slower recovery (Forbush 1937; Lockwood 1971; Iucci et al. 1979a; Belov 2009). Most FDs have a sporadic character and are induced by interplanetary disturbances such as Interplanetary Coronal Mass Ejections (ICMEs) caused by coronal mass ejections (CMEs) (Cane 2000; Gopalswamy 2010a; Richardson & Cane 2011a). FDs caused by high-speed streams (HSS) from coronal holes (CHs) have a recurrent character (Iucci et al. 1979b; Richardson 2004; Singh & Badruddin 2007b). The influence of different types of SW disturbances on galactic CR has been well-documented in scientific literature (e.g. Dumbovic et al. 2012; Chertok et al. 2013; Kumar & Baddruddin 2014a,b; Melkumyan et al., 2018, 2019). It is known that most of CMEs, and almost all energetic CMEs, are originated from the active regions being accompanied by solar flares which intensity correlated with the CME kinetic energy (e.g. Yashiro & Gopalswamy 2009). Comparison between the impact on the heliosphere of active-region (AR) and non-AR CMEs is presented in Gopalswamy et al. (2010b). The authors reveal that: (i) active regions produce almost all CMEs with above-average energy, for example geoeffective CMEs, CMEs associated with solar energetic particles, shock-driving CMEs; (ii) the quiescent filament regions produce the other type of CMEs which are not related to the sunspots and occur mostly at high latitudes during the maximum phase of solar activity. One of the factors responsible for the variability of FDs is different origin of related interplanetary transients. In Marii et al. (2020, 2021) the influences of different parts of ICMEs (turbulent sheath and magnetic obstacle) on the associated FDs are examined according to the CME origin. The events are separated into three subsets: AR CMEs, disappearing filament CMEs, and stealthy CMEs. CR variations caused by turbulent sheath and magnetic obstacle parts of the corresponding ICME are compared for the three subsets and two different linear relations are found: for AR ICMEs on one side and for filament/stealthy ICMEs on the other side.


Given the potential huge information content of these observables advocated by some recent works (Patton et al. 2017), the predictions from first principles developed in this paper could be successfully applied to forthcoming data along with the standard power spectrum based analysis and could bring additional information beyond ΛCDM parameters like massive neutrinos (Liu & Madhavacheril 2019) or dark energy (Codis et al. 2016a). Let us stress that implementing nulling in weak-lensing analysis is central in order to avoid extracting biased information from the small scales that lack a full theoretical understanding (including due to the effect of baryon physics that needs to be modelled in weak-lensing surveys Hildebrandt et al. 2018; Yoon et al. 2019). Not only this general nulling technique should be used for one-point statistics but could also be applied to standard power spectrum analysis (and more generally to the full two-point PDF) in order to disentangle the effects of the different physical scales. However, more realistic effects have to be accounted for before the here mentioned formalism could be directly applied to real data. In particular, we have not investigated the precise impact of the galaxy redshift distribution ns(z) (for which one needs to go from a set of discrete source planes to a source distribution), photometric redshift errors or shape noise, which are left for future works. Promising extensions include an application of the formalism to (i) compensated filters such as for aperture mass which require the joint modelling of the field at two different scales, (ii) two-point statistics in order to model cosmic variance, and (iii) the joint analysis of multiple redshift bins. All of these ideas are within reach of LDT as was shown in the case of the three-dimensional matter density in Bernardeau, Codis & Pichon (2015) and Codis et al. (2016b) for, respectively, the multiscale and two-point statistics.


We justify our use of the Two-Zone approximation as follows: we anticipate that the magnetic structure within the outflow would be perpendicular to the plane of the host galaxy and thus perpendicular to the magnetic field orientation within the Zone B ISM region. Indeed, such perpendicular magnetic structure in outflows is seen in simulation work where, e.g. the action of a CR-driven dynamo yields a perpendicular magnetic field configuration compared to the host galactic plane (Kulpa-Dybeł et al. 2011), or by the advection of the magnetic fields by the flows themselves (Bertone et al. 2005), by magnetic amplification via the CR streaming instability (Uhlig et al. 2012) along the outflow. This magnetic structure would also be consistent with polarised radio synchrotron emission above and below the planes of galaxies known to host outflows in the nearby Universe, with the polarisation direction aligned with the orientation of the outflow cone (see, e.g. Hummel et al. 1988; Sukumar & Allen 1990, 1991; Hummel et al. 1991; Brandenburg et al. 1993; Chyży et al. 2006; Soida et al. 2011; Mora & Krause 2013). We argue that the principle mechanism for CRs to permeate the Zone A/Zone B interface would be via diffusion. With magnetic field lines aligned in a direction parallel to the inter-zone boundary, diffusion across the interface would be severely hampered – the cross-boundary diffusion coefficient would effectively be perpendicular the the local magnetic field lines, and so would be around two orders of magnitude smaller than that along the field directions (e.g. Shalchi et al. 2004, 2006; Hussein & Shalchi 2014), and substantially less than the effective ISM diffusion coefficient. The detailed substructure of the magnetic fields in these interfacing regions is not yet fully understood (Veilleux et al. 2005), but we argue that our prescription is consistent with existing work on relevant scales and that adopting an alternative model for CR transport across this boundary at this point would not imply an interpretation that is any more physical than that adopted here. We acknowledge that, in future studies, it will be critical to assess the magnetic fields in these interfacing regions across a range of length-scales to properly determine the permeability of the Zone A/Zone B interface to diffusing CRs.


The induction equation of the magnetic field is
(10)
\begin{equation}
\frac{\partial \boldsymbol {B}}{\partial t}={\nabla }\times \left(\boldsymbol {v}\times \boldsymbol {B}-\frac{4\pi }{c}\eta \boldsymbol {J}\right),
\end{equation}
where $\boldsymbol {J}=\frac{c}{4\pi }{\nabla }\times \boldsymbol {B}$ is the current density. The induction equation is the field escaping/creating rate due to magnetic instability or the dynamo effect. For the steady-state accretion flow, we neglect the dynamo effect. In the energy equation, we assumed a balance between the heating due to viscosity and cooling due to advection, convection and radiation as
(11)
\begin{equation}
Q^{-}_{{\rm adv}}+Q^{-}_{{\rm rad}}+Q^{-}_{{\rm con}}=Q^{+}_{{\rm diss}},
\end{equation}
where $Q^{-}_{{\rm adv}}=\scriptstyle\rho (\frac{{\rm d} e}{{\rm d}t}-\frac{p}{\rho ^{2}}\frac{{\rm d}\rho }{{\rm d}t})$ is advection cooling in ADAFs. e is the gas internal energy $(e=\frac{c^{2}_{{\rm s}}}{\gamma -1})$ and γ is the specific heat ratio. Also, we consider $Q^{+}_{{\rm diss}}-Q^{-}_{{\rm rad}}=fQ^{+}_{{\rm diss}}$ in ADAFs (where f, the advection parameter, is defined by Narayan & Yi 1994). Also, the viscous heating is defined as $Q_{{\rm diss}}= f(\nu +\frac{1}{3}\nu _{{\rm con}})\Sigma r^{2} (\frac{{\rm d} \Omega }{{\rm d}r})^{2}$. The outward energy flow by convection is $Q^{-}_{{\rm con}}=- {\nabla }\cdot \boldsymbol {F}_{c}$, where $F_{{\rm con}}=-\nu _{{\rm con}} \frac{1}{\gamma -1}\frac{{\rm d} c^{2}_{{\rm s}}}{{\rm d}r}-\frac{c^{2}_{{\rm s}}}{\rho }\frac{{\rm d} \rho }{{\rm d}r}$. So, the energy equation is written by considering the above definitions and the specific internal energy of inflow ε and outflow εw on the surface of the disc as follows:
(12)
\begin{eqnarray}
&&{\frac{\Sigma v_{r}}{\gamma -1}\frac{{\rm d} c^{2}_{{\rm s}}}{{\rm d}r}-2Hc^{2}_{{\rm s}}v_{r}\frac{{\rm d}\rho }{{\rm d}r}+\frac{1}{2\pi r}\frac{{\rm d}\dot{M}(r)}{{\rm d}r}(\epsilon _{w}-\epsilon )}\nonumber \\
&&-\frac{1}{r}\frac{{\rm d}}{{\rm d}r}\left(r\nu _{{\rm con}}\frac{\Sigma }{\gamma -1}\frac{{\rm d} c^{2}_{{\rm s}}}{{\rm d}r}-2Hr\nu _{m}c^{2}_{{\rm s}}\frac{{\rm d}\rho }{{\rm d}r}\right)\nonumber \\
&& -\frac{\nu \rho }{\gamma -1}\frac{{\rm d} c^{2}_{{\rm s}}}{{\rm d}r}+\nu _{{\rm con}}c^{2}_{{\rm s}}\frac{{\rm d}\rho }{{\rm d}r} = f\Sigma \left(\alpha -\frac{1}{3}\alpha _{\rm c}\right) c_{{\rm s}}H r^{2}\left(\frac{{\rm d} \Omega }{{\rm d}r}\right)^{2}. \nonumber\\
\end{eqnarray}


The linear relationship that we observe between breakpoint energy and core temperature is in line with previous measurements (e.g. McComas et al. 1992; Štverák et al. 2009), for both the halo and strahl. According to Scudder & Olbert (1979), a linear trend in the halo relation also follows under the assumption that binary Coulomb collisions dominate electron dynamics in the solar wind. However, in order to align with available experimental data, Scudder & Olbert (1979) set a scaling factor of Ebp/kBTc = 7, which differs from our scaling factor of Ebp/kBTc = 5.5 ± 0.1. With a scaling factor of Ebp/kBTc = 7, Scudder & Olbert (1979) predict that a transformation of thermal electrons into the suprathermal population occurs as the solar wind flows out from the Sun. Findings by Štverák et al. (2009), on the other hand, show that the (nh + ns)/nc ratio remains roughly constant with heliocentric distance in the slow wind, suggesting a lack of interchange between the thermal and suprathermal populations. However Štverák et al. (2009) observes some variability in the (nh + ns)/nc ratio in the fast wind, which they attribute to either statistical effects due to a lack of samples or a possible “interplay” between thermal and suprathermal electrons. Scudder & Olbert (1979) also predict that the halo Ebp/kBTc ratio remains constant with heliocentric distance, whereas Štverák et al. (2009) find that the halo Ebp/kBTc ratio decreases with heliocentric distance. These findings by Štverák et al. (2009), along with the discrepancy between our calculated ratio of Ebp/kBTc = 5.5 ± 0.1 and the prediction of Ebp/kBTc = 7, suggest that the model of Scudder & Olbert (1979) requires a minor update to either the theory or to the input parameters. The discrepancy, however, may also be indicative of other processes, such as wave-particle scattering (e.g. Gary et al. 1994), that possibly modifies the ratio between breakpoint energy and core temperature while preserving its linear relationship.


After each step of calculations, the network should optimize the model based on its current and previous states to improve the subsequent mapping. Our model utilizes a computationally memory efficient optimization due to its dependence to only the first-order gradients, namely the ‘adaptive moment estimation’ (or Adam). For more details, we refer the readers to Kingma & Ba (2014). Adam optimization, compared to other gradient-based optimization, is very suitable for noisy and sparse gradients, and for simulated data that show very large scatter with respect to a given quantity of parameter (Kingma & Ba 2014). With this optimizer, we have to decide few parameters in advance. The learning step α and the parameters controlling the moving averages of the first- and second-order moments, namely β1 and β2 (both ∈[0,1)), respectively. For this purpose, we chose to minimize the MSE between the target and the prediction from the model: in what follows, we will alternatively call the MSE the ‘objective function’ f($\bf x$): with ${\bf x}$ the parameters of the model to be updated, such as weights and biases. At a given time t ≤ T, where T is the maximal learning time-step, we can update the parameters of the model as shown in the following:
(11)
\begin{eqnarray*}
g_t &=\nabla _\mathrm{ \text{$x$}} f(\mathrm{\text{$x$}}_{t-1}),
\end{eqnarray*}
(12)
\begin{eqnarray*}
\mu _{1,t} &=\beta _1 \times \mu _{1,t-1} + (1-\beta _1)\times g_t,
\end{eqnarray*}
(13)
\begin{eqnarray*}
\bar{\mu }_{1,t} &=\mu _{1,t}/(1-\beta _1^t),
\end{eqnarray*}
(14)
\begin{eqnarray*}
\mu _{2,t} &=\beta _2 \times \mu _{2,t-1} + (1-\beta _2)\times g_t^2,
\end{eqnarray*}
(15)
\begin{eqnarray*}
\bar{\mu }_{2,t} &=\mu _{2,t}/(1-\beta _2^t),
\end{eqnarray*}
(16)
\begin{eqnarray*}
\mathrm{\text{$x$}}_t &=\mathrm{\text{$x$}}_{t-1} - \alpha _t \times \bar{\mu }_{1,t}/ (\sqrt{\bar{\mu }_{2,t}} + \epsilon),
\end{eqnarray*}
where $\alpha _t=\alpha \sqrt{1-\beta _2^t}/(1-\beta _1^t)$ is the time-step at t. Equation (11) shows the gradients of the objective function at t with respect to the model parameters. Equations (12) and (14) update the estimations of the first and second moments. Our moments are biased towards the initial values; thus, we require equations (13) and (15) to account for the corrections. Finally, we update the model parameters with equation (16).


The direct detection of the first gravitational waves from the merger of two heavy black holes (BHs) in GW 150914 confirmed one of the toughest predictions of Einstein’s theory of general relativity. But while satisfying the world of physics in general, for astrophysics this was only the beginning: many were surprised by the large BH masses of, respectively, 36 and 29  M⊙ (Abbott et al. 2016), showcasing how the new field of multimessenger astrophysics had just re-opened the field of stellar evolution in a spectacular fashion. Stellar mass BHs had previously been revealed by their interaction in binary systems (Orosz et al. 2011), but the maximum stellar BH mass in our Milky Way is not higher than roughly 15–20  M⊙ (Belczynski et al. 2010). While we know that very massive stars (VMS) above 100  M⊙ exist (Crowther et al. 2010; Vink et al. 2015), this mass is significantly diminished via stellar winds already during core hydrogen (H) burning (Vink & Gräfener 2012). The heavy nature of the BH, as measured by LIGO/VIRGO therefore supported the assumption that the gravitational wave event occurred in a part of the Universe still pristine in its enrichment with heavy elements (‘metallicity (Z)’), lowering stellar wind mass-loss (Vink, de Koter & Lamers 2001; Vink & de Koter 2005). A low-Z solution was widely accepted until the announcement of a 70  M⊙ BH in LB-1 (Liu et al. 2019), spurring stellar evolution theorists to avoid heavy mass-loss in the Milky Way (Belczynski et al. 2020; Groh et al. 2020), either by arbitrarily lowering the mass-loss rates of VMS – seemingly contradicting VMS mass-loss calibrations (Vink & Gräfener 2012) – or by invoking the presence of a strong dipolar surface magnetic field that could quench the wind (Petit et al. 2017). While such magnetic fields in some 5–10 per cent of massive OB stars do indeed exist, no B-fields have yet been detected in VMS (Bagnulo et al. 2020). The problem of the formation of a $70\, \mathrm{ M}_\odot$ BH in a solar metallicity environment apparently resolved itself when the spectral signatures of LB-1 were re-interpreted (Abdul-Masih et al. 2020; El-Badry & Quataert 2020).


Previous works (e.g. Holt et al. 2011; Arribas et al. 2014; Villar Martín et al. 2014, 2015) have found very high reddening and densities associated with ionised outflows in local objects (e.g. Hα/Hβ ∼ 4.91 and ne ≳ 1000 cm−3, Villar Martín et al. 2014). Concerning the reddening, although we find that the outflowing gas is generally less affected by dust extinction than the disc, the median value of the total distribution is significantly affected by dust (Hα/Hβ ∼ 4.16), with tails up to Hα/Hβ ≳ 6. Similarly, the outflow density of MAGNUM galaxies is higher than the values in the disc gas, but appears to be far lower than the values found by these authors. This could stem from the fact that the galaxies studied by Holt et al. (2011), Arribas et al. (2014) are local luminous or ultra-luminous infrared galaxies (U/LIRGs), and those of Villar Martín et al. (2014, 2015) are highly obscured Seyfert 2, thus sampling sources that are more gas and dust rich compared to our sample. However, our values are also lower than the outflow densities found in Perna et al. (2017) (ne ∼ 1200 cm−3), who targeted optically selected AGNs from the SDSS, and Förster Schreiber et al. (2018b), who presented a census of ionised gas outflows in high-z AGN with the KMOS3D survey (ne ∼ 1000 cm−3). A possible explanation could be related to the high quality of our MUSE data, which also allows us to detect the faint [S II] emission associated with lower density regions. If we calculate the median densities of the disc and outflow components, weighting for the [S II] line flux, we obtain higher values (ne ∼ 170 cm−3 and ne ∼ 815 cm−3, for disc and outflow, respectively). This shows that previous outflow density values from the literature could be biased towards higher ne because they are based only on the most luminous outflowing regions, characterised by a higher S/N. This could also mean that outflows at high-z could be far more extended than the values we observe.


As a final note, we point out that correcting for the effect of neutrinos did not change the finding that KIC 08626021 has a very thin helium-pure layer on top of its envelope. Such a thin layer might be explained by the presence of any mechanism competing against the separation of He, C, and O in the envelopes of DO and hot DB white dwarfs. For instance, Fontaine & Brassard (2005; see also Brassard et al. 2007) postulated the existence of a weak stellar wind of the order of ∼2 × 10−13M⊙ yr−1 in order to account for the presence of traces of C in Teff ∼ 20 000–30 000 K DB white dwarfs. Such a wind, similar to the solar wind, would be driven by deposition of acoustic energy generated by strong convective motions which characterize the outer layers of these stars. Perhaps a more likely mechanism is convective overshooting, which was first studied by Freytag et al. (1996) in a white dwarf context and more recently by Tremblay et al. (2015) and Cukanovaite et al. (2018) through detailed 3D simulations. Brassard & Fontaine (2015) explicitly used the overshooting prescription of Freytag et al. to demonstrate that element separation is indeed considerably slowed down in cooling hot white dwarfs. They found that only a “thin” layer of pure He (logq1 ∼ −8) has accumulated at the surface of their evolving model by the time the latter has cooled down to Teff ∼ 31 000 K. This is in line with our seismic inference for KIC 08626021. In addition, the new solution for KIC 08626021 does not change the fact that no C/O/He triple transition at the core boundary is found in the model that best reproduces the pulsation frequencies of this star. If puzzling from an evolutionary perspective, our seismic probing seemingly requires that mode trapping generated by two chemical transitions around logq ∼ −2.4 and logq ∼ −3.5 must be present. This can be obtained with our current models only if a carbon buffer exists between the envelope and the core. Alternately, enforcing a triple transition and searching for a new optimal solution within this additional constraint strongly degrades the quality of the achieved best frequency match. Improving the capacity of such a configuration to reproduce the observed pulsation modes would likely require the presence of an additional structure (of unclear origin) in the envelope to provide the needed mode trapping. We therefore leave that issue open at this stage.


Such a chemical differentiation has been reported in other multiple systems, like the low-mass protostars IRAS16293-2422 (2004a; 2016; 2011) and IRAS4A (Santangelo et al. 2015; López-Sepulcre et al. 2017), and, recently, towards the intermediate-mass protostars NGC 2264 CMM3 (Watanabe et al. 2017). With four examples at hand, we speculate that it could be a general feature of multiple protostellar systems and not a “pathological anomaly”. There is no systematic trend between the millimetre thermal dust and molecular line emissions. Towards IRAS16293-2422 and IRAS4A, a rich content in COMs is observed towards the source with the less massive continuum source. Towards NGC 2264 CMM3, it is the most massive continuum component that displays a rich molecular content. The case of Cep E-mm appears similar to the latter one. High-mass star forming regions (HMSFRs) also present a rich chemical diversity. One of the best known examples is provided by Orion-KL. This source harbours: (i) a dichotomy between the spatial distribution of complex O-bearing and complex N-bearing species, with the latter species probing the hotter gas (see, e.g. Guélin et al. 2008; Favre et al. 2011; Friedel & Widicus Weaver 2012; Peng et al. 2013; Brouillet et al. 2013; Crockett et al. 2014, 2015) but also (ii) differences between supposed chemically related species (see, e.g. Favre et al. 2017; Pagani et al. 2017). Other examples are provided by W3(OH) (Qin et al. 2015; Nishimura et al. 2017) and SgrB2 (Belloche et al. 2008, 2013). In an observational study of four HMSFRs (Orion KL, G29.96, IRAS 23151+5912, and IRAS 05358+3543), Beuther et al. (2009) showed that the properties of CH3OH can be easily accounted for by the physical conditions (temperature) in the cores, whereas the N-bearing species appear to be more selective as they are detected only towards the sources at the (evolved) hot core stage. Recently, in an ALMA study of the filamentary HMSFR G35.20, Sánchez-Monge et al. (2014) found that only three out of the six continuum cores of the filament display COM emission typical of hot cores. Several hypotheses have been proposed to account for the observed chemical differentiation. López-Sepulcre et al. (2017) proposed that the COM-rich protostar is either more massive and/or subject to a higher accretion rate, resulting in a lower envelope mass. Watanabe et al. (2017) suggest that the less massive protostar is related to a younger evolutionary stage in which the hot corino (hot core) is not yet developed, meaning that its dimensions are still very small. In Cep E-mm, the presence of high-velocity SiO jets provides evidence of active mass ejection around both protostars. The short dynamical timescales (500–1000 yr) also indicate that these ejections began recently, meaning that both sources are still in an early evolutionary stage. Incidentally, Lykke et al. (2015) found an apparent correlation between the source luminosities and the relative abundance of complex organic molecules in a sample of sources including high-mass protostars. The authors have suggested that this could be the result of the timescale and the temperature experienced by a source during its evolution. The sample of sources with evidence for chemical differentiation should be increased in order to confirm this observational trend.


The data presented here comprise quasi-simultaneous observations during secondary eclipse of WASP-33 b around the V and Y bands. The predicted planet-star flux ratio in the V-band is 0.2 ppt, four times lower than the accuracy of our measurements. Therefore, we can neglect the planet imprint and use this band to measure the stellar pulsations, and most specifically to tune their current phases (see phase shifts in von Essen et al. 2014). Particularly, our model for the light contribution of the stellar pulsations consists of eight sinusoidal pulsation frequencies with corresponding amplitudes and phases. Hence, to reduce the number of 24 free parameters and the values they can take, we use prior knowledge about the pulsation spectrum of the star that was acquired during von Essen et al. (2014). As the frequency resolution is 1/ΔT (Kurtz 1983), 3.5 h of data are not sufficient to determine the pulsations frequencies. Therefore, during our fitting procedure we use the frequencies determined in von Essen et al. (2014) as starting values plus their derived errors as Gaussian priors. As pointed out in von Essen et al. (2014), we found clear evidences of pulsation phase variability with a maximum change of 2 × 10-3 c/d. In other words, as an example after one year time a phase-constant model would appear to have the correct shape with respect to the pulsation pattern of the star, but shifted several minutes in time. To account for this, the eight phases were considered as fitting parameters. The von Essen et al. (2014) photometric follow-up started in August, 2010, and ended in October, 2012, coinciding with these LBT data. We then used the phases determined in von Essen et al. (2014) during our last observing season as starting values, and we restricted them to the limiting cases derived in Sect. 3.5 of von Essen et al. (2014), rather than allowing them to take arbitrary values. The pulsation amplitudes in δ Scuti stars are expected to be wavelength-dependent (see e.g. Daszyńska-Daszkiewicz 2008). Our follow-up campaign and these data were acquired in the blue wavelength range. Therefore the amplitudes estimated in von Essen et al. (2014), listed in Table 1, are used in this work as fixed values. This approach would be incorrect if the pulsation amplitudes would be significantly variable (see e.g., Breger et al. 2005). Nonetheless, the short time span of LBT data, and the achieved photometric precision compared to the intrinsically low values of WASP-33’s amplitudes, make the detection of any amplitude variability impossible.


The faster evolutionary timescales and higher luminosities of our H-burning sequences should have an important impact on the study of the formation of PNe (Schönberner et al. 2014; Toalá & Arthur 2014). The low-mass models of Schönberner (1983), which are still in use to complement the sequences of Blöcker (1995a), show crossing timescales of ~340 kyr (0.546 M⊙) and ~20 kyr (0.565 M⊙). Our H-burning sequences of similar mass and metallicity (Z0 = 0.02) show crossing timescales about ~3.5 to ≳15 times faster and even faster in the case of M15 models. The discrepancy is even larger in the case of the low-mass models of Vassiliadis & Wood (1994). In order to be able to produce PNe, the central stars need to evolve in less than a few tens of thousand years. If that is not the case, the circumstellar material dissipates before the star becomes hot enough to ionize it. This fact, together with the very long timescales of τcross ≳ 100 kyr of the low-mass models of older grids, leads to the conventional wisdom that low-mass post-AGB stars (≲0.55 M⊙) cannot form PNe; see, e.g., Jacoby et al. (2013), Bond (2015). In this context, the new models might help to explain the existence of single CSPNe with masses lower than ~0.55 M⊙ (Althaus et al. 2010; Werner & Rauch, in prep.). The new models should also have an impact on the question of whether single stellar evolution can form PNe in globular clusters (Jacoby et al. 2013; Bond 2015). Our H-burning post-AGB sequences with ages similar to that of globular clusters (9 to 12 Gyr) have values of τcross ~ 25–70 kyr. Timescales drop to τcross ~ 5–10 kyr for post-AGB sequences with slightly younger progenitors (5 to 7 Gyr); see Tables 2 and 3. Timescales are even shorter in the case of the models of Weiss & Ferguson (2009) and M15 (see Appendix B). The much shorter timescales of the new H-burning post-AGB sequences call into question the idea that single stellar evolution cannot produce PNe in globular clusters.


We also introduce here NB2071 data, taken as part of the MDCS with the Multi-Object Infrared Camera and Spectrograph (MOIRCS; Ichikawa et al. 2006; Suzuki et al. 2008) on the Subaru Telescope (the same instrument that was used in the past MAHALO-Subaru survey; Koyama et al. 2013a). The observations were executed between April 30 and May 6, 2015, under photometric conditions with seeing FWHM ∼0.6 arcsec. The integration time is 125 min which was split into 180 s individual exposures. After combining with the existing NB2071 data (186 min integration), we reconstructed all the data using the reduction pipeline mcsred2 (Tanaka et al. 2011), which is written as iraf3 scripts (Tody 1993). As described in Shimakawa et al. (2018), we executed flat-fielding, masking objects from the combined data in the first run (thus the whole reduction process was conducted twice to remake secure object masks), sky subtraction (by median sky and then the polynomially fitted plane for residual sky subtraction), distortion correction, cross-matching, and image mosaicing with this pipeline. The reconstructed NB2071 image reaches 23.95 mag in 3σ limiting magnitude using a 1.4 arcsec diameter aperture, and its seeing FWHM is 0.63 arcsec. The image depth becomes deeper by 0.5 mag than the previous data (Koyama et al. 2013a). The world coordinate system (WCS, Calabretta & Greisen 2002; Greisen & Calabretta 2002) of the narrow-band image is carefully matched by the iraf scripts (ccmap and ccsetwcs) to that of the F814W image, based on 67 point sources. F814W has one of the best spatial resolutions amongst our data set. The standard deviation of point source separations between the NB2071 and F814 images suggests that the relative WCS uncertainty would be around 0.04 arcsec in the survey area. One should note, however, that the absolute astrometry would have 0.3 arcsec errors in right ascension and declination based on comparison with the Guide Star Catalogue 2 (Lasker et al. 2008).