adsabs/AstroCLIMB huggingface dataset:
Paper: Immediate Origin of the Moon as a Post-impact Satellite
Authors: J. A. Kegerreis, S. Ruiz-Bonilla, V. R. Eke, R. J. Massey, T. D. Sandnes, L. F. A. Teodoro
Figure caption: Illustrative snapshots of the first periapsis passage after the satellite-forming initial impact, from a simulation where the final satellite ends up on a stable orbit. Colors and annotations are the same as in Figure 1, except here purple and green highlight the material that will end up in the final satellite and that will be stripped from the initial body, respectively. The dashed line indicates the Roche limit. An animation is available at http://icc.dur.ac.uk/giant_impacts/moon_strip_orbit_slice.mp4, and with the same data rendered in 3D at http://icc.dur.ac.uk/giant_impacts/moon_strip_orbit_houdini.mp4.
Paper: Immediate Origin of the Moon as a Post-impact Satellite
Authors: J. A. Kegerreis, S. Ruiz-Bonilla, V. R. Eke, R. J. Massey, T. D. Sandnes, L. F. A. Teodoro
Figure caption: Diagrams for estimating the stripping of material when a satellite passes through periapsis within the Roche limit. Top: notation for the mass lost (hatched region) from the tidal force at a distance r from the center of a satellite with radius R and initial mass m  i , at a distance d from a planet with mass M. Bottom: notation for the time spent inside the Roche limit, R Roche (gray circle), by a satellite on an orbit (black ellipse) with a semimajor axis a, eccentricity e, and periapsis r p < R Roche. ϕ is the complement to the true anomaly, and E is the eccentric anomaly. The dotted line shows the auxiliary circle.
Paper: Immediate Origin of the Moon as a Post-impact Satellite
Authors: J. A. Kegerreis, S. Ruiz-Bonilla, V. R. Eke, R. J. Massey, T. D. Sandnes, L. F. A. Teodoro
Figure caption: The convergence and uncertainty of the mass of the initial satellite (or larger single remnant) and the periapsis of the final satellite that form in different-resolution simulations of the impact scenario in Figure 2, as a function of the number of particles. The error bars show the standard deviations across eight reoriented repeats, with points for the individual 107.5- and 108-particle simulations.
Paper: Immediate Origin of the Moon as a Post-impact Satellite
Authors: J. A. Kegerreis, S. Ruiz-Bonilla, V. R. Eke, R. J. Massey, T. D. Sandnes, L. F. A. Teodoro
Figure caption: The positions and orbits of the satellites produced by eight reoriented repeats of the same scenario as in Figures 2 and 4 with 107 particles, at the same times before (solid lines and diamonds) and after (dashed lines and circles) the first periapsis tidal-stripping event. The inner and outer gray circles indicate the planet’s radius and the Roche limit at about 1 and 2.9 R ⊕, respectively.
Paper: Immediate Origin of the Moon as a Post-impact Satellite
Authors: J. A. Kegerreis, S. Ruiz-Bonilla, V. R. Eke, R. J. Massey, T. D. Sandnes, L. F. A. Teodoro
Figure caption: The early orbital evolution of the forming satellite and inner remnant highlighted in matching colors in Figure 1. The panels show the radial distances of the bodies from the central planet, the tangential component of the force from the inner body on the satellite, the change in each body’s angular momentum and the prediction for that of the satellite from the tangential force (dashed line), the satellite’s periapsis, and its eccentricity.
Paper: Immediate Origin of the Moon as a Post-impact Satellite
Authors: J. A. Kegerreis, S. Ruiz-Bonilla, V. R. Eke, R. J. Massey, T. D. Sandnes, L. F. A. Teodoro
Figure caption: The inclined satellite produced by an impact onto a spinning proto-Earth misaligned to Theia’s orbital angular momentum, shown as in Figure 1. The ﹩\tilde{z}﹩-direction is set as the orientation of the post-impact planet’s spin angular momentum, which is estimated simply as the total over all particles within 2 R ⊕. The results are not sensitive to this choice, as using 1.5 R ⊕ or 2.5 R ⊕ only changes the inferred satellite inclination by <0.5°.
Paper: Immediate Origin of the Moon as a Post-impact Satellite
Authors: J. A. Kegerreis, S. Ruiz-Bonilla, V. R. Eke, R. J. Massey, T. D. Sandnes, L. F. A. Teodoro
Figure caption: The fractional change in mass of satellites that are partially stripped through periapsis. The black line is the predicted power law of ﹩{m}_{{\rm{f}}}/{m}_{{\rm{i}}}\propto {r}_{{\rm{p}}}^{3}﹩, scaled in magnitude to fit the slow-spinning initial satellites. The crosses show the model predictions for each simulation using Equations (1) and (A2).
Paper: Immediate Origin of the Moon as a Post-impact Satellite
Authors: J. A. Kegerreis, S. Ruiz-Bonilla, V. R. Eke, R. J. Massey, T. D. Sandnes, L. F. A. Teodoro
Figure caption: The initial conditions for an impact scenario, to scale, in the proto-Earth target’s rest frame. The angle and speed at first contact, β and v c, are set neglecting any tidal distortion before the collision. The initial separation is set such that the time to impact is 1 hr, as detailed in Kegerreis et al. (2020, Appendix A), with the velocity at contact in the −x-direction.
Paper: Immediate Origin of the Moon as a Post-impact Satellite
Authors: J. A. Kegerreis, S. Ruiz-Bonilla, V. R. Eke, R. J. Massey, T. D. Sandnes, L. F. A. Teodoro
Figure caption: The orbital evolution of the material that survived and that was stripped from the initial satellite in the periapsis passage illustrated in Figure A3, presented as in Figure A2.
Paper: The Origin of the Relation Between Stellar Angular Momentum and Stellar Mass in Nearby Disk-dominated Galaxies
Authors: Min Du, Luis C. Ho, Hao-Ran Yu, Victor P. Debattista
Figure caption: The evolution of the j s–M s relation in TNG50 from z = 1.5 to z = 0. The red, green, and blue symbols are central galaxies that correspond to spheroid-dominated galaxies with κ rot < 0.5, disk-dominated galaxies with 0.5 ≤ κ rot < 0.7, and disk-dominated galaxies with κ rot ≥ 0.7, respectively. The redshift is given at the top-left corner of each panel. The blue lines with error bars are the linear fitting results of disk-dominated galaxies. The error bars represent the standard deviation from the linear fitting, which is 0.3 dex at z = 0. The large blue dots show the trend of the median values. The shaded region shows the variance of the j s–M s relation suggested by observations at z = 0, where we combine the fitting results given by Romanowsky & Fall (2012), Fall & Romanowsky (2013), Posti et al. (2018a), Di Teodoro et al. (2021), and Mancera Piña et al. (2021a). In the third panel, the black squares show the j s–M s relation measured for disk galaxies at z = 0.5–1.5 (Swinbank et al. 2017).
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Modulation amplitudes for models with a single power law (dashed lines) and a double power law (solid lines).
Paper: The Origin of the Relation Between Stellar Angular Momentum and Stellar Mass in Nearby Disk-dominated Galaxies
Authors: Min Du, Luis C. Ho, Hao-Ran Yu, Victor P. Debattista
Figure caption: Evolution of the M tot–M s and j tot–M tot relations of central galaxies from z = 1.5 (right) to z = 0 (left) in TNG50. The red, green, and blue symbols are central galaxies that correspond to spheroid-dominated galaxies, disk-dominated galaxies with 0.5 ≤ κ rot < 0.7, and disk-dominated galaxies with κ rot ≥ 0.7, respectively. In the upper panels, we overlay the observations of disk galaxies from PFM19 and Moster et al. (2013) for comparison. Both the linear fitting and medians are measured using equal bins in log M s, thus giving the parameters β and ﹩{f}_{{\rm{m}}}^{{\prime} }﹩ of Equation (3) directly. In the bottom panels, we normalize j tot by ﹩{M}_{\mathrm{tot}}^{2/3}﹩ to highlight the discrepancy from tidal torque theory. In the bottom-left panel, the j tot–M tot relation of central galaxies in TNG100-dark is overlaid for comparison. The shaded regions correspond to the 68 and 95 percentile envelopes. The dotted line and squares are the linear fitting result and median values, respectively.
Paper: The Origin of the Relation Between Stellar Angular Momentum and Stellar Mass in Nearby Disk-dominated Galaxies
Authors: Min Du, Luis C. Ho, Hao-Ran Yu, Victor P. Debattista
Figure caption: Evolution of the j s–j tot relation of central galaxies in TNG50. The red, green, and blue symbols are central galaxies that correspond to spheroid-dominated galaxies with κ rot < 0.5, disk-dominated galaxies with 0.5 ≤ κ rot < 0.7, and disk-dominated galaxies with κ rot ≥ 0.7, respectively. The dotted lines highlight the log ﹩{j}_{{\rm{s}}}=\mathrm{log}\ {j}_{\mathrm{tot}}+{f}_{j}^{{\prime} }﹩ scaling relation in intervals of ﹩{\rm{\Delta }}{f}_{j}^{{\prime} }=0.5﹩.
Paper: The Origin of the Relation Between Stellar Angular Momentum and Stellar Mass in Nearby Disk-dominated Galaxies
Authors: Min Du, Luis C. Ho, Hao-Ran Yu, Victor P. Debattista
Figure caption: The evolution of the j–j h relation for gas (top) and young stars (bottom) in TNG50 at z = 0 (left) and z = 1.0 (right). The red, green, and blue symbols are central galaxies that correspond to spheroid-dominated galaxies with κ rot < 0.5, disk-dominated galaxies with 0.5 ≤ κ rot < 0.7, and disk-dominated galaxies with κ rot ≥ 0.7, respectively. The dotted lines highlight the scaling relation in intervals of 0.5 dex. We exclude the cases with star formation rates lower than 0.1 M ⊙ yr−1 in the last 1 Gyr (i.e., quenched galaxies), which only contribute a small fraction (∼1/4 at z = 0) of even the spheroid-dominated galaxies.
Paper: The Origin of the Relation Between Stellar Angular Momentum and Stellar Mass in Nearby Disk-dominated Galaxies
Authors: Min Du, Luis C. Ho, Hao-Ran Yu, Victor P. Debattista
Figure caption: The number distribution of the misalignment angle θ (top) and its accumulative fraction (bottom) at z = 0. The misalignment angle θ measures the angle between vectors  j  s and  j  h. The three groups of galaxies are shown in blue, cyan, and red. The black curve corresponds to the distribution of all central galaxies.
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Left: temporal variations of (a1) the electron number density (N  e ), (a2) the relative variation of N  e , (a3) the magnetic field strength (B), and (a4) the relative variation of B along the LoS for the noFS model. Right: the same as the left, but for the FS model. The dotted curves in (a1) and (b1) mark the locations where the optical depth of the 2.5 GHz emission reaches unity for LoS+ (white) and LoS− (yellow), respectively.
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Intensity (left) and its relative variation (right) at five frequencies for the noFS model (top), the FS model (LoS+; middle), and FS model (LoS–; bottom). The curves of relative variation are smoothed with a window of two periods.
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Panel (a): the number density of the nonthermal electrons (N  b ). Panel (b): the magnetic field strength (B). Panel (c): the Razin frequency (f  R ) along the LoS. Panel (d): the intensity profiles. Panel (e): the optical depth averaged between the X and O modes. For the FS model, the results for LoS+ and LoS− are discriminated by the solid and dashed–dotted lines in panels (d) and (e).
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Modulation amplitudes of the FS model (dashed lines) and the FS_conB model (solid lines).
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Modulation amplitudes of the FS model (dashed lines) and the FS_conNb model (solid lines).
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Similar to Figure 4, but for the noFS_DPL and FS_DPL models.
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Modulation amplitudes at different frequencies for the FS and noFS models.
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Similar to Figure 4, but for the FS_conB model.
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Similar to Figure 4, but for the FS_conNb model.
Paper: Clustering Behavior in Solar Flare Dynamics
Authors: Elmer C. Rivera, Jay R. Johnson, Jonathan Homan, Simon Wing
Figure caption: (a) Difference in the joint probability of two waiting times δ CDF = CDF(data) − 〈CDF(surrogates)〉 when comparing flares with lookahead p = 1 (〈A〉 is an ensemble average of property A over the surrogates). The black contour shows ﹩{\delta }_{\mathrm{CDF}}=0.5\max ({\delta }_{\mathrm{CDF}})﹩, and the white dashed lines show the mean waiting time. (b) Statistical significance of δ CDF.
Paper: Clustering Behavior in Solar Flare Dynamics
Authors: Elmer C. Rivera, Jay R. Johnson, Jonathan Homan, Simon Wing
Figure caption:  δ CDF of three sequential waiting times. The data show an enhancement in the number of triplet events with similar waiting times around 3 hr.
Paper: Clustering Behavior in Solar Flare Dynamics
Authors: Elmer C. Rivera, Jay R. Johnson, Jonathan Homan, Simon Wing
Figure caption: Changes in δ CDF with lookahead p equal (a) 1, (b) 3, (c) 6, and (d) 10 for the flare sequence of three waiting times.
Paper: Clustering Behavior in Solar Flare Dynamics
Authors: Elmer C. Rivera, Jay R. Johnson, Jonathan Homan, Simon Wing
Figure caption: Fraction ﹩F(p)=\max ({\delta }_{\mathrm{CDF}}(p))/\max ({\delta }_{\mathrm{CDF}}(p=0))﹩ as a function of lookahead p (when p = 0 all data are completely correlated).
Paper: Clustering Behavior in Solar Flare Dynamics
Authors: Elmer C. Rivera, Jay R. Johnson, Jonathan Homan, Simon Wing
Figure caption: Maximum δ CDF of three waiting times that occur in sequence as a function of lookahead p.
Paper: Filament Leg–Leg Reconnection as a Source of Prominent Supra-arcade Downflows
Authors: Jaroslav Dudík, Guillaume Aulanier, Jana Kašparová, Marian Karlický, Alena Zemanová, Juraj Lörinčík, Miloslav Druckmüller
Figure caption: Details of supra-arcade downflows. Top row (a)–(d): SADs, including double P-SAD1, around 20:30 UT. Bottom row (e)–(h): P-SAD2 after 21:00 UT. The P-SAD2 itself is the apex part of a very faint loop-like intensity depression (panel (g)).
Paper: Influence of Fine Structures on Gyrosynchrotron Emission of Flare Loops Modulated by Sausage Modes
Authors: Mijie Shi, Bo Li, Mingzhe Guo
Figure caption: Distribution of the thermal electron number density (N  e ) at t = 0 for the noFS model (top) and the FS model (bottom), in the x–y (left, with z = 0) and y–z (right, with x = 0) planes. The red dotted lines mark the LoS projected onto the y–z plane. Two LoS orientations are indicated by “observer+” (LoS+) and “observer–” (LoS–), respectively.
Paper: Cosmic-Ray Ionization Rate in Protoplanetary Disks with Sheared Magnetic Fields
Authors: Yuri I. Fujii, Shigeo S. Kimura
Figure caption: Top panel: the radial distribution of ionization rate, at 2H from the midplane based on the new estimate of the cosmic-ray ionization rate (solid green) with ζ ISM = 3 × 10−16 s−1 using the effective column density along the elongated path, together with the contribution of X-ray (orange) and short-lived radionuclides (SLR; pink), is displayed with the thick blue curve. The conventional estimate of ζ CR based on ζ ISM = 10−17 s−1 with Γdetour = 1 (the dotted green line) makes up the thin blue curve of the conventional ionization rate. Middle panel: the same as with the top panel, but for the midplane of the disk. The dashed pink line is the ionization rate of the long-lived radionuclides (LLR). Bottom panel: the total ionization rate at z = 3H, 2H, 1H, and midplane using the cosmic-ray ionization rate of this work. The case with the absence of SLR and the estimate using the conventional cosmic-ray ionization rate are plotted in light blue and gray, respectively. The x-axis in each plot starts from 10 au.
Paper: Cosmic-Ray Ionization Rate in Protoplanetary Disks with Sheared Magnetic Fields
Authors: Yuri I. Fujii, Shigeo S. Kimura
Figure caption: The distribution of ionization rate for our new model considering the propagation of cosmic rays along magnetic fields and that for the conventional model considering the vertical attenuation of cosmic rays in the disk around IM Lup. The white lines represent the scale height of the disk (which is ﹩\sqrt{2}﹩ times larger than the definition of Zhang et al. 2021), and the green dots mark the regions where the cosmic rays are the dominant ionization source.
Paper: Cosmic-Ray Ionization Rate in Protoplanetary Disks with Sheared Magnetic Fields
Authors: Yuri I. Fujii, Shigeo S. Kimura
Figure caption: The effective column densities that cosmic rays have to pass through from the closer surface to reach each height of the MMSN at 1, 10, and 100 au. The dashed black line is the vertically measured column density that is used in conventional studies for 1 au. The thin horizontal line shows the attenuation length of cosmic rays.
Paper: Cosmic-Ray Ionization Rate in Protoplanetary Disks with Sheared Magnetic Fields
Authors: Yuri I. Fujii, Shigeo S. Kimura
Figure caption: Radial distributions of ambipolar Elsässer number at the midplane of the disk around IM Lup.
Paper: Cosmic-Ray Ionization Rate in Protoplanetary Disks with Sheared Magnetic Fields
Authors: Yuri I. Fujii, Shigeo S. Kimura
Figure caption: The top panel shows the ratio of the azimuthal and vertical components of the magnetic field strength at each height from the midplane. The purple jagged line represents 〈B  y /B  z 〉. We also plot 〈B  y 〉/〈B  z 〉 in green for comparison. The bottom panel presents the effective column densities that cosmic-ray particles have to go through from the closer surface to reach the corresponding heights. The dashed curves are the vertical column densities that are used in the conventional estimates, and the dotted horizontal line represents the attenuation length of cosmic rays.
Paper: Cosmic-Ray Ionization Rate in Protoplanetary Disks with Sheared Magnetic Fields
Authors: Yuri I. Fujii, Shigeo S. Kimura
Figure caption: Schematic view of our scenario. An hourglass-shaped magnetic-field configuration focuses cosmic rays from a molecular cloud core to a protoplanetary disk. The purple oval represents the area from which the disk can receive cosmic-ray particles. The magnetic fields are stretched to azimuthal direction by shearing motion.
Paper: Erratum: “In Search of Recent Disruption of (3200) Phaethon: Model Implication and Hubble Space Telescope Search” (2018, ApJL, 864, L9)
Authors: Quanzhi Ye, 泉志 叶, Paul A. Wiegert, Man-To Hui, 文韬 许
Figure caption: Updated lower panel of the original Figure 4 in Ye et al. (2018) showing the behavior of the synthetic fragment of various sizes. It can be estimated that the observation is sensitive to a fragment with magAB ≈ 26.
Paper: Magnetic Reconnection in Black Hole Magnetospheres: Lepton Loading into Jets, Superluminal Radio Blobs, and Multiwavelength Flares
Authors: Shigeo S. Kimura, Kenji Toma, Hirofumi Noda, Kazuhiro Hada
Figure caption: Photon spectrum of a reconnection-driven flare from Sgr A* (solid red line). Parameters are M = 4.0 × 106 M ⊙, ﹩\dot{m}=6\times {10}^{-7}﹩, f  l =0.6, and ξ  hl  = 0.5. The X-ray flare data (cyan and magenta regions) are taken from Nowak et al. (2012) and Barrière et al. (2014), respectively. The black-dashed line is the sensitivity curve for FORCE (100 s: Nakazawa et al. 2018).
Paper: Magnetic Reconnection in Black Hole Magnetospheres: Lepton Loading into Jets, Superluminal Radio Blobs, and Multiwavelength Flares
Authors: Shigeo S. Kimura, Kenji Toma, Hirofumi Noda, Kazuhiro Hada
Figure caption: Photon spectrum of a reconnection-driven flare from M87. Parameters are M = 6.3 × 109 M ⊙, ﹩\dot{m}=5\times {10}^{-5}﹩, f  l  = 1.5, and ξ  hl  = 0.5. The blue-dashed, green-dotted, and red-solid lines are for the high-energy flaring state, the low-energy flaring state, and their sum, respectively. The data points are obtained from Table A8 in EHT MWL Science Working Group et al. (2021), which is in the quiescent state. Our model predicts flares of ∼10 times higher luminosity. The black- and gray-dotted lines are sensitivity curves for HiZ-GUNDAM (2 × 104 s: Yonetoku et al. 2020) and AMEGO (106 s: McEnery et al. 2019), respectively.
Paper: Magnetic Reconnection in Black Hole Magnetospheres: Lepton Loading into Jets, Superluminal Radio Blobs, and Multiwavelength Flares
Authors: Shigeo S. Kimura, Kenji Toma, Hirofumi Noda, Kazuhiro Hada
Figure caption: Schematic picture of our lepton loading scenario. The magnetic field above and below the midplane of a MAD transiently pushes out the accreting matter in a nonaxisymmetric manner, which triggers magnetic reconnection with σ  B  ≫ 1. The magnetic reconnection accelerates nonthermal electrons that emit luminous gamma rays. A fraction of these gamma rays interact with each other, producing e + e − pairs above and below the reconnection region. The pair plasma is thermalized, and subsequently will be accelerated to relativistic speed. We can observe it as a superluminal radio blob after it becomes optically thin.
Paper: Magnetic Reconnection in Black Hole Magnetospheres: Lepton Loading into Jets, Superluminal Radio Blobs, and Multiwavelength Flares
Authors: Shigeo S. Kimura, Kenji Toma, Hirofumi Noda, Kazuhiro Hada
Figure caption: Contours of radio luminosity as a function of M and ﹩\dot{m}﹩ with f  l  = 1.0 and ξ  hl  = 0.5. The red lines show the contours of ﹩{\mathrm{log}}_{10}({L}_{\mathrm{radio}})﹩ in cgs unit. The dotted gray line shows t ssa = t ±,syn, and the dashed black line shows t dyn = t ±,syn. The blue stars show the parameters for Sgr A* and M87.
Paper: Magnetic Reconnection in Black Hole Magnetospheres: Lepton Loading into Jets, Superluminal Radio Blobs, and Multiwavelength Flares
Authors: Shigeo S. Kimura, Kenji Toma, Hirofumi Noda, Kazuhiro Hada
Figure caption: The ratio of toroidal to poloidal magnetic fields measured by FIDOs in the Boyer–Lindquist coordinates as a function of the distance from the BH horizon.
Paper: Statistical Evidence for Small-scale Interchange Reconnection at a Coronal Hole Boundary
Authors: Emily I. Mason, Vadim M. Uritsky
Figure caption: (a) Diagram illustrating the basic concept of the correlation integral; concentric circles of increasing radius encompass a linearly increasing number of points on the line (points shown in orange), but a greater-than-linearly increasing number of points on the purple line (points in blue). (b) Top: a log–log plot of the correlation integral (the normalized number of points encompassed in the CH boundary, averaged over all processed image frames) vs. the bounding circle radius; the dotted black lines between 6 and 25 pixels show the region with the most relevant physical scales for this boundary. Bottom: log–linear plot of the scale-dependent correlation dimension obtained using a sliding window of variable size n vs. the bounding circle radius; the same scales are highlighted as in the above plot for clarity.