adsabs/AstroCLIMB huggingface dataset:
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Left panel: asteroseismic Hertzsprung–Russell diagram (νmax vs. Teff). Right panel: Hertzsprung–Russell diagram. The νmax estimates were adopted from A. Serenelli et al. (2017) for the dwarfs and subgiants (yellow symbols), M. H. Pinsonneault et al. (2018) and J. Yu et al. (2018) for the first-ascent RGB stars (orange symbols), and He-core burning giants (purple symbols). Their estimates of Teff were taken from APOGEE DR17 (Abdurro’uf et al. 2022), and luminosity estimates were taken from the Gaia DR2 catalog (Gaia Collaboration et al. 2018). The large filled red circles and open blue squares show our Kepler and TESS CDGs, respectively. The CDG highlighted with a green circle is HD 91622, which lacks Teff (and carbon abundance) from high-resolution spectra; its Teff was adopted from T. Matsuno et al. (2024). Kernel density histograms are included to show the distributions for various parts of the sample, with the color scheme following the Hertzsprung–Russell diagram, and the dashed histogram showing our CDG sample. Horizontal lines mark CDG luminosity peaks: a solid line at ﹩\mathrm{log}(L/{L}_{\odot })=1.78﹩ dex aligns with the core He-burning phase for low-mass stars (i.e., ﹩\mathrm{log}(L/{L}_{\odot })\simeq 1.55\mbox{--}1.85﹩ dex; L. Girardi 2016), and a dashed line at ﹩\mathrm{log}(L/{L}_{\odot })=2.15﹩ dex marks the primary peak where most CDGs lie.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Seismic mass vs. [C/Fe] (left panel) and vs. [N/Fe] (right panel) for the CDGs, underluminous stars, Li-rich giants, α-rich stars, and a large sample of RC stars with symbols having the same meaning as in Figure 10. We determine luminosities for the Li-rich giants in the same manner as our CDGs. Using this, we estimated the seismic masses of these stars using mass from Equation (2). The “normal” RC stars show a correlation between mass and nitrogen (and carbon) abundance. This reflects first dredge-up surface pollution from early on the RGB (e.g., I. Iben & A. Renzini 1984). The trend shows fairly sharp edges, allowing us to make a cut in N (or C) that varies with mass (dashed lines). This helps in distinguishing the chemically peculiar stars. To the right of the N line, the stars can be considered N rich, for their mass. The vertical shaded region at [N/Fe] = +0.8 ± 0.05 dex denotes the upper limit of our CDG sample’s N enhancement as well as the highest N abundance possible for scaled-solar composition, if the ON cycle was activated after all C is burned to N. Solar abundances are from N. Grevesse et al. (2007).
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Comparison of the expected νmax values (using Equation (1)) against the observed νmax for the CDGs exhibiting clear detections of solar-type oscillations. Giants classified based on asteroseismic analysis form the background from J. Yu et al. (2018; see key). Their expected νmax values were calculated using Teff and ﹩\mathrm{log}g﹩ values taken from APOGEE DR17 (Abdurro’uf et al. 2022). The color bar indicates the spectroscopic surface gravity of each CDG. Large open circles represent our Kepler CDGs, while open squares indicate our TESS CDGs. The CDGs that are reported to be in multiple systems or in a binary system in the literature are filled with colors corresponding to their spectroscopic surface gravity. KIC 8352953, which is classified as an RGB star in J. Yu et al. (2018) and has a νmax ≈ 230 μHz, corresponding to the lower-RGB phase, is not included. The bottom panel shows the star-by-star residuals between expected νmax and observed νmax, expressed in units of μHz. See text for details.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Trends of sodium abundance vs. the [C+N+O/Fe] abundance ratio. Giants classified based on asteroseismic analysis form the background from B. Mosser et al. (2014) and J. Yu et al. (2018; small filled circles; see key). The underluminous stars from Y. Li et al. (2022) are shown by orange squares. The abundance ratios of the normal giants and the underluminous stars are from APOGEE DR17. The Group 1, Group 2, and Group 2α CDGs are represented by blue circles, red triangles, and black squares, respectively. The Li-rich giants (black crosses) are from the H.-L. Yan et al. (2021) study. These Li-rich giants are the low-spectral-resolution RC sample that had good-quality APOGEE DR17 data (59 stars). The α-rich young (orange crosses) and old stars (green crosses) were compiled by S. Hekker & J. A. Johnson (2019) from the P. Jofré et al. (2016) and M. H. Pinsonneault et al. (2018) studies. Solar abundances are from N. Grevesse et al. (2007). Contours highlight the separation into three groups based on their Na and CNO abundances.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Carbon abundance as a function of ﹩\mathrm{log}(L/{L}_{\odot })﹩ for the CDGs (red symbols) with measured νmax, excluding KIC 8352953, a lower-luminosity RGB star, and HD 91622, which lacks carbon abundance measurements from high-resolution spectra. Contours represent the density distribution of CDGs. RC stars from J. Yu et al. (2018; gray circles) form the background, with the color scale indicating the number density of stars (darker colors correspond to higher densities). Kernel density histograms for both CDGs and RC stars are shown along the axes, following the same color scheme. The solar carbon abundance is from N. Grevesse et al. (2007).
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Comparison of seismic surface gravities using νmax values from this study vs. spectroscopic surface gravities for CDGs from literature, excluding HD 91622, since it lacks spectroscopic ﹩\mathrm{log}g﹩ measurement. Background RGB and RC stars from J. Yu et al. (2018) use spectroscopic ﹩\mathrm{log}g﹩ from APOGEE DR17, with seismic ﹩\mathrm{log}g﹩ derived using J. Yu et al. (2018) νmax and APOGEE DR17 Teff. The black dashed line denotes the one-to-one relation. CDGs with spectroscopic ﹩\mathrm{log}g﹩ from APOGEE DR17 (black) and optical spectra (blue) are also shown. The bottom panel shows star-by-star residuals between spectroscopic and seismic ﹩\mathrm{log}g﹩.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Seismic mass vs. ﹩\mathrm{log}{\rm{(}}L/{L}_{\odot })﹩ for CDGs, with Group 1, Group 2, and Group 2α shown as blue circles, red triangles, and black squares, respectively. Kernel density histograms illustrate the distributions for each group, using the corresponding group colors. Contours represent the density distribution of the full sample.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Comparison of seismic masses for the entire seismic CDG sample (43 stars) calculated using Equation (2) with νmax from the pyMON pipeline vs. nonseismic masses from Equation (4). The black dashed line again indicates the one-to-one relation, and kernel density histograms show the mass distributions. The zoomed inset highlights Kepler stars. The bottom panel shows star-by-star residuals between nonseismic and seismic masses, expressed in units of M⊙.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Comparison of seismic masses for 27 CDGs with published ﹩{\nu }_{{\rm{\max }}}﹩ estimates. Masses are derived using ﹩{\nu }_{{\rm{\max }}}﹩ values from this study (via the pyMON pipeline) vs. published ﹩{\nu }_{{\rm{\max }}}﹩ values, both calculated with Equation (2). The bottom panel shows star-by-star residuals, expressed in units of M⊙. The agreement is excellent, apart from M. Hon et al. (2021; limited data coverage; see Section 4.1).
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Left panel: the three groups of CDGs, including α-rich young and old stars compiled by S. Hekker & J. A. Johnson (2019) and local giants from R. E. Luck & U. Heiter (2007), are shown in the Toomre diagram. Dashed lines show constant values of the total space velocity, vtot = (﹩{U}_{\mathrm{LSR}}^{2}﹩+﹩{V}_{\mathrm{LSR}}^{2}﹩+﹩{W}_{\mathrm{LSR}}^{2}﹩)1/2 at 70 and 180 km s−1, demarcating thin-disk and thick-disk components, respectively (Nissen et al. 2004; K. A. Venn et al. 2004). Right panel: spatial distribution above/below the Galactic plane vs. the galactocentric distance. The commonly accepted scale heights of the thin disk and thick disk are indicated at Z = ± 0.3 kpc (dotted lines) and Z = ±1 kpc (dashed lines), respectively (L. S. Sparke & J. S. I. Gallagher 2007). The Sun (filled yellow circle) is at R = 8.2 kpc and Z = 0.025 kpc.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: [Mg/Fe] ratio as a function of [Fe/H]. Giants classified based on asteroseismic analysis form the background from B. Mosser et al. (2014) and J. Yu et al. (2018; small filled circles; see key). The α-rich young (orange crosses) and old stars (green crosses) are compiled by S. Hekker & J. A. Johnson (2019). Both the normal giants and these α-rich stars have abundance ratios from APOGEE DR17. The Group 1, Group 2, and Group 2α CDGs are represented by blue circles, red triangles, and black squares, respectively. The black dashed line shows the separation between thin- and thick-disk stars based on the [Mg/Fe] ratio, similar to V. Z. Adibekyan et al. (2011).
Paper: A Gravitational Millilensing Candidate in GRB 111012A with a Possible Compact Merger Origin
Authors: Shuo Xiao, Yang Lai, Tong-Lei Liao, Zheng-Huo Jiang, Shao-Wei Xiong, Yan-Qiu Zhang, Wei Xie, Jian-Chao Sun
Figure caption: Left panel: energy-resolved light curves at time bin size of 22 ms for GRB 111012A observed by Fermi/GBM NaI 3 and NaI 4 detectors. Right panel: ACF of the light curve for GRB 111012A at different energy bands. The autocorrelation analysis indicates a high degree of similarity between the two pulses, with a peak separation of approximately 3.1 s. For each energy range, the significance and time delay are as follows—8–50 keV: significance = 3.30σ, time delay = 3.32  ±  0.11 s; 50–100 keV: significance = 4.28σ, time delay = 3.08  ±  0.08 s; 100–300 keV: significance = 2.94σ, time delay = 3.15  ±  0.10 s. These results suggest that the temporal structure is consistent across energy bands, reinforcing the lensing hypothesis.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption:  ﹩\mathrm{log}(L/{L}_{\odot })﹩ is shown as a function of ﹩{\nu }_{{\rm{\max }}}﹩ for CDGs. Group 1, Group 2, and Group 2α stars are indicated by blue circles, red triangles, and black squares, respectively. RGB stars (yellow circles) and He-core burning giants (green circles) from M. H. Pinsonneault et al. (2018) and J. Yu et al. (2018) form the background, with the color scale representing the number density of stars (darker colors indicate higher density). Kernel density histograms for each group are shown along the axes, following the same color scheme.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Log-normal fits to binary separation distributions in the Galactic field, following R. J. Parker & M. R. Meyer (2014). The fit to A-star binaries (red dashed) is from R. J. De Rosa et al. (2014), G-dwarfs (black dashed–dotted) from D. Raghavan et al. (2010), and M-dwarfs (black dotted) from M. Janson et al. (2012). Each distribution is normalized to the observed binary fraction for that stellar type. Vertical solid lines mark estimated orbital separations for 5 of the 10 Group 2α CDG binaries with available astrometric parameters (see text for details). The hatched region spans the range of these systems (4900–41,000 au), illustrating that they lie in the very wide binary regime.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Power spectra of eight CDGs (gray) using Kepler (top panel) and TESS data (bottom panel). The smoothed power spectrum is shown in red, and the linear background fit in blue. The power excess window is shaded black and bounded by vertical yellow lines. Vertical red dashed lines indicate the measured νmax values using the pyMON pipeline. For stars with literature νmax values (e.g., J. Yu et al. 2018; M. Hon et al. 2021), these are shown as vertical green lines.
Paper: A Gravitational Millilensing Candidate in GRB 111012A with a Possible Compact Merger Origin
Authors: Shuo Xiao, Yang Lai, Tong-Lei Liao, Zheng-Huo Jiang, Shao-Wei Xiong, Yan-Qiu Zhang, Wei Xie, Jian-Chao Sun
Figure caption: The relationship between the ACF significance and the time bin size. The vertical dashed red line indicates the optimal bin size, which corresponds to the highest ACF significance.
Paper: Asteroseismology of Carbon-deficient Red Giants: Merger Products of Hierarchical Triple Systems?
Authors: Sunayana Maben, Simon W. Campbell, Timothy R. Bedding, Gang Zhao, Madeline Howell, Yerra Bharat Kumar, Bacham E. Reddy
Figure caption: Power spectrum of HD 124721, a CDG with an anomalous peak at 50 μHz, calculated from a single sector of TESS data. The solar-like oscillations are centered at 35 μHz.
Paper: A Gravitational Millilensing Candidate in GRB 111012A with a Possible Compact Merger Origin
Authors: Shuo Xiao, Yang Lai, Tong-Lei Liao, Zheng-Huo Jiang, Shao-Wei Xiong, Yan-Qiu Zhang, Wei Xie, Jian-Chao Sun
Figure caption: Background-subtracted light curves with a time bin size of 22 ms of GRB 111012A, corrected for relative amplitude and time delay using the best-fit parameters obtained by minimizing the χ2 statistic. The top panel shows the first pulse (black, scaled by the best-fit flux ratio recho) and the second pulse (orange, shifted by the best-fit time delay toffset). The inset gives the values of recho and toffset with 1σ uncertainties. The bottom panel presents the residuals after subtraction of the scaled first pulse from the shifted second pulse. The χ2 comparison yields a p-value of ∼1, strongly supporting the interpretation that the two pulses are statistically consistent with arising from a common origin.
Paper: A Gravitational Millilensing Candidate in GRB 111012A with a Possible Compact Merger Origin
Authors: Shuo Xiao, Yang Lai, Tong-Lei Liao, Zheng-Huo Jiang, Shao-Wei Xiong, Yan-Qiu Zhang, Wei Xie, Jian-Chao Sun
Figure caption: Counts ratios of Pulse 2 to Pulse 1 for different energy ranges of GRB 111012A, calculated using background-subtracted light curves. The ratio decreases with increasing energy, suggesting an inverse correlation between energy and flux ratio. This trend is consistent with similar observations for GRB 950830 in comparable energy bands (O. Mukherjee & R. J. Nemiroff 2024a). The error bars represent the standard deviation of the flux ratios estimated through Monte Carlo simulations, and the horizontal error bars correspond to the energy range width. The energy ranges span from 8 to 300 keV on a logarithmic scale.
Paper: A Gravitational Millilensing Candidate in GRB 111012A with a Possible Compact Merger Origin
Authors: Shuo Xiao, Yang Lai, Tong-Lei Liao, Zheng-Huo Jiang, Shao-Wei Xiong, Yan-Qiu Zhang, Wei Xie, Jian-Chao Sun
Figure caption: Left panel: cross-correlation function (CCF) analysis between the 8–100 and 100–300 keV energy bands of GRB 111012A. The red dashed line marks the best measured spectral lag of −0.006 ± 0.013 s, which is statistically consistent with zero. This result indicates the absence of a significant spectral lag, a characteristic feature of sGRBs. Right panel: MVT versus burst duration for Fermi/GBM GRBs and the vertical dashed line at T90 = 2 s marking the conventional division between the two classes. The red star indicates the first pulse of GRB 111012A, with T90 ≈ 1.09 s and Δtmvt ≈ 0.086 s.
Paper: A Gravitational Millilensing Candidate in GRB 111012A with a Possible Compact Merger Origin
Authors: Shuo Xiao, Yang Lai, Tong-Lei Liao, Zheng-Huo Jiang, Shao-Wei Xiong, Yan-Qiu Zhang, Wei Xie, Jian-Chao Sun
Figure caption: Band model fit results for the two pulses in GRB 111012A. Left panel: first pulse, with best-fit parameters: ﹩\alpha =-0.5{0}_{-0.11}^{+0.12}﹩, ﹩{E}_{{\rm{peak}}}=168.8{0}_{-19.93}^{+26.70}﹩ keV, ﹩\beta =-2.4{7}_{-5.53}^{+0.38}﹩. Right panel: second pulse, with best-fit parameters: ﹩\alpha =-1.2{6}_{-0.22}^{+0.23}﹩, ﹩{E}_{{\rm{peak}}}=132.4{7}_{-109.68}^{+142.81}﹩ keV, ﹩\beta =-2.3{8}_{-5.62}^{+0.73}﹩. The energy range used for the fit is 10–500 keV, excluding 30–40 keV, based on NaI 3 and NaI 4 detectors.
Paper: Modeling the Excitation, Propagation, and Damping of Quasiperiodic Fast Magnetosonic Waves in Realistic Coronal Active Region Magnetic Field Structures
Authors: Leon Ofman, Tongjiang Wang, Xudong Sun, Meng Jin
Figure caption: The QFP wave event observed in AR 11166 on 2011 March 10 by SDO/AIA in (a) 171 Å and (b) 193 Å channels. White arrows in (a) mark the AR, flare source, and fan loop associated with the event. Two white curves indicate the initial EUV wave fronts. The white box marks a region where the propagating waves in the running-difference images are shown in Figure 2.
Paper: Modeling the Excitation, Propagation, and Damping of Quasiperiodic Fast Magnetosonic Waves in Realistic Coronal Active Region Magnetic Field Structures
Authors: Leon Ofman, Tongjiang Wang, Xudong Sun, Meng Jin
Figure caption: The potential magnetic field extrapolation using the HMI vector magnetogram of AR 11166, the source of the QFP waves observed by SDO/AIA on 2011 March 10 at about 06:40 UT. The red (positive polarity) and blue (negative polarity) colors indicate the photospheric magnetic field in the range ±1000 G. The “cylindrical equal area” (CEA) map projection coordinates are used here (see X. Sun 2013).
Paper: Modeling the Excitation, Propagation, and Damping of Quasiperiodic Fast Magnetosonic Waves in Realistic Coronal Active Region Magnetic Field Structures
Authors: Leon Ofman, Tongjiang Wang, Xudong Sun, Meng Jin
Figure caption: The initial state of the 3D MHD model (t = 0). (a) The magnetic field lines reconstructed using potential field extrapolation with the Green’s function method of the radial magnetic field for AR 11166. (b) The gravitationally stratified density in the x–z plane at y = −0.72, overlaid with several field lines that are calculated from the (Bx, Bz) components in this 2D plane. (c) The fast magnetosonic speed, Vf, in the x–y plane at z = 1.42. The arrowheads mark the location of the QFP wave train source in the 3D MHD model: Source A at (−0.71, −0.2) (yellow arrowhead), and Source B at (−1.1, −0.5) (white arrowhead). (d) Vf in the x–z plane at y = −0.72.
Paper: Modeling the Excitation, Propagation, and Damping of Quasiperiodic Fast Magnetosonic Waves in Realistic Coronal Active Region Magnetic Field Structures
Authors: Leon Ofman, Tongjiang Wang, Xudong Sun, Meng Jin
Figure caption: The temporal evolution of the velocity components and perturbed magnetic field components, ΔBx,y,z, due to the QFP waves launched at Source B in the modeled AR 11166. (a) The temporal evolution at the location ( −1.49, −1.36, 1.7), marked with a blue “x” in Figure 9(a); (b) the temporal evolution for the same case but at location (1.20, −0.01, 3.5), marked with a yellow “x” in Figure 9(a). The line styles are solid: x-components; dashes: y-components; dots: z-components.
Paper: Modeling the Excitation, Propagation, and Damping of Quasiperiodic Fast Magnetosonic Waves in Realistic Coronal Active Region Magnetic Field Structures
Authors: Leon Ofman, Tongjiang Wang, Xudong Sun, Meng Jin
Figure caption: The temporal evolution of the velocity components (top panel) and the magnetic field component perturbations ΔBx,y,z (lower panel) at the location ( −0.7, −0.7, 1.7) for QFP waves with the parameters Vd = 0.02, ω = 0.249, launched at Source A in the modeled AR 11166. The start time of the plot corresponds to the launch time of the perturbation. The sampled spatial location in the x–y plane is marked with a yellow “x” in Figure 5(a). The line styles are solid: x-components; dashes: y-components; dots: z-components. The time is in units of τA = 5.9 s, and the total time corresponds to 12.74 minutes.
Paper: Modeling the Excitation, Propagation, and Damping of Quasiperiodic Fast Magnetosonic Waves in Realistic Coronal Active Region Magnetic Field Structures
Authors: Leon Ofman, Tongjiang Wang, Xudong Sun, Meng Jin
Figure caption: The time–distance plot of the perturbed density obtained from the 3D MHD model of AR 11166 for the case in Figure 6(a) at height z = 2, at y = −0.72. The temporal cadence is 3τA in this figure.
Paper: Simulations of Multiple Dust Ring Formation in a Subsolar-metallicity Protoplanetary Disk
Authors: Ryoki Matsukoba, Eduard I. Vorobyov, Takashi Hosokawa
Figure caption: Radial profiles of disk structure and dust properties in the early phase. Each row shows the radial profiles of the surface densities (top), the maximum dust size (middle), and the Stokes number (bottom) at the same epochs as in Figure 1. The lines provide the azimuthally averaged values, and the shaded layers show the ranges of variation of these values at a given radius, with the upper and lower boundaries corresponding to the maximum and minimum values. In the top panels, the lines and colors indicate different components: gas (orange solid), grown dust (green dashed), and small dust (blue dotted). For clarity, the shaded layers are shown only for the gas and grown dust components. The densities of the grown and small dust components are multiplied by 1000 to make comparisons easier. In the middle panels, the lines depict the maximum dust size (red solid line) and the fragmentation barrier (black dashed line).