adsabs/FOCAL huggingface dataset:
For the radio galaxies in our sample, we estimate the minimum jet power, Pj following Wójtowicz et al. (2020):
(4)$$\begin{eqnarray}
P_{\rm j} &amp;\sim &amp; 1.5 \times 10^{45} \times \left(\frac{{\rm LS}}{{\rm 100 \, pc}} \right)^{9/7} \left(\frac{\tau _{\rm j}}{{\rm 100 \, yr}} \right)^{-1} \\
&amp;&amp;\times \, \left(\frac{L_{\rm 5 \, GHz}}{10^{42} \,{\rm erg \, s^{-1}}} \right)^{4/7} {\rm erg\, s^{-1}} ,
\end{eqnarray}$$where LS is the linear size, τj is the source age, and L$_{\rm 5 \, GHz}$ is the luminosity at 5 GHz. In equation (4), we consider the linear size and the luminosity at 5 GHz reported in Tables A1–A3. We assume ages between about 100 yr, for the most compact sources, and 105 yr for sources with LS of several kpc, as derived from radiative and kinematic ages of sources (e.g. Murgia et al. 1999; Fanti & Fanti 2002; Murgia 2003; Polatidis & Conway 2003; Giroletti & Polatidis 2009). We end up with minimum jet powers for galaxies between 1040 and 1046 erg s−1. The higher values are obtained for sources at higher redshift, and for 3C 346, which is among the marginally detected sources from our analysis. However, the majority of the galaxies have L$_{\rm \, 5 GHz} \lt 10^{43}$ erg s−1 and estimated minimum jet power Pj  1044 erg s−1. As shown in Fig. 11, this requires a UV luminosity above 1045 erg s−1 in order to detect a cumulative signal by the stacking analysis. This is far from the expectation from Stawarz et al. (2008), in which the optimal conditions occurred for sources with jet power ∼1046 erg s−1, LS  100 pc, and at redshift 0.2 (∼1 Gpc). For our estimated jet power, the highest expected gamma-ray luminosity for sources with LS  100 pc is 1044 erg s−1. The fact that young radio galaxies are faint emitters of gamma rays is also suggested by the results of the stacking analysis, which set the upper limit to their emission, as a whole population, an order of magnitude below the Fermi-LAT threshold. This indicates that only the closest sources could be detected by Fermi-LAT, while if we consider objects at higher and higher redshift, boosting effects are necessary for their detection.
Citation: Murgia 2003
Citation function: Uses
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.
Citation: Maraston et al. 2013
Citation function: Uses
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.
Citation: Salmonson 2003
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Citation: van Eerten & MacFadyen 2012
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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.
Citation: Lesgourgues 2011
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Citation: Crocce & Scoccimarro 2006
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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.
Citation: De Pontieu et al. 2011
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Citation: Velli et al. 2015
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Citation: Velli et al. 2015
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Citation: Velli et al. 2015
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Citation: Li et al. 2018a
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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.
Citation: Mei et al. 2012
Citation function: Uses
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).
Citation: Bruno & Carbone 2013
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Citation: Bruno & Carbone 2013
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Citation: Bruno & Carbone 2013
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Citation: Bruno & Carbone 2013
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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.
Citation: Körding, Jester & Fender 2008
Citation function: Compare/Contrast
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.
Citation: Bharadwaj & Sethi 2001
Citation function: Motivation