adsabs/FOCAL huggingface dataset:
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.
Citation: Dib et al. 2010
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H2O ice on Pluto has long escaped spectroscopic detection, and based on initial New Horizons data appears to be exposed only in a number of specific locations, usually associated with red color, suggestive of water ice/tholin mix (Grundy et al. 2015; Cook et al. 2015). Nonetheless, water ice is likely to be ubiquitous in Pluto’s near subsurface, given its cosmogonical abundance, Pluto’s density, and its presence on Charon’s surface6. Absorption coefficients for pure water ice (kH2O) at sub-mm-to-cm wavelengths are discussed extensively by Mätzler (1998), who also provides several analytic formulations to estimate them as a function of frequency and temperature along with illustrative plots. We use the Mishima et al. (1983) formulation (see Appendix of Mätzler 1998). Its applicability is normally restricted to temperatures above 100 K, but Fig. 2 of Mätzler (1998) indicates the trend with temperature. Absorption coefficients extrapolated to 50 K (estimated as half the values at 100 K) are shown in Fig. 5. At 500 μm, our best estimate is kH2O = 0.25 cm-1, comparable to the above values for CH4 and N2 ices. The corresponding penetration length is therefore comparable to the diurnal skin depth but remains negligible compared to the seasonal skin depth, even for seasonal Γ = 25 MKS. According to these calculations, the seasonal layer would be probed only at a wavelength of ~4 mm and beyond. We also remark that the expression from Mishima et al. (1983) would give a penetration depth of 56 m at 2.2 cm, which is an order of magnitude larger than indicated by the laboratory measurements of Paillou et al. (2008). In addition, small concentrations of impurities can dramatically reduce the microwave transparency of water ice (e.g., Chyba et al. 1998 and references therein). Therefore, the above calculations likely indicate upper limits to the actual penetration depth of radiation in a H2O ice layer, from which we conclude that the seasonal layer is not reached at the Herschel wavelengths.
Citation: Paillou et al. (2008)
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Citation: Grundy et al. 2015
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So far, only one ancient and massive intruder has been identified unambiguously, with its body now nothing but an enormous cloud of tidal wreckage scattered throughout the inner Milky Way. The existence of a vast debris structure left behind by this merger event, known today as the Gaia-Sausage/Enceladus (GS/E), was suggested before Gaia (see Evans 2020, for the historical development). In particular, Deason et al. (2013) argued that the rapid transition in the Galactic stellar halo structural properties at break radius of 20–30 kpc is likely associated with the apocentric pileup of a relatively early (8–10 Gyr ago) and single massive accretion event. It is hypothesized that the progenitor dwarf galaxy was massive enough for its orbit to shrink and radialize quickly as a result of a complex interplay between dynamical deceleration, host recoiling, and self-friction (Vasiliev et al. 2022). Sinking deep in the heart of the Milky Way, the dwarf sprayed the bulk of its stars in a region enclosed by its last apocenter, i.e., some ∼30 kpc (see Deason et al. 2018). As a result, the region of the Galactic halo within this so-called break radius (see Deason et al. 2011) is inundated with the GS/E stars, consistently showing up as the most striking substructure even in relatively small volumes around the Sun (see examples of pre-Gaia hints in, e.g., Chiba & Yoshii 1998; Brook et al. 2003; Meza et al. 2005; Nissen & Schuster 2010; Hawkins et al. 2015). Subsequently, the Gaia data made crystal clear the unusually strong radial anisotropy of the relatively metal-rich GS/E debris and helped to reveal its dominance in the solar neighborhood (see Belokurov et al. 2018; Haywood et al. 2018b; Myeong et al. 2018b). The genesis of the GS/E debris cloud was also unambiguously confirmed by its unique chemical fingerprint (see, e.g., Helmi et al. 2018; Mackereth et al. 2019) and the large group of globular clusters (GCs) associated with it (see, e.g., Myeong et al. 2018c, 2019; Massari et al. 2019). Close to the Sun, the GS/E structure has been thoroughly scrutinized both kinematically and chemically (see Evans et al. 2019; Necib et al. 2019; Sahlholdt et al. 2019; Das et al. 2020; Feuillet et al. 2020, 2021; Kordopatis et al. 2020; Molaro et al. 2020; Monty et al. 2020; Aguado et al. 2021a; Buder et al. 2021a; Bonifacio et al. 2021; Carollo & Chiba 2021; Matsuno et al. 2021). Outside of the solar neighborhood, fewer studies exist; nonetheless, the global structure of the GS/E cloud is starting to come into focus (see, e.g., Iorio & Belokurov 2019; Lancaster et al. 2019; Simion et al. 2019; Naidu et al. 2020; Balbinot & Helmi 2021; Bird et al. 2021; Iorio & Belokurov 2021; Wu et al. 2022).
Citation: Mackereth et al. 2019
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Citation: Iorio & Belokurov 2019
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In general, the Hall time-scale for magnetic field evolution depends on the strength of the magnetic field, as seen in equation (4). For young NSs with fields below 1014 G, this time-scale may be longer than the observed SNR age. Therefore, magnetic field growth does not have a dramatic effect on these young NSs. However, many of these systems are observed to have a braking index n  3 (Espinoza 2012; Archibald et al. 2016). A possible explanation for these low braking indices may be through the emission of a relativistic particle wind (Thompson & Blaes 1998; Harding, Contopoulos & Kazanas 1999; Tong et al. 2013). However, the conclusive detection of wind nebulae around magnetars in particular is challenging due to the presence of dust-scattering haloes that accompany these X-ray bright, heavily absorbed objects (Esposito et al. 2013; Safi-Harb 2013). Only a handful of such nebulae have been proposed to be associated with highly magnetized NSs. For example, a wind nebula has been proposed to surround the magnetar Swift J1834.9–0846 in W41 (Younes et al. 2016), and the luminosity of a particle wind was estimated for SGR 1806–20 based on the X-ray and radio observations of the wind-powered nebula G10.0–0.3 (Thompson & Duncan 1996; Marsden, Rothschild & Lingenfelter 1999; Gaensler et al. 2005). In the pulsar wind model, relativistic particles load the magnetosphere with charge and distort the dipole field at large scales outside of the light cylinder. Besides affecting the NS spin-down, the emission of a relativistic wind can also offer an explanation for the significant timing noise that generally affects magnetar observations (Tsang & Konstantinos 2013). The HBPs J1119–6127 and J1846–0258 are clearly associated with pulsar wind nebulae (Gavriil et al. 2008; Kumar & Safi-Harb 2008; Ng et al. 2008; Safi-Harb & Kumar 2008; Safi-Harb 2013), suggesting that particle wind emission should play an important role in their evolution. We also expect that AXP and SGR evolution may be affected by wind emission due to candidate wind nebulae, but do not consider these models for the CCOs that do not show any evidence of PWN. However, we note that braking exclusively due to a steady particle wind produces a torque with a braking index n = 1, too low for the NSs with secure SNR associations in Table 1.
Citation: Gaensler et al. 2005
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Running penumbral waves in velocity and intensity observations were first reported by Giovanelli (1972) and Zirin & Stein (1972). Later, they were found in the photosphere as well (Musman et al. 1976), but there they appear to be more intermittent and to have higher radial phase velocity (40–90 km s−1) than the waves in Hα. Whereas the velocity amplitudes are less in the photosphere than in the chromosphere, the density is very low there and most of the wave energy lies in the photosphere and subphotosphere. Larger amplitudes on the disk-side penumbra demonstrate an alignment of the oscillations along the magnetic field. Running waves are also detected in the umbra, but the waves were believed to be unrelated to those in the penumbra (Kobanov & Makarchik 2004). In the chromosphere, the frequency of travelling waves decreases as they propagate from the umbra into the outer penumbra (e.g., Lites 1988). A similar effect is also found in measurements of the propagation velocity of travelling waves (Brisken & Zirin 1997; Sigwarth & Mattig 1997; Alissandrakis et al. 1998; Kobanov & Makarchik 2004; Tziotziou et al. 2006, 2007). Generally, the waves decelerate from 40 km s−1 near the inner part of the penumbra to 10 km s−1 or less near the outer edge of the penumbra. More recently, from a multi-wavelength study including the coronal channels of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO), Jess et al. (2015) revealed the presence of a wide range of frequencies, with longer periodicities preferentially occurring at increasing distance from the umbra. The phase speeds also tend to decrease with increasing periodicity as the waves propagate away from the umbral barycenter. These observations also suggest that these slow waves are driven by a regular coherent source. The physical nature of running penumbral waves has been controversial. Some researchers have regarded them as trans-sunspot waves originating from umbral oscillations since they detected waves starting from the umbra and propagating through the penumbra (e.g., Alissandrakis et al. 1992; Tsiropoula et al. 1996, 2000). However, others suggest that the trans-sunspot (i.e., outward) motion is apparent to a given line of sight, and that these oscillations actually represent the upward propagation of field-guided magnetoacoustic waves from the photosphere (e.g., Christopoulou et al. 2000, 2001; Georgakilas et al. 2000; Rouppe van der Voort et al. 2003; Bogdan & Judge 2006; Kobanov et al. 2006; Bloomfield et al. 2007; Jess et al. 2013, 2015). The gradual change in the inclination of the penumbral field lines is responsible for changes in the oscillation periods and phase speeds.
Citation: Jess et al. (2015)
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Citation: Jess et al.; 2015
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Quasi-periodic pulsations (QPPs) often refer to the quasi-periodic intensity variations during solar/stellar flares (see Zimovets et al. 2021, for a recent review). In many observations, the flare QPPs were found to show a nonstationary property in the time series integrated over the whole Sun/star or over the oscillation region, for instance, each pulsation has an anharmonic and symmetric triangular profile shape (e.g., Kolotkov et al. 2015; Nakariakov et al. 2019). The signature of flare QPPs can be detected in flare light curves across a broad band of the electromagnetic spectrum, i.e., radio/microwave emissions (Ning et al. 2005; Reznikova & Shibasaki 2011; Nakariakov et al. 2018; Yu & Chen 2019), UV/EUV wavelengths (Shen et al. 2018; Hayes et al. 2019; Reeves et al. 2020; Miao et al. 2021), SXR/HXR and γ-ray channels (Nakariakov et al. 2010; Ning 2017; Hayes et al. 2020; Li et al. 2020c), and the Hα (Srivastava et al. 2008; Kashapova et al. 2020; Li et al. 2020b) or Lyα (Van Doorsselaere et al. 2011; Milligan et al. 2017; Li 2021) emissions. The quasi-periods of these QPPs were reported from subseconds to tens of minutes (e.g., Tan et al. 2010; Shen et al. 2013, 2019; Kolotkov et al. 2018; Karlický & Rybák 2020; Clarke et al. 2021). It should be stated that the observed periods are generally related to the specific channels or flare phases (Tian et al. 2016; Dennis et al. 2017; Pugh et al. 2019), suggesting that the various classes of QPPs could be produced by different generation mechanisms (e.g., Kupriyanova et al. 2020). In the literature, the flare-related QPPs were most often explained by magnetohydrodynamic (MHD) waves, more specifically sausage waves, kink waves, and slow waves (Li et al. 2020a; Nakariakov & Kolotkov 2020; Wang et al. 2021), or by a repetitive regime of magnetic reconnection that could be spontaneous (i.e., self-oscillatory process) or triggered owing to external MHD oscillations (Thurgood et al. 2017; Yuan et al. 2019; Clarke et al. 2021). They can also be interpreted in terms of the LRC-circuit oscillation in current-carrying loops (Tan et al. 2016; Li et al. 2020b) or caused by the interaction between supra-arcade downflows and flare loops (Xue et al. 2020; Samanta et al. 2021).
Citation: Tan et al. 2010
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C-statistic (e.g. Jang & Miller 1997) is the most commonly used and the one-way analysis of variance (ANOVA; de Diego 2010) the most powerful test for verifying the presence of variability in a DLC. However, we did not employ either of these tests because, de Diego (2010) has questioned the validity of the C-test by arguing that the C-statistics does not have a Gaussian distribution and the commonly used critical value of 2.567 is too conservative. On the other hand, the ANOVA test requires a rather large number of data points in the DLC, so as to have several points within each sub-group used for the analysis. This is not feasible for our DLCs which typically have no more than about 30–45 data points. Therefore, we have instead used the F-test which is based on the ratio of variances, F = variance(observed)/variance(expected) (de Diego 2010; Villforth, Koekemoer & Grogin 2010), with its two versions : (i) the standard F-test (hereafter Fη-test, Goyal et al. 2012) and (ii) scaled F-test (hereafter Fκ-test, Joshi et al. 2011). The Fκ-test is preferred when the magnitude difference between the object and comparison stars is large (Joshi et al. 2011). Onward Paper II, we have only been using the Fη-test because our objects are generally quite comparable in brightness to their available comparison stars. An additional gain from the use of the Fη-test is that we can directly compare our INOV results with those deduced for other major AGN classes (Goyal et al. 2013). An important point to keep in mind while applying the statistical tests is that the photometric errors on individual data points in a given DLC, as returned by the algorithms in the iraf and daophot softwares are normally underestimated by the factor η which ranges between 1.3 and 1.75, as estimated in independent studies (e.g. Gopal-Krishna, Sagar & Wiita 1995; Garcia et al. 1999; Sagar et al. 2004; Stalin et al. 2004a; Bachev, Strigachev & Semkov 2005). Recently, using a large sample, Goyal et al. (2013) estimated the best-fitting value of η to be 1.5, which is adopted here. Thus, the Fη statistics can be expressed as


\begin{equation*}
F_{1}^{\eta } = \frac{\sigma ^{2}_{({\rm q-s1})}}{ \eta ^2 \langle \sigma _{{\rm q-s1}}^2 \rangle }, \hspace{5.69046pt} F_{2}^{\eta } = \frac{\sigma ^{2}_{({\rm q-s2})}}{ \eta ^2 \langle \sigma _{{\rm q-s2}}^2 \rangle }, \hspace{5.69046pt} F_{{\rm s1-s2}}^{\eta } = \frac{\sigma ^{2}_{({\rm s1-s2})}}{ \eta ^2 \langle \sigma _{{\rm s1-s2}}^2 \rangle },\end{equation*}

 where $\sigma ^{2}_{({\rm q-s1})}$, $\sigma ^{2}_{({\rm q-s2})}$ and $\sigma ^{2}_{({\rm s1-s2})}$ are the variances of the ‘quasar–star1’, ‘quasar–star2’ and ‘star1–star2’ DLCs and $\langle \sigma _{{\rm q-s1}}^2 \rangle =\sum _{\boldsymbol {i}=0}^{N}\sigma ^2_{i,{\rm err}}({\rm q-s1})/N$, $\langle \sigma _{{\rm q-s2}}^2 \rangle$ and $\langle \sigma _{{\rm s1-s2}}^2 \rangle$ are the mean square (formal) rms errors of the individual data points in the ‘quasar–star1’, ‘quasar–star2’ and ‘star1–star2’ DLCs, respectively. η is the scaling factor (= 1.5) as mentioned above.
Citation: Goyal et al. 2013
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Citation: Goyal et al. (2013)
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In local galaxies, the ISM conditions are often described by some physical quantities such as ionization parameter (q), gaseous metallicity (Z) and electron density (ne). At high redshift, the ionization parameter is raised by a large flux of ionizing photons in ISM originated from hot O, B stars due to intensive star formation in relatively small galaxies. Previous studies suggest a high ionization parameter of SF galaxies at z > 2 compared to that of local galaxies (Erb et al. 2010; Nakajima et al. 2013; Masters et al. 2014; Nakajima & Ouchi 2014). Secondly, the chemical abundance of SF galaxies at z ∼ 2 is lower by 0.1–0.3 dex for a given stellar mass compared to those at low-z (Erb et al. 2006a; Sanders et al. 2014; Steidel et al. 2014). This leads to more compact and hotter O, B stars due to lower opacity (Ezer & Cameron 1971; Maeder 1987), and thus UV radiation becomes harder and produces more ionizing photons. Thirdly, the strength of collisionally excited emission lines (e.g. [O iii], [N ii]) strongly depends on the electron density. It is closely related to the number of electrons to collide since the excitation potential of this line is ∼1 eV, which is nearly the same as the energy of electrons at the virial temperature (∼104 K) (Dyson & Williams 1980). Due to low excitation potential, the transition of collisionally excited line is reliant on electron density compared to gaseous metallicity. Recent observations have suggested a high electron density (ne > 100 cm−3) in SF galaxies at z ∼ 2 (Newman et al. 2012; Masters et al. 2014; Shirazi, Brinchmann & Rahmati 2014; Wuyts et al. 2014). This value is larger than that of normal SF galaxies at low-z by an order of magnitude, and close to that of interacting galaxies which are seen as (ultra)luminous infrared (IR) galaxies in the present-day Universe (Krabbe et al. 2014). Such a large electron density contributes to the offset of galaxy distributions on the BPT diagram together with other physical parameters (Brinchmann, Pettini & Charlot 2008a). In this way, the cosmic dependence of the BPT diagram can be attributed to such physical parameters which determine ISM conditions.
Citation: Dyson & Williams 1980
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Citation: Newman et al. 2012
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Citation: Krabbe et al. 2014
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The kinematic analysis was performed by using the selected sample of stars in the MUSE catalogue (see Section 3) and by following the maximum-likelihood approach described by Pryor & Meylan (1993). The method is based on the assumption that the probability of finding a star with a velocity of vi ± ϵi at a projected distance from the cluster centre Ri can be approximated as 
(1)$$\begin{eqnarray*}
p(v_i,\epsilon _i,R_i) = \frac{1}{2\pi \sqrt{\sigma ^2 + \epsilon _i^2}}exp{\frac{(v_i-v_0)^2}{-2\left(\sigma ^2 + \epsilon _i^2\right)}}
\end{eqnarray*}$$where v0 and σ are the systemic radial velocity and the intrinsic dispersion profile of the cluster, respectively. Rotation was included in the analysis by adding the following angular dependence (e.g. Copin et al. 2001; Krajnović et al. 2006; Kamann et al. 2018a) to the mean velocity of equation (1). 
(2)$$\begin{eqnarray*}
v_0 = v_0 + v_{rot}(R_i)sin(\theta _i - \theta _0(R_i))
\end{eqnarray*}$$where vrot and θ0 represent the projected rotation velocity and the rotation axis angle respectively as a function of the projected distance R to the cluster centre. The axis angle as well as the position angle θi of a star are measured from north through east. We restricted the prior for θ0 to a 180° wide interval and we allowed the rotation velocity to assume both positive and negative values, in order to avoid a skewed rotation velocity probability distribution in case of very small or no rotation (see also Kamann et al. 2020). In particular, we used an iterative procedure in which we adopted an angular interval [α; α + 180°) centred on the most probable rotation axis angle. This is useful to avoid skewness in the probability distribution of θ0 when its value is close to 0° or 180°. We split the sample in five concentric annuli centred on the cluster centre and with width varying in such a way that each bin contains the same number of stars (80). Only stars with r  32 arcsec were considered in the analysis as they guarantee an almost complete coverage within each annulus (Fig. 1).
Citation: Krajnović et al. 2006
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Citation: Pryor & Meylan (1993)
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