adsabs/AstroCLIMB huggingface dataset:
Paper: Diffusion of Relativistic Charged Particles and Field Lines in Isotropic Turbulence. I. Numerical Simulations
Authors: Marco Kuhlen, Philipp Mertsch, Vo Hong Minh Phan
Figure caption: Same as Figure 13, but for rg/Lc = 0.89.
Paper: Diffusion of Relativistic Charged Particles and Field Lines in Isotropic Turbulence. I. Numerical Simulations
Authors: Marco Kuhlen, Philipp Mertsch, Vo Hong Minh Phan
Figure caption: Same as Figure 12, but for a turbulence level of η = 0.5.
Paper: Diffusion of Relativistic Charged Particles and Field Lines in Isotropic Turbulence. I. Numerical Simulations
Authors: Marco Kuhlen, Philipp Mertsch, Vo Hong Minh Phan
Figure caption: Comparison of the running diffusion coefficients obtained with the derivative and fractional definitions, see Equations (23) and (31).
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Composite plot presenting the upper flux limit used for the common color scale for the ENA sky maps presented in Figures 4–8 as a function of central energy. Energy passband ranges are marked as color rectangles and labeled. At the top of the plot, we mark an extend in energy for the ENA large-scale structures discussed in the paper.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: ENA heliosphere mapping begins near solar maximum of solar cycle 23, as tracked by the sunspot number variation in time, with Cassini/MIMI/INCA observations (years with available Cassini data are symbolically marked with orange boxes) and continues nowadays with the IBEX measurements (years with available IBEX data are symbolically marked with blue boxes). Seven years of simultaneous data collection by these two missions are available (symbolically marked with two-color boxes). Solar cycle numbers are marked with numbers. The gray bars symbolically mark 3 yr periods used to combine observational data as discussed later in the text
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: ENA sky maps from 0.03 keV up to 44 keV average over years of low or moderate solar activity from 2009–2011 in Mollweide projection centered in the Nose direction in turbo color palette. See Figure A1 for maps in batlow color map.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Variations in time of the ENA sky structures in the Tailward heliosphere at 1.7, 4.3, 8, and 44 keV from top to bottom. The maps are combined over 2003–2005, 2009–2011, 2012–2014, 2014–2016, 2017–2019, and 2020–2022 from left to right. All maps are at a common color scale range. The vertical dashed line separates combined maps 2003–2005 from the rest of the maps for which transition in time is continuous. See Figure A5 for maps in batlow color map.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Sky coverage of the available heliospheric ENA measurements by INCA for the combined 3 yr maps. Maps are presented in Tail-center orientation and different colors indicate number of years used to create the combined three-year map (blue = 1, green = 2, orange = 3).
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: The same as the top panel in Figure 4, but in Tail-centered map orientation. See Figure A3 for maps in batlow color map.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Relative uncertainties of the ENA flux presented in Figure 4 in a range from 0–1. See Figure A2 for maps in batlow color map.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Variations in time of the ENA sky structures in the Noseward heliosphere at 0.4 keV (top), 1.1 keV (middle), and 2.7 keV (bottom). The maps are combined over 2009–2011, 2012–2014, 2014–2016, 2017–2019, and 2020–2022 from left to right. All maps are at a common color scale range. See Figure A4 for maps in batlow color map.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Relative uncertainties of the ENA flux presented in Figure 8 in (a) range from 0–1. See Figure A6 for maps in batlow color map.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Location of the southern heliotail lobe determined at energies from 4.3 keV up to 44 keV based on the M. A. Dayeh et al. (2022) method. Data collected by IBEX-Hi at 4.3 keV are depicted with an empty star symbol. Data from the Cassini/INCA are depicted with a triangle symbol with energies marked by different colors (18 keV in blue, 29 keV in green, and 44 keV in red). The epoch the data correspond to is labeled with the year numbers next to the symbols (for IBEX) or the group of symbols (for INCA).
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Latitudinal variation of the ENA flux (normalized) at the Tail direction longitude at energies from 4–44 keV during solar maximum (left) and solar minimum (right).
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Variations in time of the ENA sky structures in the Tailward heliosphere at 1.7, 4.3, 8, and 44 keV from top to bottom. The maps are combined over 2003–2005, 2009–2011, 2012–2014, 2014–2016, 2017–2019, and 2020–2022 from left to right. All maps are at a common color scale range. The vertical dashed line separates combined maps 2003–2005 from the rest of the maps for which transition in time is continuous.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: ENA sky maps from 0.03 keV up to 44 keV average over years of low or moderate solar activity from 2009–2011 in Mollweide projection centered in the Nose direction in batlow color palette.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Relative uncertainties of the ENA flux presented in Figure A5 in a range from 0–1.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Variations in time of the ENA sky structures in the Noseward heliosphere at 0.4 keV (top), 1.1 keV (middle), and 2.7 keV (bottom). The maps are combined over 2009–2011, 2012–2014, 2014–2016, 2017–2019, and 2020–2022 from left to right. All maps are at a common color scale range.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Relative uncertainties of the ENA flux presented in Figure A1 in a range from 0–1.
Paper: Evolution of Large-scale Structures in the Energetic Neutral Atom Sky Maps in Energy and Solar Activity
Authors: Justyna M. Sokół, Jonathan Gasser, Merav Opher, Marc Kornbleuth, Kostas Dialynas, André Galli, Maher A. Dayeh, Stephen A. Fuselier, Daniel B. Reisenfeld, Herbert O. Funsten
Figure caption: Same as in Figure A1, but in Tail-centered map orientation.
Paper: The Role of Farside Magnetic Structures in Modeling the 2024 Solar Eclipse
Authors: Guanglu Shi, Jiahui Shan, Li Feng, Jun Chen, Weiqun Gan
Figure caption: Comparisons of the plasma parameters and energy densities derived from the AWSoM-R model using different synoptic maps. (a) Plasma parameter distributions of the radial magnetic field (first row), electron number density (second row), radial speed (third row), and electron temperature (fourth row) on the spherical shell at a heliocentric distance of 1.5 R⊙. The columns, from left to right, present the results for the AG and GJ1–GJ3 maps, respectively. The GJ2 and GJ3 results, indicated by the red–black color bar, represent the relative differences compared to the GJ1 distributions. The black box represents the region where the full-disk magnetic field on that day is replaced in the original GJ1 map. The red boxes represent the regions where the full-disk GONG magnetograms from 4 and 8 days later are replaced, respectively. The fifth row presents the signed log-Q distribution corresponding to closed magnetic fields at the photospheric boundary. The sixth row presents the comparison between the coronal Carrington map and the simulated HCS at 3.0 R⊙. (b) Energy density profiles as a function of heliocentric distance for the regions marked by blue boxes in panel (a), including the active region (R1), the quiet region (R2), and the polar region (R3).
Paper: The Role of Farside Magnetic Structures in Modeling the 2024 Solar Eclipse
Authors: Guanglu Shi, Jiahui Shan, Li Feng, Jun Chen, Weiqun Gan
Figure caption: Comparison of simulated and observed WL images within the FOV of the TSE and LASCO C2. (a) Composite observations of the TSE and LASCO C2 and an image enhanced using the WOW algorithm. The zoomed-in region, indicated by the purple box, is overplotted with the magnetic field lines traced from the simulation results using the GJ3 map. (b) The first row shows WL synthetic images generated from simulations using the AG and GJ1–GJ3 maps, respectively, with enhancement applied using the NRGF algorithm. The second row presents different images between the synthetic WL images and their corresponding smoothed versions, to enhance fine coronal structures. (c) Comparison between the simulated pB profiles (colored lines) and the radiometrically calibrated observations (black lines) from the 2024 TSE (left) and LASCO C2 (right) at heliocentric distances of 1.2 R⊙ and 4.5 R⊙, respectively.
Paper: The Role of Farside Magnetic Structures in Modeling the 2024 Solar Eclipse
Authors: Guanglu Shi, Jiahui Shan, Li Feng, Jun Chen, Weiqun Gan
Figure caption: Synoptic maps used in the 2024 TSE simulation. The seventh realization of the ADAPT-GONG map (panel (a), labeled as “AG”) at 18:00 UT and the standard GONG Janus daily synoptic map (panel (b), labeled as “GJ1”) at 19:04 UT on 2024 April 8. The black dashed box represents the region where a 1 hr averaged full-disk magnetogram is replaced in the original GJ1 map. The composite synoptic maps, labeled as “GJ2” (panel (c)) and “GJ3” (panel (d)), generated by replacing the GONG full-disk magnetograms measured after 4 and 8 days on the corresponding region (represented by the red dashed boxes) in the GJ1 map. Each panel includes the magnetic flux balance coefficient. The viewpoint of Earth is shifted to Carrington longitude 180° for better visualization. The date corresponding to Carrington longitude is indicated at the top of the panels.
Paper: The Role of Farside Magnetic Structures in Modeling the 2024 Solar Eclipse
Authors: Guanglu Shi, Jiahui Shan, Li Feng, Jun Chen, Weiqun Gan
Figure caption: Comparison of simulated plasma parameters on the POS. (a) Distributions of plasma parameters in the low corona (−6.0–6.0 R⊙) as viewed from Earth. The top to bottom rows represent the total magnetic field strength, electron number density, radial speed, and electron temperature. The columns from left to right correspond to simulation results using the AG and GJ1–GJ3 maps as boundary conditions. (b) Plasma parameter profiles extracted from the heliocentric distance of 1.2 R⊙ on the POS. The colored lines represent the simulation results, while the black line represents the electron number density profile inverted from the coronal pB observed during the 2024 TSE.
Paper: The Role of Farside Magnetic Structures in Modeling the 2024 Solar Eclipse
Authors: Guanglu Shi, Jiahui Shan, Li Feng, Jun Chen, Weiqun Gan
Figure caption: Comparison of plasma parameters measured in situ by PSP (black line) with simulation results based on the AG and GJ1–GJ3 maps (colored lines). The Dist indexes marked in the corners quantify the agreements between the observations and the model predictions.
Paper: The Global Structure of the Heliosphere
Authors: Nikolai V. Pogorelov, Federico Fraternale, Gary P. Zank, Ming Zhang
Figure caption: Partial and bin pressures of CRs measured by V1, and plasma pressures in our simulation. Panel (a): Partial CR pressures (from Equation (11), energies from 3 MeV E) are shown as a function of energy for the LISM model (black solid curve); V1/CRS data from the LISM (time interval 2012.8–2018, 122–140 au, black points); V1/CRS data from the IHS (2011–2012.3, 116–120 au, blue points); and the bin pressures for the same data sets (from Equation (12), green and magenta points). The total (magnetic and thermal) MHD pressure from the simulation is shown for comparison for a distance of 1000 au (orange line) and near the HP (red line). Panel (b): Differences between the CR pressures in the LISM and in the IHS from V1 data. The pressure difference is shown for the individual energy bins of the instrument and for the partial pressures. For comparison, the difference in magnetic pressure across the HP from V1/MAG is also indicated. The horizontal error bars indicate the observation bin width, while the vertical error bars include both the statistical uncertainties and physical fluctuations in the selected intervals. Panel (c): Simulated thermal and magnetic pressures along the V2 trajectory, compared with observational data. We show the GCR pressure estimates from this study (purple points), the average magnetic pressures in the IHS and in the OHS from V2 measurements (red points), and data-based pressure estimates in the IHS from K. Dialynas et al. (2020) (black point) and G. Gloeckler & L. A. Fisk (2016) (green point). The horizontal error bars represent the range in radial distance over which the measurements were performed, while the vertical bars at the two V1/MAG data points indicate the range of fluctuations over these intervals, as obtained from the daily-averaged data in the IHS and OHS, respectively.
Paper: Probing the Turbulent Corona and Heliosphere Using Radio Spectral Imaging Observation during the Solar Conjunction of the Crab Nebula
Authors: Peijin Zhang, Surajit Mondal, Bin Chen, Sijie Yu, Dale Gary, Marin M. Anderson, Judd D. Bowman, Ruby Byrne, Morgan Catha, Xingyao Chen, Sherry Chhabra, Larry D'Addario, Ivey Davis, Jayce Dowell, Katherine Elder, Gregg Hallinan, Charlie Harnach, Greg Hellbourg, Jack Hickish, Rick Hobbs, David Hodge, Mark Hodges, Yuping Huang, Andrea Isella, Daniel C. Jacobs, Ghislain Kemby, John T. Klinefelter, Matthew Kolopanis, Nikita Kosogorov, James Lamb, Casey J. Law, Nivedita Mahesh, Brian O'Donnell, Kathryn Plant, Corey Posner, Travis Powell, Vinand Prayag, Andres Rizo, Andrew Romero-Wolf, Jun Shi, Greg Taylor, Jordan Trim, Mike Virgin, Akshatha Vydula, Sandy Weinreb, David Woody
Figure caption: Deconvolved 2D elliptical Gaussian source shape statistics of Crab (Tau A) during the transit: the bottom x-axis is the date of the observation, the observation time is 20:30 UT of each day, and the top x-axis shows the distance of the Crab to the Sun as solar radius. Column (a) shows the angular distance of the minor axis and radial direction of different frequencies. Column (b) presents the source size measured as major (blue) and minor (orange) axes. Column (c) is the anisotropic ratio, measured as the ratio of the major and minor axes. The statistics and fitted results are also shown in Table 1. The red points in column (c) are from the angular Gaussian fitting method. We note that the data point of June 13 and 15 is marked as half-transparent in column (b) and red in column (c) because it is measured by fitting an angular 2D Gaussian, detailed in Section 2.2.
Paper: The Global Structure of the Heliosphere
Authors: Nikolai V. Pogorelov, Federico Fraternale, Gary P. Zank, Ming Zhang
Figure caption: Effects of interstellar turbulence on the heliopause thickness and heliotail length. (Left panel) Models (3D, isotropic) for the global (LISM) and locally generated (OHS) magnetic turbulence power spectrum used for the estimates of the mixing length. The green points show the power spectral density (PSD) of magnetic fluctuations present in our simulations in the heliotail along a direction parallel to the heliopause intersecting the HP, where the Kelvin–Helmholtz instability exists. The black points show the spectrum of V1 data in the OHS from 2021.5 to 2023.5, converted to 3D. (Right panel) Estimated mixing-length scale as a function of distance along the downwind direction in the tail. The maximum thicknesses of the heliosphere in the x–z plane, parallel and perpendicular to the B–V plane, are shown with the dashed and solid cyan curves, respectively.
Paper: Probing the Turbulent Corona and Heliosphere Using Radio Spectral Imaging Observation during the Solar Conjunction of the Crab Nebula
Authors: Peijin Zhang, Surajit Mondal, Bin Chen, Sijie Yu, Dale Gary, Marin M. Anderson, Judd D. Bowman, Ruby Byrne, Morgan Catha, Xingyao Chen, Sherry Chhabra, Larry D'Addario, Ivey Davis, Jayce Dowell, Katherine Elder, Gregg Hallinan, Charlie Harnach, Greg Hellbourg, Jack Hickish, Rick Hobbs, David Hodge, Mark Hodges, Yuping Huang, Andrea Isella, Daniel C. Jacobs, Ghislain Kemby, John T. Klinefelter, Matthew Kolopanis, Nikita Kosogorov, James Lamb, Casey J. Law, Nivedita Mahesh, Brian O'Donnell, Kathryn Plant, Corey Posner, Travis Powell, Vinand Prayag, Andres Rizo, Andrew Romero-Wolf, Jun Shi, Greg Taylor, Jordan Trim, Mike Virgin, Akshatha Vydula, Sandy Weinreb, David Woody
Figure caption: Time-lapse overlap of the Crab Nebula during the solar transit from 2024 June 9 to June 22. Each panel shows the radio image observed at 20:30:05 UT ±5 s (near local noon at OVRO) on the respective days. The corresponding date is indicated by the red bars on top of each panel. The image of the Sun shown in all panels is from 2024 June 12. The FWHM size of the synthesized beam at each frequency and the intrinsic size of the Crab Nebula are marked by red and green circles, respectively.
Paper: Probing the Turbulent Corona and Heliosphere Using Radio Spectral Imaging Observation during the Solar Conjunction of the Crab Nebula
Authors: Peijin Zhang, Surajit Mondal, Bin Chen, Sijie Yu, Dale Gary, Marin M. Anderson, Judd D. Bowman, Ruby Byrne, Morgan Catha, Xingyao Chen, Sherry Chhabra, Larry D'Addario, Ivey Davis, Jayce Dowell, Katherine Elder, Gregg Hallinan, Charlie Harnach, Greg Hellbourg, Jack Hickish, Rick Hobbs, David Hodge, Mark Hodges, Yuping Huang, Andrea Isella, Daniel C. Jacobs, Ghislain Kemby, John T. Klinefelter, Matthew Kolopanis, Nikita Kosogorov, James Lamb, Casey J. Law, Nivedita Mahesh, Brian O'Donnell, Kathryn Plant, Corey Posner, Travis Powell, Vinand Prayag, Andres Rizo, Andrew Romero-Wolf, Jun Shi, Greg Taylor, Jordan Trim, Mike Virgin, Akshatha Vydula, Sandy Weinreb, David Woody
Figure caption: Brightness angular distribution of the Crab on June 13 and June 15. Panels (a1–a3) and (b1–b3) present the brightness temperature distribution sampled at a heliocentric distance of the Crab on different position angles (counterclockwise from the east direction). The black dots mark the peak locations in the distribution. The blue lines in panels (a0) and (b0) show the angular distribution of white-light brightness from LASCO. Panels (a) and (b) on the right present the contours of the source at 36 MHz overlaid on LASCO C2/C3 white-light images of the corresponding nearest time point.
Paper: Probing the Turbulent Corona and Heliosphere Using Radio Spectral Imaging Observation during the Solar Conjunction of the Crab Nebula
Authors: Peijin Zhang, Surajit Mondal, Bin Chen, Sijie Yu, Dale Gary, Marin M. Anderson, Judd D. Bowman, Ruby Byrne, Morgan Catha, Xingyao Chen, Sherry Chhabra, Larry D'Addario, Ivey Davis, Jayce Dowell, Katherine Elder, Gregg Hallinan, Charlie Harnach, Greg Hellbourg, Jack Hickish, Rick Hobbs, David Hodge, Mark Hodges, Yuping Huang, Andrea Isella, Daniel C. Jacobs, Ghislain Kemby, John T. Klinefelter, Matthew Kolopanis, Nikita Kosogorov, James Lamb, Casey J. Law, Nivedita Mahesh, Brian O'Donnell, Kathryn Plant, Corey Posner, Travis Powell, Vinand Prayag, Andres Rizo, Andrew Romero-Wolf, Jun Shi, Greg Taylor, Jordan Trim, Mike Virgin, Akshatha Vydula, Sandy Weinreb, David Woody
Figure caption: The source shape modeled as a 2D elliptical Gaussian and angular Gaussian, for the Crab imaging of 82 MHz on 2024 June 15. The left panel is the 2D Gaussian, where the blue and red dotted lines show the direction of the major and minor axes. The middle panel is the deconvolved Gaussian fitting. The right panel is the angular Gaussian fitted result, where the red and blue dotted lines indicate the θ direction and R radius.