adsabs/AstroCLIMB huggingface dataset:
Paper: Observational Signatures of Tearing Instability in the Current Sheet of a Solar Flare
Authors: Lei Lu, Li Feng, Alexander Warmuth, Astrid M. Veronig, Jing Huang, Siming Liu, Weiqun Gan, Zongjun Ning, Beili Ying, and Guannan Gao
Figure caption: Panel (a): DEM of the quiet coronal region (R1 in Figure 1(g)). Panels (b)–(i): DEM of the blob region (R2 in Figure 1(g)) at eight selected times. The yellow, cyan, and purple colors represent regions in which 50%, 80%, and 95% of 100 Monte Carlo (MC) solutions are contained, respectively. The black line represents the best-fit DEM distribution. The total emission measure and the DEM-weighted temperatures are given in each panel. Three standard deviations (3σ) of the 100 Monte Carlo simulations are regarded as the uncertainties.
Paper: Multipoint Interplanetary Coronal Mass Ejections Observed with Solar Orbiter, BepiColombo, Parker Solar Probe, Wind, and STEREO-A
Authors: Christian Möstl, Andreas J. Weiss, Martin A. Reiss, Tanja Amerstorfer, Rachel L. Bailey, Jürgen Hinterreiter, Maike Bauer, David Barnes, Jackie A. Davies, Richard A. Harrison, Johan L. Freiherr von Forstner, Emma E. Davies, Daniel Heyner, Tim Horbury, and Stuart D. Bale
Figure caption: CME event on 2020 June 23. (a) WSA/THUX background solar wind in the solar equatorial plane and (b) in a meridional plane at the Earth longitude for 2020 June 27 01:00 UT. (c) STEREO-A HI1/2 Jmap with HI1 images of the CME, and the HELCATS time-elongation track of the CME front overlaid as red crosses. (d) In situ magnetic-field data at PSP, and (e) BepiColombo in RTN coordinates and (f) Wind in HEEQ coordinates (total field magnitude in black, Br magenta, Bt orange, Bn blue). (g) Visualization of 3DCORE flux-rope modeling for the 2020 June 25 ICME at PSP in three different viewing angles, with the location of the magnetic flux rope and positions of the spacecraft given for the time 2020 June 25 07:00 UT. In panels (d)–(f), solid vertical lines indicate ICME start times, and dashed lines the boundaries of the magnetic obstacle. In panel (d) the results from 3DCORE ABC–SMC fitting method are given as shaded areas for each magnetic-field component. Note the time shift of 4 days in panels (e) and (f) compared to panel (d).
Paper: Multipoint Interplanetary Coronal Mass Ejections Observed with Solar Orbiter, BepiColombo, Parker Solar Probe, Wind, and STEREO-A
Authors: Christian Möstl, Andreas J. Weiss, Martin A. Reiss, Tanja Amerstorfer, Rachel L. Bailey, Jürgen Hinterreiter, Maike Bauer, David Barnes, Jackie A. Davies, Richard A. Harrison, Johan L. Freiherr von Forstner, Emma E. Davies, Daniel Heyner, Tim Horbury, and Stuart D. Bale
Figure caption: 2020 November 29 CME. (a) WSA/THUX background solar wind in the solar equatorial plane and (b) in a meridional plane at the PSP longitude on 2020 December 1 12:00 UT. (c) GCS fit to STEREO-A COR2 and SOHO LASCO/C3, (d) PSP, and (e) STEREO-A in situ magnetic-field data. (f) Visualization of 3DCORE flux-rope modeling for the 2020 December 1 ICME at PSP in three different viewing angles, with the location of the magnetic flux rope and positions of the spacecraft given for the time 2020 December 1 02:00 UT. In panel (d) the results from 3DCORE ABC–SMC fitting to the PSP flux rope are given as shaded areas for each magnetic-field component.
Paper: Inertial-range Magnetic-fluctuation Anisotropy Observed from Parker Solar Probe’s First Seven Orbits
Authors: L.-L. Zhao, G. P. Zank, L. Adhikari, and M. Nakanotani
Figure caption: The power-law index q of the magnetic trace PSD as a function of radial distance R during PSP's fifth and seventh orbits. The color map indicates the angle between the mean magnetic field in each 1 hr interval and the radial direction θBR. The blue lines with crosses represent the average values of the spectral indices.
Paper: Inertial-range Magnetic-fluctuation Anisotropy Observed from Parker Solar Probe’s First Seven Orbits
Authors: L.-L. Zhao, G. P. Zank, L. Adhikari, and M. Nakanotani
Figure caption: The left panel shows statistics of the transverse-to-longitudinal (Pxx + Pyy)/Pzz power anisotropy (compressibility) as a function of θBR during PSP's fifth orbit. The right panel shows the transverse power anisotropy Pyy/Pxx as a function of θBR. The color map indicates the radial distance R dependence. The black and blue lines with crosses in the left and right panels represent the average values of (Pxx + Pyy)/Pzz and Pyy/Pxx, respectively.
Paper: Inertial-range Magnetic-fluctuation Anisotropy Observed from Parker Solar Probe’s First Seven Orbits
Authors: L.-L. Zhao, G. P. Zank, L. Adhikari, and M. Nakanotani
Figure caption: The transverse-to-longitudinal power anisotropy (Pxx + Pyy)/Pzz as functions of the proton plasma beta βp (left panel) and the ratio of magnetic-fluctuation amplitude and mean magnetic-field strength δB/B0 (right panel) during PSP's fifth orbit. The color map indicates the θBR dependence for both panels. The two solid black lines denote power-law fits for the relation with βp and δB/B0, respectively. The two blue dashed lines are from Smith et al. (2006) and are used to fit the corresponding relation of intervals with open field lines at 1 au.
Paper: Inertial-range Magnetic-fluctuation Anisotropy Observed from Parker Solar Probe’s First Seven Orbits
Authors: L.-L. Zhao, G. P. Zank, L. Adhikari, and M. Nakanotani
Figure caption: Statistics of the transverse power anisotropy Pyy/Pxx as a function of the sampling angle θBR during PSP's fifth orbit. The data are split into two groups by radial distance from the Sun. The left panel is for radial distances between 0.13 and 0.3 au; the right panel is for radial distances between 0.3 and 0.6 au. The red curves are the model results.
Paper: Improving Planet Detection with Disk Modeling: Keck/NIRC2 Imaging of the HD 34282 Single-armed Protoplanetary Disk
Authors: Juan Quiroz, Nicole L. Wallack, Bin Ren, Ruobing Dong, Jerry W. Xuan, Dimitri Mawet, Maxwell A. Millar-Blanchaer, and Garreth Ruane
Figure caption: Keck/NIRC2 imaging and modeling of the HD 34282 system in the L′-band. (a) Reduction result of the original exposures. (b) SPHERE ﹩{{ \mathcal Q }}_{\phi }﹩ image, following annotations in Figure 2 of de Boer et al. (2021). (c) SPHERE contours overlaid on the NIRC2 image: we confirm the existence of the B1 spiral. (d) Best-fit disk model for the NIRC2 ring. (e) Best-fit disk model with instrumentation effects taken into account (i.e., convolution, transmission) for a representative one of the 69 exposures: the actual convolution is performed for all of the exposures. (f) Reduction residuals after removing the best-fit instrumental disk model from the original exposures. Note: the images are shown in log scale, the dashed central region with a 20 pixel radius is masked out in our data analysis; and the SPHERE data have different display limits than the NIRC2 data.(The data used to create this figure are available.)
Paper: Improving Planet Detection with Disk Modeling: Keck/NIRC2 Imaging of the HD 34282 Single-armed Protoplanetary Disk
Authors: Juan Quiroz, Nicole L. Wallack, Bin Ren, Ruobing Dong, Jerry W. Xuan, Dimitri Mawet, Maxwell A. Millar-Blanchaer, and Garreth Ruane
Figure caption: 5σ detection limit of point sources as a function of radial separation for our observations. The red dashed line is the contrast curve for the original data, and the black solid line is the contrast curve for the data with the best-fit disk model removed. By dividing the two contrast curves (see blue dashed–dotted line), we obtain a better overall detection limit. For the disk region, when removing the disk, we are more sensitive by a factor of ∼2 over the original data in panel (a), and ∼1.6 for the high-pass filtered data in panel (b).
Paper: Improving Planet Detection with Disk Modeling: Keck/NIRC2 Imaging of the HD 34282 Single-armed Protoplanetary Disk
Authors: Juan Quiroz, Nicole L. Wallack, Bin Ren, Ruobing Dong, Jerry W. Xuan, Dimitri Mawet, Maxwell A. Millar-Blanchaer, and Garreth Ruane
Figure caption: Mass limits using the AMES–Cond models for our observations with the disk present (in red) and after removing the disk (in black) as a function of separation in au (after accounting for the effects of an inclination-based projection). The width of the shaded regions account for uncertainties in the distance, age, and magnitude of the host star. We are sensitive to planets ∼10 MJupiter smaller after removing the best-fitting disk model in the region where the disk is present. Note: the minimum stellocentric separation presented here is outside the coronagraph to avoid possible coronagraphic occultation; future analysis at shorter separations should take the occultation probability into account.
Paper: Follow-up Observations of the Prolonged, Super-Eddington, Tidal Disruption Event Candidate 3XMM J150052.0+015452: the Slow Decline Continues
Authors: Dacheng Lin, Olivier Godet, Natalie A. Webb, Didier Barret, Jimmy A. Irwin, S. Komossa, Enrico Ramirez-Ruiz, W. Peter Maksym, Dirk Grupe, and Eleazar R. Carrasco
Figure caption: Top panel: the long-term evolution of the X-ray luminosity (0.34–11.5 keV, source rest frame, corrected for both Galactic and intrinsic absorption) from XMM-Newton (red triangles), Chandra (blue squares), and Swift observations (green circles). Errors are at the 90% confidence level, except for C1, for which the 3σ upper limit was given. The solid line is a model of disrupting a 0.75 M⊙ star by a BH of mass 2.2 × 105 M⊙ with slow circularization and super-Eddington effects (see text). The dashed line plots a standard TDE model of t−5/3, assuming a peak X-ray luminosity the same as XJ1500+0154 and occuring at two months after the stellar disruption. Bottom panels: sample unfolded X-ray spectra. X1, C10, X4–X6, and X7 are fitted with a diskbb (red dotted line) plus PL (green dotted–dashed line) model, while the others were fitted with the nthComp model. For visual purpose, the spectra are rebinned to be above 2σ in each bin in the plot, and for XMM-Newton observations, only pn spectra are shown.
Paper: Follow-up Observations of the Prolonged, Super-Eddington, Tidal Disruption Event Candidate 3XMM J150052.0+015452: the Slow Decline Continues
Authors: Dacheng Lin, Olivier Godet, Natalie A. Webb, Didier Barret, Jimmy A. Irwin, S. Komossa, Enrico Ramirez-Ruiz, W. Peter Maksym, Dirk Grupe, and Eleazar R. Carrasco
Figure caption: Left panels: the two HST images around the field of XJ1500+0154. The blue cross marks the center of its host galaxy, and the green circle of radius 0.″18 (0.5 kpc) indicates the 95% positional uncertainty of the source from the Chandra observation C10. Right panels: GALFIT residuals with two Sérsic functions.
Paper: Plasma Emission Induced by Electron Beams in Weakly Magnetized Plasmas
Authors: Yao Chen, Zilong Zhang, Sulan Ni, Chuanyang Li, Hao Ning, and Xiangliang Kong
Figure caption: (a) Energy variations of the six field components and the negative change of the total electron energy (−ΔEk) for Case R (solid lines) and Case T (dashed lines); (b) energy variations of specific field components of various wave modes for Case R (BL for the beam-Langmuir mode, W for Whistler, O–F for the fundamental, and H for the harmonic PE); panels (c)–(e) illustrate the VDFs at three moments. Overplotted in panel (c) are two resonance curves of the W mode with the following (ω, k, θ) values: [0.1 Ωce, 4.5 Ωce/c, 30°] and [0.3 Ωce, 12.3 Ωce/c, 60°]. The two dashed lines in panels (a)–(b) represent ﹩t=80\ {\omega }_{\mathrm{pe}}^{-1}﹩ and ﹩t=300\ {\omega }_{\mathrm{pe}}^{-1}﹩.
Paper: Plasma Emission Induced by Electron Beams in Weakly Magnetized Plasmas
Authors: Yao Chen, Zilong Zhang, Sulan Ni, Chuanyang Li, Hao Ning, and Xiangliang Kong
Figure caption: Intensity maps of the six field components in the wave-vector k space for Case R. Right columns of panels are the zoomed-in version of the square region plotted in the top-left panel. The dashed line indicates the propagation angle of (θ = 30°) along which the ω, k dispersion maps are plotted in Figure 3.
Paper: Plasma Emission Induced by Electron Beams in Weakly Magnetized Plasmas
Authors: Yao Chen, Zilong Zhang, Sulan Ni, Chuanyang Li, Hao Ning, and Xiangliang Kong
Figure caption: The Fourier spectra in the k space for density fluctuations of electrons (δne) and protons (δnp). The bottom panels are for the low-frequency regime of the (ω, k) spectra; overplotted dashed lines are the standard IA dispersion relation.
Paper: Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection
Authors: B. Ripperda, M. Liska, K. Chatterjee, G. Musoke, A. A. Philippov, S. B. Markoff, A. Tchekhovskoy, and Z. Younsi
Figure caption: Plasmoid-mediated reconnection, which takes place at sufficiently high resolutions in MHD, is seen in a 3D GRMHD simulation for the first time. Resolving the dynamics of X-points and plasmoids in the current sheet can be the key to understanding the source of black hole nonthermal emission, e.g., high-energy flares. Dimensionless temperature T = p/ρ, plasma-β, and density ρ (from left to right) in the meridional plane before (top row), during (middle row) in the inner 10rg, and after (bottom row) the large magnetic flux eruption in the inner 40rg. During the magnetic flux eruption, the accretion disk is ejected, and the broad accretion inflow is reduced to a thin plasmoid-unstable current sheet, indicated by X-points and magnetic nulls shown by the antiparallel in-plane field lines (in green; see inset in panel (D)) and the high β (inset panel (E)). The hot (﹩T\sim {\sigma }_{\max }﹩) exhaust of the reconnection layer heats the jet sheath. Reconnection transforms the horizontal field in the current sheet to a vertical field that is ejected in the form of hot coherent flux tubes (panel (G)) at low β and density (panels (H), (I)).
Paper: Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection
Authors: B. Ripperda, M. Liska, K. Chatterjee, G. Musoke, A. A. Philippov, S. B. Markoff, A. Tchekhovskoy, and Z. Younsi
Figure caption: Our extreme-resolution simulation reveals small-scale structure and interface instabilities of magnetic flux bundles escaping from the black hole, in an equatorial slice through the system. Dimensionless temperature T = p/ρ, plasma-β, and density ρ (from left to right) in the equatorial plane before a large magnetic flux eruption (top row), during the magnetic flux eruption (middle row) in the inner 10rg and after the magnetic flux eruption (bottom row) in the inner 40rg. Gaps of low β and density form during the preeruption quiescence, while many azimuthal RTI modes accrete. During the magnetic flux eruption a single large T > 1 spiral forms with a gap where the sheet moved out of the equatorial plane. Magnetic flux escapes through the spiral current sheet, while accretion continues over a small angle ϕ < 2π at x ≈ 2rg and y ≈ −1 to y ≈ −2. In the bottom row, the inner 10rg is in quiescent accretion state, and a hot flux tube that is ejected from the reconnection layer is in orbit at x ≈ 10rg to x ≈ 30rg and y ≈ − 10rg to y ≈ 20rg. The low-β flux tube shows clear signatures of instabilities at its boundaries mixing low-density plasma into the disk.
Paper: Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection
Authors: B. Ripperda, M. Liska, K. Chatterjee, G. Musoke, A. A. Philippov, S. B. Markoff, A. Tchekhovskoy, and Z. Younsi
Figure caption: Volume rendering of the temperature T = p/ρ shows plasmoids and hot current sheets. Extreme resolution allows the current sheets to become thinner and hotter than typically seen in GRMHD simulations. (Panel (A):) During a large flare, a relativistically hot T > 1 spiral current sheet forms. Accretion occurs over a small azimuthal angle ϕ < 2π in the T < 1 (white) regions. The green field lines, seeded in the current sheet (T > 1), remain in the current sheet and are mostly attached to the black hole. Blue field lines are seeded in the disk, where some disk field lines are accreting onto the black hole in the T < 1 region. (Panel (B):) In the quiescent state, T ≤ 1 everywhere, and both green and blue field lines (with the same seeds as in panel (A)) are in the disk, accreting onto the black hole. The inset (C) shows a zoom into the inner rg in the flare state with multiple escaping flux loops (green field lines). In the small black box, we highlight an escaping flux tube with vertical field as the result of reconnection (green) and an infalling flux tube (purple). We also show a plasmoid, indicated by the helical field line (green) in the second small black box.
Paper: Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection
Authors: B. Ripperda, M. Liska, K. Chatterjee, G. Musoke, A. A. Philippov, S. B. Markoff, A. Tchekhovskoy, and Z. Younsi
Figure caption: The equatorial current sheet that forms during the magnetic flux eruption is unresolved at low and standard resolutions (panels (A), (B)) such that magnetic field lines (green lines) diffuse through the current sheet and do not reconnect, due to the high numerical resistivity. At high and extreme resolutions (C,D), the field lines are antiparallel in the current sheet, and they reconnect in well-defined X-points. Smaller current sheets are resolved in the accretion disk at high and extreme resolutions, potentially heating the plasma through reconnection. Panel (E) shows the magnetic flux on the horizon for the four numerical resolutions. The extreme- and high-resolution runs show two and three large flare periods, respectively, indicated by flux decay at a rate ∝ e−t/500 governed by the reconnection rate (dashed black lines). A miniflare is indicated by the small flux drop at t ≈ 6800rg c−1 in the extreme-resolution run. The standard- and low-resolution runs show a faster flux decay ∝ e−t/350 governed by the enhanced reconnection rate due to an increased numerical resistivity. Flares in the extreme-resolution run are accompanied by clear drops in the mass accretion rate (panel (G)), due to the expulsion of the disk over a large azimuthal angle. Panel (F) shows a cut through the equatorial current sheet at x ≈ 1.5rg during the flare state (indicated by the red dashed line in panels (A)–(D)). Both the (nearly) radial field BL and the (nearly) toroidal field BM components (see definition in the text) change sign in the equatorial current sheet, while BN is (close to) zero, indicating zero-guide field reconnection. Panel (H) shows the flow speeds left and right of the current sheet. After correcting for the bulk flow, we measure the reconnection rate to be vrec ≈ 0.01c. We confirm this measurement at 10 radial cuts during separate flare periods.
Paper: Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection
Authors: B. Ripperda, M. Liska, K. Chatterjee, G. Musoke, A. A. Philippov, S. B. Markoff, A. Tchekhovskoy, and Z. Younsi
Figure caption: Smaller flux eruptions show shorter current sheets, potentially powering miniflares that are not accompanied by a large-scale evacuation of the accretion disk. Meridional (top row) and equatorial (bottom row) cuts of temperature T = p/ρ (left), plasma-β (middle), and density ρ (right) during the miniflare at t = 6852rg c−1. The magnetic flux is expelled through a smaller (w ≲ 3rg) current sheet, close to the horizon, in a short time ≪ 100rg c−1. The accretion disk is not expelled over a large azimuthal angle, yet the flare is accompanied by a significant drop in the mass accretion rate (see Figure 4(G)) and clear gaps in the density (F). Multiple small current sheets are visible in the accretion disk at x ≥ 3rg indicated by the high plasma-β (B).
Paper: Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection
Authors: B. Ripperda, M. Liska, K. Chatterjee, G. Musoke, A. A. Philippov, S. B. Markoff, A. Tchekhovskoy, and Z. Younsi
Figure caption: Lorentz factor Γ (top rows) and temperature T = p/ρ for the extreme-resolution 3D run with density floor ﹩{\sigma }_{\max }=25﹩ (left) and two supplementary 2D runs with density floors ﹩{\sigma }_{\max }=60﹩ (middle) and ﹩{\sigma }_{\max }=100﹩ (right). Reconnection heats up the plasma in the equatorial current sheet to ﹩T\sim {\sigma }_{\max }﹩ and ﹩{\rm{\Gamma }}\sim \sqrt{{\sigma }_{\max }}﹩. The hot reconnection exhaust heats up the jet sheath up to temperatures proportional to the magnetization in the jet. We observe limb-brightened jets up to at least 20rg.
Paper: Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection
Authors: B. Ripperda, M. Liska, K. Chatterjee, G. Musoke, A. A. Philippov, S. B. Markoff, A. Tchekhovskoy, and Z. Younsi
Figure caption: Top row: profiles of the magnetic field in minimum variance coordinates in a current sheet in the high- (A), standard- (B), and low-resolution (C) runs, as in Figure 4. Bottom row: profile of the inflow speed into the current sheet, showing a reconnection rate of 0.01c for high resolution (D), and enhanced reconnection rates of 0.02c (standard resolution; E) and 0.025c (low resolution; F) as a result of a larger numerical resistivity and a broader current sheet (top panels).
Paper: Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection
Authors: B. Ripperda, M. Liska, K. Chatterjee, G. Musoke, A. A. Philippov, S. B. Markoff, A. Tchekhovskoy, and Z. Younsi
Figure caption: Magnetic flux on the horizon (top) and mass accretion rate at 5rg (bottom) for low (green line), standard (blue line), high (red line), and extreme (magenta line) resolution. Large flares, accompanied by a significant drop of 1 order of magnitude in the mass accretion rate, show a faster flux decay time ∝ e−t/350 than the flux decay at higher resolution ∝ e−t/500 due to the enhanced reconnection rate at lower resolutions. Miniflares not accompanied by a significant flux drop follow the flux decay rate ∝ e−t/500 because the current sheet is shorter and therefore better resolved due to the spherically logarithmic grid close to the event horizon.
Paper: Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection
Authors: B. Ripperda, M. Liska, K. Chatterjee, G. Musoke, A. A. Philippov, S. B. Markoff, A. Tchekhovskoy, and Z. Younsi
Figure caption: Dimensionless temperature T = p/ρ (left), plasma-β (middle), and density ρ (right) in the meridional plane (first and third rows) and equatorial plane (second and fourth rows) during a magnetic flux eruption in the inner 10rg (first and second row) and during quiescence in the inner 40rg (third and fourth row).
Paper: First Evidence of Intrinsic Alignments of Red Galaxies at z > 1: Cross Correlation between CFHTLenS and FastSound Samples
Authors: Motonari Tonegawa, and Teppei Okumura
Figure caption: Projected correlation functions, wg+ (top) and wg× (bottom) as a function of transverse separation ﹩{\bar{r}}_{p}﹩. We use the FastSound sample for the galaxy density field for all the measurements presented here. We use the different shape samples as the galaxy shape field for different lines: red galaxies (red lines) and blue galaxies (blue solid lines). The blue dashed line is the GI correlation of the FastSound blue galaxies measured by Tonegawa et al. (2018). The dark and light red shaded regions in the top panel indicate the 68% and 95% confidence intervals of the best-fitting NLA model obtained for red galaxies at ﹩{\bar{r}}_{p}\gt 3\,{h}^{-1}\,\mathrm{Mpc}﹩ denoted by the vertical lines. The error bars are obtained from the diagonal elements of the covariance matrix, ﹩{C}_{\mathrm{ii}}^{1/2}﹩.
Paper: First Evidence of Intrinsic Alignments of Red Galaxies at z > 1: Cross Correlation between CFHTLenS and FastSound Samples
Authors: Motonari Tonegawa, and Teppei Okumura
Figure caption: Constraints on the amplitude of the NLA model as a function of redshift. The points are color-coded according to the mean sample luminosity, and different symbols are assigned to different survey samples (see Table 1). The dashed lines are the best-fitting model prediction at z = 0.54 obtained by Joachimi et al. (2011; Equation (7)) for 〈Mr〉 = −21.45 (green) and −20.35 (blue).