adsabs/FOCAL huggingface dataset:
Given the time-consuming nature of simulating energetic particle acceleration in multiple contracting and reconnecting (merging) small-scale magnetic islands produced by magnetohydrodynamic (MHD) turbulence and particle-in-the-cell (PIC) models on large spatial scales and in three dimensions, there has been an increased effort to develop statistical kinetic transport theories that capture the essential physics of particle acceleration in multi-island regions (de Gouveia dal Pino & Lazarian 2005; Drake et al. 2006, 2010, 2013; Bian & Kontar 2013
). Recently, Zank et al. (2014) developed a comprehensive kinetic transport theory for small-scale flux ropes (helical magnetic field structures) which, for the first time, unified three different mechanisms currently thought to play an important role in the energization of suprathermal particles traversing solar wind regions containing numerous contracting and reconnecting (merging) small-scale flux ropes. It was argued that magnetic flux ropes in the solar wind can be viewed to first order as being quasi-two-dimensional (quasi-2D) helical contracting and merging flux-rope structures based on three-dimensional (3D) simulations of compressible MHD turbulence that included a strong guide magnetic field (Dmitruk et al. 2004). The three acceleration mechanisms include (i) curvature and grad-B drift acceleration in the motional electric fields generated by the plasma flow at the endpoints of contracting magnetic flux ropes (Drake et al. 2006), (ii) curvature and grad-B drift acceleration in the motional electric fields induced by x-point plasma outflows generated near the center of merging neighboring magnetic islands (Drake et al. 2013), and (iii) acceleration due to field-aligned guiding center motion in the secondary reconnection electric field formed in the x-point region at the center of reconnecting islands (Oka et al. 2010). Interestingly, in Zank et al. (2014) contracting flux ropes were modeled to behave in a compressible manner so that betatron acceleration by the increasing flux-rope field strength also contributes to particle energization. Both Drake et al. (2013) and Zank et al. (2014) consider reconnecting (merging) magnetic islands/flux ropes as incompressible phenomena so that negative betatron acceleration from the decreasing flux-rope field strength reduces particle energization. Zank et al. (2014) found that the mean electric field induced by contracting and merging flux ropes naturally accelerates suprathermal test particles to hard power-law distributions in the supersonic, slow solar wind. The results show that the power-law index depends on the Alfvén Mach number and on the ratio of the diffusion timescale to that for island contraction.
Citation: Dmitruk et al. 2004
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As for Mg, one would expect to find a positive correlation between δ29Si and initial 18O/16O ratios for the parent stars of category A grains if these quantities represent GCE. Indeed, there is a correlation between δ29Si and initial 18O/16O, as can be seen from Figure 10. The observed trend is a bit shallower than predicted by the GCE model of Timmes & Clayton (1996), which was inferred and extended to higher metallicities from predicted 18O/16O ratios at [Fe/H] = −0.3 (18O/16O = 0.56 × solar) and [Fe/H] = 0 (18O/16O = 1.26 × solar); corresponding δ29Si values are −500‰ ([Fe/H] = −0.3) and +260‰ ([Fe/H] = 0), respectively. It is interesting to note that astronomical observations of a variety of sources have not detected a variation in Si isotope ratios with galactocentric radius, which stands in contrast to the monotonically decreasing trend for the 18O/16O ratio (Monson et al. 2017) and our observations for category A grains. Following the approach of Nguyen et al. (2010), we have inferred a GCE relationship between δ29Si and initial 18O/16O, which is based on a tight correlation between 29Si/28Si and 46Ti/48Ti ratios in SiC mainstream grains (Figure 11, left; data from Hoppe et al. 1994; Alexander & Nittler 1999; Huss & Smith 2007) and a correlation between 46Ti/48Ti and initial 18O/16O ratios in presolar oxide grains (Figure 11, right; data from Choi et al. 1998; Hoppe et al. 2003), interpreted to represent largely GCE. Error-weighted linear regressions yield δ46Ti = (0.98 ± 0.08) × δ29Si-(11 ± 7) for SiC mainstream grains and 





 for Group 1 oxides. Combining the two equations gives 





, which is labeled as “SiC-Oxides GCE” in Figure 10. Note that this equation is different from the one presented by Nguyen et al. (2010), which was recognized to be in error (L. Nittler 2018, private communication). Gyngard et al. (2018) recently reported a slightly shallower slope for the δ46Ti versus δ29Si of SiC mainstream grains than inferred here, which would make the δ46Ti versus 





 relationship a bit steeper. Our data for category A grains fall to the right of the SiC-Oxides GCE line but are fully compatible with this line if errors for the SiC-Oxides GCE line are taken into account (Figure 10). Finally, the good correlation between δ25Mg and δ29Si (Figure 12) rounds out the picture emerging from presolar silicate category A grains, suggesting that a subset of presolar Group 1 silicates carries resolvable signatures of the GCE of O, Mg, and Si isotopes.
Citation: Hoppe et al. 1994
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In the first scenario, we assume that neither the characteristic velocity dispersion (σ*) nor the number density (n*) of galaxies evolves with redshifts (νn = νv = 0). Given the redshift coverage of the lensing galaxies in the lens sample (0.06  zl  1.0), if we constrain a non-evolving VDF using the lens data, then, assuming the VDF evolution with redshift is smooth, the fits on the VDF parameters may represent the properties of ETGs at an effective epoch of z ∼ 0.5. Such non-evolving VDF has been extensively applied in the previous studies on lensing statistics (Chae & Mao 2003; Ofek et al. 2003; Capelo & Natarajan 2007; Cao et al. 2012a). By applying the above-mentioned χ2 – minimization procedure to Sample A – we obtain the best-fitting values and corresponding 1σ uncertainties (68.3 per cent confidence level): $\alpha =0.66^{+2.13}_{-0.66}$, $\beta =2.28^{+0.24}_{-0.18}$. It is obvious that the full sample analysis has yielded improved constraints on the high-velocity exponential cut-off index β, compared with the previous analysis of using the distribution of image separations observed in CLASS and PANELS to constrain a model VDF of ETGs (Chae 2005). Suffering from the limited size of lens sample, such analysis (Chae 2005) found that neither of the two VDF parameters (α, β) can be tightly constrained, due to the broad regions in the α − β plane. Consequently, the image separation distribution is consistent with the SDSS measured stellar VDF (Sheth et al. 2003) and the Second Southern Sky Redshift Survey (SSRS2) inferred stellar VDF (Chae & Mao 2003), although the two stellar VDFs are significantly different from each other concerning their corresponding parameter values. We also consider constraints obtained for the Sample B (defined in previous section), with the likelihood is maximized at $\alpha =1.00^{+2.38}_{-1.00}$ and $\beta =2.34^{+0.26}_{-0.24}$, from which one could clearly see the marginal consistency between our fits and recent measurements of three stellar VDFs (especially the SDSS DR5 VDF of ETGs).
Citation: Chae & Mao 2003
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Citation: Chae & Mao 2003
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Cosmic rays (CRs) play a vital role in the chemistry of cold (10–30 K), dense (>102 cm−3) molecular clouds as they can pierce deep into them, unlike interstellar UV radiation (for a review see Indriolo & McCall 2013). These high-energy interstellar particles primarily consisting of protons can be heavier elements and electrons, and have large energy ranges, up to zetaelectronvolt energies (Blandford et al. 2014). Although the energies can be high, it is the lower energy CRs (≤1 TeV) that affect the dense interiors (Viti et al. 2013; Padovani et al. 2020). In these regions, CRs have a wide variety of effects, one of the most important is being a producer of atomic hydrogen through the dissociation of H2 (van der Werf et al. 1988; Montgomery et al. 1995; Li & Goldsmith 2003; Goldsmith & Li 2005; Padovani et al. 2018a). Other important effects are being the dominant source of ionization; regulating the degree of coupling of the gas and the magnetic field; having an important role in the dynamics and the collapse timescale of collapsing clouds (e.g., Padovani et al. 2013, 2014); providing heating and energy to dust grains (de Jong & Kamijo 1973; Shingledecker et al. 2018; Kalvāns & Kalnin 2019; Sipilä et al. 2020, 2021; Silsbee et al. 2021) producing internal UV photons (Prasad & Tarafdar 1983); may have a role on the charge distribution on dust grains (Ivlev et al. 2015); influencing disk growth (Kuffmeier et al. 2020); and affecting deuteration (Caselli et al. 2008). For example, each species ionized by a CR releases an electron. This secondary electron can cause further collisions, which in turn, depending on the energy, can induce more ionization and heating (Ivlev et al. 2021). If a secondary electron does not have enough energy to ionize a species, the species may become excited (Shingledecker & Herbst 2018). Excited species produced by CR bombardment have energy levels higher than their base counterparts, allowing these excited species to overcome some reaction barriers that would otherwise be difficult in cold environments. These species have been shown to drive more complex chemistry from reactions that can form interstellar complex organic molecules (Abplanalp et al. 2016).
Citation: van der Werf et al. 1988
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We now turn to constraining c1. First, note that $\mathcal {Z} \gt 0$ for all x. In practice, we ask that $\mathcal {Z} \gt \mathcal {Z}_{\rm {min}}$ for some fiducial $\mathcal {Z}_{\rm {min}} \approx 0.01$. For x ≫ 1, this gives
(42)$$\begin{eqnarray*}
c_1 \gt \left(\mathcal {Z}_{\mathrm{min}}-\frac{\mathcal {S}}{\mathcal {A}}\right)\, x^{-\frac{1}{2}\left[\sqrt{\mathcal {P}^2+\, 4\mathcal {A}} - \mathcal {P}\right]}_{\mathrm{max}},
\end{eqnarray*}$$where xmax is the outer radius of the disc at which we apply this condition.3 Secondly, the total metal flux into the disc across the outer boundary cannot exceed that supplied by advection of gas with metallicity $\mathcal {Z}_{\rm CGM}$ into the disc, since otherwise this would imply the presence of a metal reservoir external to the disc that is supplying metals to it, which is true only in special circumstances, e.g. during or after a merger (Torrey et al. 2012; Hani et al. 2018), or due to long-term wind recycling through strong galactic fountains (Grand et al. 2019). Mathematically, this condition can be written as
(43)$$\begin{eqnarray*}
-\underbrace{\frac{\dot{M} \mathcal {Z}}{2\pi x}}_\text{adv. flux} - \underbrace{\kappa \Sigma _g\frac{\partial \mathcal {Z}}{\partial x}}_\text{diff. flux} \ge -\underbrace{\frac{\dot{M} \mathcal {Z}_{\rm {CGM}}}{2\pi x}}_\text{CGM flux}.
\end{eqnarray*}$$For x ≫ 1, this translates to,
(44)$$\begin{eqnarray*}
c_1 \le \frac{2\mathcal {P}\left(\mathcal {Z}_{\mathrm{CGM}} - \mathcal {S}/\mathcal {A}\right)}{\mathcal {P}+\sqrt{\mathcal {P}^2+\, 4\mathcal {A}}}\, x^{-\frac{1}{2}\left[\sqrt{\mathcal {P}^2+\, 4\mathcal {A}} - \mathcal {P}\right]}_{\mathrm{max}}.
\end{eqnarray*}$$Thus, we find that c1 is bounded within a range dictated by the two conditions above. Given a value of c1, we can also calculate the Σg-weighted and $\dot{\Sigma }_{\star }$-weighted mean metallicity in the model,
(45)$$\begin{eqnarray*}
\overline{\mathcal {Z}}_{\Sigma _\mathrm{ g}} = \frac{\int ^{x_\mathrm{max}}_{x_{\mathrm{min}}} 2\pi x \Sigma _{\mathrm{ g}0} s_\mathrm{ g} \mathcal {Z} dx}{\int ^{x_\mathrm{max}}_{x_{\mathrm{min}}} 2\pi x \Sigma _{\mathrm{ g}0} s_\mathrm{ g} dx},
\end{eqnarray*}$$
 (46)$$\begin{eqnarray*}
\overline{\mathcal {Z}}_{\dot{\Sigma }_{\star }} = \frac{\int ^{x_\mathrm{max}}_{x_{\mathrm{min}}} 2\pi x \dot{\Sigma }_{\star 0} \dot{s}_{\star } \mathcal {Z} dx}{\int ^{x_\mathrm{max}}_{x_{\mathrm{min}}} 2\pi x \dot{\Sigma }_{\star 0} \dot{s}_{\star } dx}.
\end{eqnarray*}$$Finding $\overline{\mathcal {Z}}$ is helpful because we can use it to produce a mass-metallicity relation (MZR) that can serve as a sanity check for the model. We show in a companion paper that our model can indeed reproduce the MZR (Sharda et al. 2020b).
Citation: Hani et al. 2018
Citation function: Uses
The 3D view provided in Figure 1 can be completed through the time evolution of the cross section of the same tube presented in Figure 2 for times t = 13, 35, 48 and 62. In the figure, magnetic field strength (top row) and vorticity (bottom row) maps are drawn on a vertical cut that coincides with the midplane of the box perpendicular to the initial axis of the tube. We confirm that most of the magnetic flux is concentrated at the very top of the structure. The general appearance and evolution of the structures shown are strongly reminiscent of those described by Moreno-Insertis & Emonet (1996), Emonet & Moreno-Insertis (1998) and Cheung et al. (2006) using 2D simulations. We recall a few salient features obtained in those papers and reproduced here: in the initial stages (two leftmost panels), the rising portion of the flux tube has a mushroom shape, akin to an air bubble rising in water (e.g., Davies & Taylor 1950; Collins 1965; Parlange 1969; Wegener & Parlange 1973; Hnat & Buckmaster 1976; Ryskin & Leal 1984; Christov & Volkov 1985). Within the ascending portion of the tube, vorticity is generated at the boundary layer between the tube and the ambient flow, in fact with opposite sign on the either side of the head (bottom row in the figure). Magnetic flux is dragged along the sides of the tube into a trailing pair of counter-rotating vortices. Later in time the wake is fragmented into smaller and smaller vortices because the Reynolds number increases in time due to the expansion of the tube (Cheung et al. 2006). The AMR device allows to see this fragmentation in much more detail than could be obtained in the original work of Emonet & Moreno-Insertis (1998). Inside the head of the tube, on the other hand, the plasma and magnetic field are executing a twisting oscillation, with small velocity compared to the global rise speed. This description of the time evolution of the flux tube structure generally applies to other simulations with comparable levels of refinement even when the twist and curvature vary. The cases with untwisted flux tubes, instead, follow a somewhat different pattern and their evolution is described in the following.
Citation: Davies & Taylor 1950
Citation function: Similarities
Figure 3 shows the metallicity distribution of the LS. We divided the whole region into square bins with size 3 km s−1 and used color to represent the mean metallicity of each bin. The most prominent feature is the Hyades–Pleiades structure, which includes the Hyades stream (peak 0) and Pleiades stream (peak 1). It exhibits a very metal-rich and consistent distribution; it is well known that the Hyades cluster has a high metallicity ([Fe/H] ∼ 0.13, Heiter et al. 2014). We speculate that some stars of the Hyades stream might be remnants of the Hyades cluster, while others may be the dynamical effect of non-axisymmetric components (Famaey et al. 2008). Though not in sharp contrast, there is a valley with lower metallicity between the horizontal V = −50 km s−1 structure and center. To better present the gap, we picked up a window in the metallicity distribution. We divided the window into parallelogram bins, and the edge parallel to the V axis of each bin equals 1 km s−1. The right panel of Figure 4 shows that the mean metallicity of each bin distributes along with the V direction. In Figure 3, the Hercules I (peak 6) and Hercules II (peak 4) have different metallicities, and peak 4 is definitely different from peak 12 (NEW2). That the Hercules stream has a wide metallicity range (Table 1) is in accord with the purported effect of Galactic bar resonances (Kalnajs 1991; Dehnen 2000; Fux 2001). The upper left side of this plot contains stars moving faster than the LSR. In this region the kinematics suggest peak 13 and peak 14 may be part of the thin disk, although their metallicities are quite low. The Sirius stream (peak 2) is a little more metal-poor than its surroundings and has a very small metallicity scatter. This is similar to the results of Klement et al. (2008), and this supports the notion that the Sirius stream (or at least a part of it) comprises remnants evaporated from a cluster. According to De Silva et al. (2007), HR1614 (peak 11) may be dispersed remnants of star-forming events. New1 (peak 9) is close to peak 11 in both kinematics and metallicity; part of its member stars may be remnants of star-forming events, too. New2 (peak 12) has a large metallicity scatter. It is possible to be induced by other dynamical n:1 resonance of the bar. The γ Leo stream (peaks 7, 10) is more metal-poor than our Sun, and it is rapidly moving toward the center of the Galaxy. Considering that there is a radial metallicity gradient in the Galaxy, we conjecture this structure has drifted inwards from beyond the solar Galactocentric radius.
Citation: Famaey et al. 2008
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The numerous historical radial-velocity (RV) measurements of Capella have been discussed at length in our T09 study, which highlighted how challenging it has been to determine accurate values for the rapidly rotating secondary star (





 km s−1), whereas those of the sharp-lined primary (





 km s−1) have been quite consistent over the last century. T09 presented 162 new RV determinations for both components based on spectra obtained at the CfA covering only a very narrow wavelength range (45 Å). The RVs were measured using the two-dimensional cross-correlation algorithm TODCOR (Zucker & Mazeh 1994), with synthetic templates appropriate for each star. Because of the limited wavelength coverage, those measurements are susceptible to systematic errors resulting mostly from lines shifting in and out of the spectral window as a function of orbital phase. Therefore, an effort was made to control those biases by performing numerical simulations to determine corrections to the velocities, which were at the level of the final uncertainties in the individual measurements for the secondary, and slightly larger for the primary. Final errors in the RVs as measured from the scatter in the orbital fit were about 0.44 km s−1 for the primary and 0.89 km s−1 for the secondary. A sign that systematic errors remained at some level in the CfA velocities was evident in the residuals of the secondary star shown in Figure 2 of T09, in which a pattern can be seen as a function of orbital phase, with a peak semi-amplitude of about twice the typical error. Possible explanations for this, as discussed by T09, include the presence of spots on the active secondary star, or template mismatch.6

6
In particular, due to limitations in the available library of synthetic spectra they used, the macroturbulent velocity of the templates (





 km s−1) was not quite as large as appropriate for giant stars. This also resulted in an overestimation of the rotational velocities of the components, as discussed by T09.
 An additional indication of possible biases was the fact that a small offset (0.267 ± 0.079 km s−1) was found between the primary and secondary velocities in the global orbital fit of T09 that could not be accounted for by differences in the gravitational redshift between the stars, and was ascribed to similar reasons as the secondary residual pattern.
Citation: Zucker & Mazeh 1994
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The recent detection of X-ray pulsations in PSR J1023+0038 during the accretion active state (Archibald et al. 2015; Bogdanov et al. 2015) implies that channelled accretion, similar to that seen in higher luminosity accreting millisecond X-ray pulsars, is occurring at a much lower accretion rate, implying that the inner edge of the accretion disc lies close to rcor and a propeller does not form. In this case material can accumulate near rcor and non-stationary accretion can occur as matter piles up around the intrinsically unstable magnetospheric boundary. Accretion discs accreting on to the magnetosphere of a rotating star can end up in a trapped state, in which the inner edge of the disc stays near rcor. The captured material can form a quasi-spherical shell (Pringle & Rees 1972; Shakura et al. 2012) or a new disc structure, known as a ‘dead-disc’ and episodic accretion can occur (D'Angelo & Spruit 2010, 2012). As noted by Patruno et al. (2014), variations in the mass accretion rate of the accretion disc can move the inner disc radius by a factor of 2 or 3. The viscous time-scale defines the time-scale for this drift and to reach a viscous time-scale of 10–100 s requires a region with an annulus of radius ∼10–100 km. The thermal time-scale is given by ttherm ∼ (H/R)2 tvis (where H and R are the height and radius of the disc) and for an inner thin disc with H/R  0.02 implies ttherm few seconds, much lower than the time-scales observed. Thus, in principle, fluctuations in the mass accretion rate can move rm outside rlc ,which allows the radio pulsar to turns on, triggering a transition to the passive state, where the lower X-ray luminosity is produced by a shock between the pulsar wind and innermost accretion flow. An increase in the mass accretion rate pushes the inner edge of the disc back inside the light cylinder and turns off the radio pulsar. The X-ray pulsations are only observed in the active state and not in the passive-state light curves, which suggests that the switching between the passive and active states results in transitions between a non-accreting pure propeller mode and an accreting trapped-disc mode (Archibald et al. 2015).
Citation: Shakura et al. 2012
Citation function: Background