adsabs/FOCAL huggingface dataset:
The observation of FRB 200428 suggests the FRBs are accompanied by XRBs. The energy ratio between radio burst and XRB is about 





. If this value is valid for FRB 121102, the X-ray energy release in one period for FRB 121102 is about
17





The typical active timescale of magnetars is about 100 yr (Beloborodov & Li 2016). The total energy release of XRBs in the active phase is
18





where τ is the active timescale of the magnetar. For FRB 121102, 





 is assumed. Compared to the rotational energy, the magnetic energy is the main reservoir responsible for powering FRBs. The magnetic energy of magnetar is
19





where 





 G is the interior magnetic field strength, and R = 12 km is the magnetar radius. This value is smaller than the required XRB energy. The XRB energy is shared by the ultrarelativistic ejecta and the baryon shell with a subrelativistic velocity vw. It has been found that the kinetic energy of the baryon shell is comparable to the flare energy (Metzger et al. 2019; Margalit et al. 2020b). We assume that the baryon shell is subrelativistic with a typical velocity 





. Based on the above assumptions, the baryonic mass ejected by magnetar in the active time can be derived as
20





This value is much larger than the typical mass (





) of a magnetar outer crust (Gudmundsson et al. 1983; Glendenning & Weber 1992). According to the structure of magnetars, the core is mainly composed of superfluid. The ejected baryon matter of the magnetar is mainly provided by crust. The baryonic mass estimated in this model is larger than the typical mass of a magnetar outer crust, indicating that the outer crust of the magnetar cannot eject enough baryonic matter required by the model. In Figure 2, we show the constraints on MB using Equation (20). If the radiation efficiency 





 from FRB 200428 is used, the required baryonic mass MB is always larger than 





 for the whole parameter ranges as shown in the left panel of Figure 2. If τ = 100 yr is fixed, the same result is shown in the right panel of Figure 2. The outer crust of magnetars is not sufficient to provide such a large baryonic mass, which challenges the synchrotron maser shock model. Interestingly, if the inner crust is included, the total mass of crust is about 0.01 M⊙ (Chamel & Haensel 2008), which is larger than the required baryonic mass. Theoretically, the physical mechanism and the rate of the baryonic mass ejection are both uncertain. More investigations are required. We also use the bursts of FRB 121102 observed by FAST to estimate the required baryonic mass (Li et al. 2019). The observation of FAST provides the information on the lowest-energy bursts of FRB 121102 so far. In a 56.5 hr observation, 1121 bursts were observed. The total energy of these bursts is 3.14 





 erg.3

3
D. Li & P. Wang 2020, private communications.
 Therefore, the average energy release in one period is about 





 erg. Using the same formulae as above, the baryon mass can be approximated as
21





which is similar to that derived from GBT observation.
Citation: Glendenning & Weber 1992
Citation function: Compare/Contrast
The intrinsic (edge-on) ellipticity (ϵint) has been estimated using the observed V/σ and ϵ based on the theoretical prediction of intrinsic shape for varying inclination under the assumption of rotating oblate system (Binney 2005). Cappellari et al. (2007) has shown that intrinsic ellipticity correlates with the anisotropy parameter using early-type galaxies from the SAURON IFS survey (de Zeeuw et al. 2002). Cappellari et al. (2016) presented the relationship between the intrinsic and observed ellipticities:
(14)$$\begin{eqnarray*}
\epsilon = 1-\sqrt{1+\epsilon _{\rm int} (\epsilon _{\rm int}-2) \sin ^2 i}.
\end{eqnarray*}$$The observed V/σ with an inclination i can be corrected to the intrinsic (V/σ)int for an edge-on (i = 90°) view (Binney & Tremaine 1987):
(15)$$\begin{eqnarray*}
\left(\frac{V}{\sigma }\right) = \left(\frac{V}{\sigma }\right)_{\rm int} \frac{\sin i}{\sqrt{1-\delta \cos ^2 i}},
\end{eqnarray*}$$where δ is an approximation to the anisotropy parameter β such as δ ≈ β = 0.7ϵint. For each component, we generated a grid with varying ϵint and i. Then, we calculated corresponding ϵ and V/σ for each ϵint and i using equations (14) and (15). The ϵint has been derived from the grid which has the best matched ϵ and V/σ to the observation. Note that V/σ for the bulge and disk components are measured using Re, PA, and ϵ of each component in this section, whereas all kinematic measurements in the other sections except for this section and Fig. 13 used the structural parameters from galaxies. Measuring V/σ at the effective radius of each component gives more galaxies with kinematics for both components: 664 and 633 are available for measuring bulge and disk components (respectively), and 468 galaxies have kinematics available for both components. On the other hand, the above method is not valid for slowly rotating bulges (e.g. below the green line in Fig. 13) because they are not oblate rotators. In that instance, we adopt ϵint = ϵ as our best estimate of the intrinsic ellipticity (although it is strictly a lower limit).
Citation: Binney & Tremaine 1987
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This section discusses the results of planet–planet scattering in systems with two giant planets in four simulation sets (Table 1). The statistics use only simulations with one surviving planet after the other planet is ejected via planet–planet scattering (23.26% of all simulations; see Table 1), which is around 5500 simulations in each set. In two-planet systems, the instability boundary is very narrow. If both planets survive, its very likely they have none or very little interactions, so it is not very interesting to study them for our purpose. Simulations with planet–star (2.71% of all simulations) or planet–planet collisions (73.61% of all simulations; see Table 1) are excluded from the statistics, as obliquity evolution for the collision of fluid bodies is beyond the scope of this work (see Li & Lai 2020; Li et al. 2020). Simulations with energy error 




∣



δ
E


E



∣


 greater than 





(


10


−
4


)


 are also excluded (0.36% of all simulations), which is an adequate threshold for multiplanet systems (Barnes & Quinn 2004; Raymond et al. 2010). A negligible fraction of systems (0.03% of all simulations) that do not experience planet destruction in 108 yr are also excluded. Figures 5 and 6 show the distribution of the surviving planet’s final spin orientation and obliquity for simulation sets 1–3. The spin inclination is measured relative to the z-axis, which is aligned with the inner planet’s initial spin and orbit normal. The final spin and obliquity distribution is quite broad compared with the orbital inclination distribution (Figure 7). Overall, the final spin and obliquity distributions (Table 3) are broader than the inclination distributions, with 19.51% planets’ obliquity beyond 40°, and 8.77% of the surviving planets are on retrograde obliquity (i.e., the rotation is in reversed direction relative to the orbit). The inclination distribution only has 0.12% planets beyond 40°. The rate of highly oblique planets (>40°) are 17.86%, 31.98%, and 10.43% in sets 1, 2, and 3. There are 5.07% surviving planets on retrograde obliquity in the base set, 21.46% in set 2, and 3.21% in set 3. The distribution of obliquity for set 3 is more clustered at lower regions compared to the other sets. From the rate of high and retrograde obliquity in set 2 (the inner planet ends up at 0.19 au after the outer planet is ejected), we may expect a high rate of highly oblique planets close to the central star, and some oblique planets farther out (Figures 5 and 6). A moderate peak in Figure 6 for close-in planets in sets 1 and 2 between obliquities 170°–180° implies that Venus-like obliquity is possible. The simulation results imply that planets closer to the star receive more torque from it and become more evolved in obliquity.
Citation: Raymond et al. 2010
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Recently, Esteban et al. (2022) examined the abundances in the Galaxy as measured from a number of sources, including H ii  regions from Arellano-Córdova et al. (2020, 2021), with the goal of assessing the large abundance dispersion that De Cia et al. (2021) measure in Galactic neutral clouds. The direct abundances in the H ii  regions are calculated using T

e
[N ii] in the low-ionization zone and T

e
[O iii] in the high-ionization zone, only applying the Esteban et al. (2009) T

e
–T

e
 relation when one of these temperatures is missing. From the 42 Galactic regions, the dispersion about the O/H gradient is ∼0.07 dex, which is similar to the dispersion in metallicity measured from B-type stars, classical Cepheids, and young clusters in the Galaxy (Esteban et al. 2022), and significantly less than the dispersion measured in the neutral clouds. Méndez-Delgado et al. (2022a) corroborate the low dispersion in the Arellano-Córdova et al. (2020, 2021) H ii  regions when considering nonzero temperature fluctuations and updated H ii  region positions. In the spiral galaxy M101, Kennicutt et al. (2003) determine the abundance gradient from 20 H ii  regions, the majority of which have direct T

e
[O iii] and T

e
[S iii] measurements, and nine of which have direct T

e
[N ii]. Citing the tight correlation they observe between T

e
[O iii] and T

e
[S iii], Kennicutt et al. (2003) use an average of the direct T

e
[O iii] and the inferred T

e
[O iii] from T

e
[S iii] to obtain the high-ionization zone temperature, and they use the direct T

e
[N ii] in the low-ionization zone, when available. Although this sample consists of only 20 regions, there is a clear abundance gradient in M101 with very little dispersion about the gradient. The dispersion reported by CHAOS (0.097 dex; Rogers et al. 2021) is slightly larger than the gradient from Kennicutt et al. (2003) would indicate, but this could be due to the inclusion of H ii  regions with a single direct T

e
.
Citation: Esteban et al. (2022)
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Citation: Esteban et al. 2022
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The newly discovered arcs and new spectroscopic redshifts have been incorporated into updated HFF+ versions of the Abell 2744 and MACSJ0416.1-2403 lensing models (Table 5); many of these have 





 (see Figure 8 for a comparison of the arc redshift distributions adopted by the pre-HFF and new HFF+ lensing models; Cypriano et al. 2004; Okabe & Umetsu 2008; Zitrin et al. 2009; 2013; Okabe et al. 2010a, 2010b; Merten et al. 2011; Christensen et al. 2012; Mann & Ebeling 2012; Jauzac et al. 2014; Lam et al. 2014; Richard et al. 2014; Balestra et al. 2015; Diego et al. 2015; Grillo et al. 2015; Jauzac et al. 2015; Rodney et al. 2015; Wang et al. 2015; Kawamata et al. 2016). The incorporation of these new multiple image systems often results in a reduction in the statistical uncertainty in the galaxy magnifications for a given model. All of the public HFF lensing models provide a range of possible realizations from which the statistical uncertainty of a given model set may be calculated (typically 100 but no fewer than 30). We plot the cumulative distribution of the galaxy magnification uncertainties σ(model)/





, for the galaxies and photometric redshifts provided by the ASTRODEEP catalogs (Merlin et al. 2016; Castellano et al. 2016a) for Abell 2744 (Figure 9) and MACSJ0416.1-2403 (Figure 10). Generally, the statistical uncertainties are reduced for the models computed with the new HFF data sets, with more dramatic reductions for the methods that rely strongly upon the strong-lensing constraints. The parametric methods (CATS, Sharon, Zitrin, GLAFIC) report median statistical magnification errors of 0.2%–5%, while the non-parametric methods (Bradac Williams, Diego) report median statistical magnification errors of 2%–11% for the post-HFF calculations (green curves), versus 2%–22% and 2%–17% respectively for pre-HFF models (blue curves). (We note that the statistical errors for the MACSJ0416.1-2403 Bradac post-HFF models (Hoag et al. 2016) included additional uncertainties due to the photometric redshift uncertainties of the multiple images. These were not included in the pre-HFF Bradac model, and thus may explain why the post-HFF statistical errors are larger for this model.)
Citation: Jauzac et al. 2015
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Citation: Wang et al. 2015
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As an illustrative example we apply the general results obtained in the last section to the IGM shortly after the reionization onset at a redshift of about z = 10. To this end we calculate the effective growth rate of a Maxwell–tensor distributed electron–proton plasma with a kinetic temperature of 





 for both particle species and an electron density of 





 being traversed by a highly relativistic beam with a Lorentz factor of 





. The corresponding fluctuations of the background plasma are dominated by a recently discovered damped, aperiodic mode 





 with 





 (Felten et al. 2013). Schlickeiser & Felten (2013) found that its quantitative description can be simplified by introducing the dimensionless wavenumber κ and the dimensionless frequency y defined by
79







80





where kc is the inverse of the electron skin depth
81





modified in such a way that it absorbs all remaining prefactors that occur in the dispersion relation:
82





Here, 





 denotes the thermal velocity of the electrons. In terms of these variables the dispersion relation takes a simple form and is given by (Schlickeiser & Felten 2013)
83





with
84





For our present purposes it is more convenient to consider the frequency y as the independent variable rather than the wavenumber κ. This approach can easily be reversed by the approximation for the inverse dispersion relation derived by Schlickeiser & Felten (2013),
85





(This procedure was also carried out during the creation of Figures 1 and 3 shown below.) Our task is to compute the effective growth rate (78), which for aperiodic modes reads
86





Making use of definitions (79)–(80) and the dispersion relation (83) we can rewrite this as
87





where we introduced the abbreviations
88







89







90





Next, we will turn to the transversal dispersion function of the unperturbed thermal background plasma (Schlickeiser & Felten 2013)
91





Making use of (79)–(80) and (83) once more we can write the derivative as a function of y alone:
92





Plugging this expression into Equation (87) we arrive at the effective growth rate
93





where
94





Note that to zeroth order in ε this result reproduces the dispersion relation (83) of the unperturbed growth rate, and that it contains an additional first order correction term that accounts for the presence of the beam.
Citation: Schlickeiser & Felten (2013)
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Citation: Schlickeiser & Felten 2013
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Citation: Schlickeiser & Felten (2013)
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Citation: Schlickeiser & Felten 2013
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Except for WR 134, the detected frequencies are high, from 3 d−1 up to 14 d−1. This cannot be easily reconciled with an orbital period (the companion would travel inside the WR star), nor a rotation rate (it would be above break-up velocity). Therefore, the most probable culprits are pulsations. WR 66 very probably possesses a close neighbour (see Section 2.1), which could cast doubt on the identification of the pulsating star, but that is not the case for the other stars (including WR 123: see Lefèvre et al. 2005). Pulsations here are thus considered to originate from the WR star itself, and such a possibility has actually been considered before. Pushed by the observational considerations of Vreux (1985), the first pulsation models for WRs were elaborated more than 30 years ago, with predicted periods of about one hour (Maeder 1985; Scuflaire & Noels 1986). Subsequent work by Glatzel et al. (1999) focused on strange modes in small and hot helium stars (often taken as behaving similarly to WRs) and the predicted pulsations had periods of several minutes with amplitudes of several mmag. After the discovery of a 2.45 d−1 signal in WR 123 (Lefèvre et al. 2005), i.e. at a much lower frequency than expected, the models were revisited. Strange modes were extended to stars with larger radii (Dorfi, Gautschy & Saio 2006; Glatzel 2008), while predictions of g-modes excited by the κ mechanism were made for WRs by Townsend & MacDonald (2006). In both cases, the predicted periods could be made compatible with the 10-h signal observed in WR 123. The signals we observe have frequencies in the same range, even for the 2-min cadence data, which allows us to probe very high frequencies, but no coherent signal is detected above 14 d−1: WRs thus seem to pulsate only at moderately high frequencies. Furthermore, Townsend & MacDonald (2006) expected pulsations with frequencies that are higher in early WN (2–8 d−1) than in late WN (1–2 d−1). For our pulsators, only WR 7 has an early WN type and its frequency values are not particularly higher: its main signals are in the same frequency range as those of the late-type WR 66. Moreover, the highest frequencies are all found in late WN stars. However, Townsend & MacDonald (2006) models were made for ‘general/typical’ stars, not specific ones. In addition, since the WR light mostly comes from inside the wind, the filtering effect of the wind on a signal from the underlying hydrostatic surface needs to be assessed in detail. New, dedicated models will be needed for a more in-depth comparison between observations and predictions.
Citation: Scuflaire & Noels 1986
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We first consider the case in which the star is surrounded by a gaseous atmosphere. The star surface is divided in six angular patches in magnetic colatitude, centred at the values θ = {0°, 10°, 30°, 50°, 70°, 89°}. By using the magnetic and temperature profiles previously described we compute, for each θ, the local magnetic field strength, B, the angle θB between the magnetic field and the normal to the surface, and hence the temperature, T. We then compute a set of atmospheric models corresponding to the six θ angles. Since the models are computed using different integration grids in the photon phase space (because the choice of the photon trajectories along which the radiative transfer is solved needs to be optimized to ensure fast convergence at the different values of magnetic field strength and inclination, see Lloyd 2003), we reinterpolate all model outputs over a common grid. This results in three 4D arrays for the emergent intensity $I^i_\nu (\boldsymbol k,\theta ) \equiv I^i(E,\mu _k,\phi _k,\theta )$ (i = 1, …, 3) which contain the total intensity and the intensities for the ordinary and extraordinary modes, respectively. In order to take into account the emission from the southern magnetic hemisphere of the star, we use the previous 4D arrays with the substitutions θB → π − θB and ϕk → π − ϕk, which is justified by the symmetry properties of the opacities. By using the ray tracing method described in Section 2, we can then compute light curves, phase resolved spectra and polarization fractions for each choice of the angles χ and ξ. As an example, Fig. 3 shows the X-ray light curve (0.12–0.39 keV) and the phase-dependent polarization degree in the X-ray and optical7 (B-filter) bands, for χ = 90° and ξ = 15°. For this particular viewing geometry, the X-ray pulsed fraction is 1 per cent, in agreement with the observed data and, as illustrated in the figure, the polarization degree is expected to be substantial and constant in phase.
Citation: Lloyd 2003
Citation function: Uses; Uses
However, this approximation holds only for luminosities â² 0.3LEdd. At higher accretion rates, the hardening factor Îº increases with luminosity and can be as high as â2.5â3 for some Galactic BHs (e.g., GRO J1655â40 at outburst peak, and GRS 1915+105) and for ULXs in the slim-disk state (Watarai & Mineshige 2003; Kawaguchi 2003; Shrader & Titarchuk 2003; Isobe et al. 2012). This is why at near-Eddington luminosities, the fitted color temperature Tin increases faster than the standard  high/soft state relation (âanomalous regimeâ; Kubota & Makishima 2004; Abe et al. 2005). Given the luminosities of M83 ULX-1 in the three XMM-Newton epochs, and the fact that a disk model with p â 0.6 provides the best fit to the data, we argue that the source was likely to be in the anomalous regime (slightly below Eddington) or in the slim disk regime (slightly above Eddington), and, therefore, we take a hardening factor Îº â 3 for BH mass estimates. Following Vierdayanti et al. (2008), we also take Î¾ â 0.353, which takes into account the transonic flow in the pseudo-Newtonian potential. Taking an average normalization constant Ndisk = (2.5 Â± 0.5) Ã 10â3 from our diskpbb fit (Table 2), we obtain a âtrueâ inner disk radius Rin â (73 Â± 15)(cosâÎ¸)â1/2âkm. This corresponds to an âapparentâ BH mass
2Finally, we need to take into account that the inner radius of a slim disk extends slightly inside the innermost stable circular orbit, so that the true mass is MBH â 1.2MX (Vierdayanti et al. 2008). This gives our final best estimate of the BH mass as
3In principle, the estimated mass can be as high as â60âM in the (implausible) extreme Kerr scenario; however, the fact that the system appears to be in the anomalous regime (upper end of the high/soft state) or in the slim disk state for a moderate bolometric luminosity â2 Ã 1039âergâsâ1 (and possibly even lower, considering the 2014 January spectrum) suggests that the BH mass is closer to â¼10â20âM. The same argument holds if we interpret the X-ray spectra as Comptonized emission from a warm, optically thick corona, which is typical of sources at LX â 1â3LEdd (Gladstone et al. 2009).
Citation: Kubota & Makishima 2004
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