adsabs/AstroCLIMB huggingface dataset:
Paper: Tracking Halo Orbits and Their Mass Evolution around Large-scale Filaments
Authors: Hannah Jhee, Hyunmi Song, Rory Smith, Jihye Shin, Inkyu Park, Clotilde Laigle
Figure caption: Phase-space distributions at z = 0 of halos subsampled by time since first crossing: [0, 1), [1, 2.5), [2.5, 6), and [6, 13.5) Gyr from left to right. The number of halos in each panel is 498, 491, 470, and 219, respectively. The color map is according to the mean time since first crossing (〈t FC〉) of halos in a given hexagonal bin.
Paper: Tracking Halo Orbits and Their Mass Evolution around Large-scale Filaments
Authors: Hannah Jhee, Hyunmi Song, Rory Smith, Jihye Shin, Inkyu Park, Clotilde Laigle
Figure caption: The three-dimensional dark matter density distribution of one of the realizations of N-cluster Run (left) and large-scale filament structures identified by DISPERSE in red (right).
Paper: Tracking Halo Orbits and Their Mass Evolution around Large-scale Filaments
Authors: Hannah Jhee, Hyunmi Song, Rory Smith, Jihye Shin, Inkyu Park, Clotilde Laigle
Figure caption: The matrix of the Pearson correlation coefficients among six parameters shown in Table 1. The correlation coefficients are calculated using crossers only.
Paper: Perfecting Our Set of Spectrophotometric Standard DA White Dwarfs
Authors: Annalisa Calamida, Thomas Matheson, Edward W. Olszewski, Abhijit Saha, Tim Axelrod, Clare Shanahan, Jay Holberg, Sean Points, Gautham Narayan, Konstantin Malanchev, Ryan Ridden-Harper, Nicola Gentile-Fusillo, Roberto Raddi, Ralph Bohlin, Armin Rest, Ivan Hubeny, Susana Deustua, John Mackenty, Elena Sabbi, Christopher W. Stubbs
Figure caption: Hammer–Aitoff projection of our network of spectrophotometric standard DAWDs. This includes 19 DAWDs distributed in the Northern hemisphere and around the celestial equators (blue stars) and 13 in the Southern hemisphere (pink).
Paper: Perfecting Our Set of Spectrophotometric Standard DA White Dwarfs
Authors: Annalisa Calamida, Thomas Matheson, Edward W. Olszewski, Abhijit Saha, Tim Axelrod, Clare Shanahan, Jay Holberg, Sean Points, Gautham Narayan, Konstantin Malanchev, Ryan Ridden-Harper, Nicola Gentile-Fusillo, Roberto Raddi, Ralph Bohlin, Armin Rest, Ivan Hubeny, Susana Deustua, John Mackenty, Elena Sabbi, Christopher W. Stubbs
Figure caption: Spectra collected with the Goodman spectrograph on the 4 m SOAR telescope (NOIRLab) for the 13 confirmed spectrophotometric standard DAWDs with HST and LCO follow-up observations.
Paper: Perfecting Our Set of Spectrophotometric Standard DA White Dwarfs
Authors: Annalisa Calamida, Thomas Matheson, Edward W. Olszewski, Abhijit Saha, Tim Axelrod, Clare Shanahan, Jay Holberg, Sean Points, Gautham Narayan, Konstantin Malanchev, Ryan Ridden-Harper, Nicola Gentile-Fusillo, Roberto Raddi, Ralph Bohlin, Armin Rest, Ivan Hubeny, Susana Deustua, John Mackenty, Elena Sabbi, Christopher W. Stubbs
Figure caption: Spectra collected with the Goodman spectrograph on the 4 m SOAR telescope (NOIRLab) for candidate DAWDs that were discarded from the Southern hemisphere sample (continues in Figure 4). The first and second star, WD0756-607 and WD0418-534, were excluded from our network of standards due to their variability and other reasons. See text for more details.
Paper: Perfecting Our Set of Spectrophotometric Standard DA White Dwarfs
Authors: Annalisa Calamida, Thomas Matheson, Edward W. Olszewski, Abhijit Saha, Tim Axelrod, Clare Shanahan, Jay Holberg, Sean Points, Gautham Narayan, Konstantin Malanchev, Ryan Ridden-Harper, Nicola Gentile-Fusillo, Roberto Raddi, Ralph Bohlin, Armin Rest, Ivan Hubeny, Susana Deustua, John Mackenty, Elena Sabbi, Christopher W. Stubbs
Figure caption: Same as Figure 3 but for different candidate DAWDs discarded from our Southern hemisphere sample. The last star could be a DQWD, showing the C2 Swan band at λ ≈ 5150 Å.
Paper: The Metallicity and Distance of NGC 2403 from Blue Supergiants
Authors: Fabio Bresolin, Rolf-Peter Kudritzki, Miguel A. Urbaneja
Figure caption: Position of the spectroscopic targets in a g-band image of NGC 2403 taken from the Sloan Digital Sky Survey. The boxes represent the footprints of the ACS observations, source of the HST photometry. The different colors of the markers and labels are only used to enhance their visibility. The outer ring represents the projected circle having a radius equal to the isophotal radius r 25.
Paper: The Metallicity and Distance of NGC 2403 from Blue Supergiants
Authors: Fabio Bresolin, Rolf-Peter Kudritzki, Miguel A. Urbaneja
Figure caption: Fits of the model (red curve) to the observed (black curve) Balmer lines H4 to H10 for the A2 Ia star #28 (left) and the B1 Ia star #43 (right). The abscissa reports the distance in Å from the line center. Some moderate nebular line contamination can be noticed in the case of the Hβ (H4) line for #28, while for #43 the contamination is much stronger, affecting also Hγ (H5).
Paper: The Metallicity and Distance of NGC 2403 from Blue Supergiants
Authors: Fabio Bresolin, Rolf-Peter Kudritzki, Miguel A. Urbaneja
Figure caption: Fits of the model (red curve) to the observed (black curve) metal lines of stars #28 (type A2 Ia; at the top in each panel) and #38 (A1–A2 Ia; bottom) inside three wavelength windows. Lines from the main atomic species used to calculate the synthetic spectra are identified.
Paper: The Metallicity and Distance of NGC 2403 from Blue Supergiants
Authors: Fabio Bresolin, Rolf-Peter Kudritzki, Miguel A. Urbaneja
Figure caption: Examples of the stellar classification analysis. Each subpanel includes both the identification from Table 1 (column (1)) and the spectral type. The spectra are smoothed to an FWHM resolution of 5 Å. The main spectral features used for the classification are identified.
Paper: The Metallicity and Distance of NGC 2403 from Blue Supergiants
Authors: Fabio Bresolin, Rolf-Peter Kudritzki, Miguel A. Urbaneja
Figure caption: Fits of the model (red curve) to the observed (black curve) metal lines of star #43 (type B1 Ia) inside five wavelength windows. Lines from the main atomic species used to calculate the synthetic spectra are identified.
Paper: The Metallicity and Distance of NGC 2403 from Blue Supergiants
Authors: Fabio Bresolin, Rolf-Peter Kudritzki, Miguel A. Urbaneja
Figure caption: Spectroscopic Hertzsprung–Russell diagram for the blue supergiant sample of Table 2. A selection of intermediate-mass evolutionary tracks with rotation from Ekstrom et al. (2012) is included.
Paper: The SDSS-Gaia View of the Color–Magnitude Relation for Blue Horizontal-branch Stars
Authors: Fabrícia O. Barbosa, Rafael M. Santucci, Silvia Rossi, Guilherme Limberg, Angeles Pérez-Villegas, Hélio D. Perottoni
Figure caption: Left panels: color–magnitude diagrams showing BHBs used to define the calibrations. Dashed–dotted line represents the polynomial fit defined in D11. Solid lines represent the calibration for (g − r)0 and (u − r)0 color presented in this work (Equations (1) and (2), respectively, from top to bottom). Median errors of the data are indicated in the bottom right corner of each panel. Right panels: difference between distances calculated with D11's calibration and those presented in this work, respectively, (g − r)0 (top) and (u − r)0 (bottom).
Paper: The SDSS-Gaia View of the Color–Magnitude Relation for Blue Horizontal-branch Stars
Authors: Fabrícia O. Barbosa, Rafael M. Santucci, Silvia Rossi, Guilherme Limberg, Angeles Pérez-Villegas, Hélio D. Perottoni
Figure caption: Comparison between the distances estimated by Equation (2) (﹩{D}_{{(u-r)}_{0}}﹩), geometric (D geo, left) and photogeometric (D phot, right) distances from Bailer-Jones et al. (2021). Colors indicate Gaia G magnitude and gray area indicates the region of 1σ. Median errors are indicated in the bottom right corner of the top panels.
Paper: The SDSS-Gaia View of the Color–Magnitude Relation for Blue Horizontal-branch Stars
Authors: Fabrícia O. Barbosa, Rafael M. Santucci, Silvia Rossi, Guilherme Limberg, Angeles Pérez-Villegas, Hélio D. Perottoni
Figure caption: Boxplot for relative distance difference using each calibration presented in this work (Equations (1) and (2)) and that from D11. D  V21 is the distance provided by Vasiliev & Baumgardt (2021), inferred from Gaia EDR3 data. The number of data points in each cluster is displayed at the bottom of the panel.
Paper: The SDSS-Gaia View of the Color–Magnitude Relation for Blue Horizontal-branch Stars
Authors: Fabrícia O. Barbosa, Rafael M. Santucci, Silvia Rossi, Guilherme Limberg, Angeles Pérez-Villegas, Hélio D. Perottoni
Figure caption: Error comparison between fits for some combinations of magnitudes, colors, and [Fe/H] from TuringBot.
Paper: Quijote-PNG: Quasi-maximum Likelihood Estimation of Primordial Non-Gaussianity in the Nonlinear Dark Matter Density Field
Authors: Gabriel Jung, Dionysios Karagiannis, Michele Liguori, Marco Baldi, William R. Coulton, Drew Jamieson, Licia Verde, Francisco Villaescusa-Navarro, Benjamin D. Wandelt
Figure caption: The typical size of the bias on estimated parameters, divided by their corresponding Fisher error bars, as a function of the number of simulations used to compute derivatives. We analyze QUIJOTE simulations for three different cosmologies, fiducial (left panel), ﹩{f}_{\mathrm{NL}}^{\mathrm{local}}=100﹩ (middle panel), and ﹩{f}_{\mathrm{NL}}^{\mathrm{equil}}=100﹩ (right panel), and include both the power spectrum and the bispectrum up to ﹩{k}_{\max }=0.5\,h\,{\mathrm{Mpc}}^{-1}﹩. The solid lines correspond to data sets of 10 simulations, while the dashed lines correspond to data sets of 100 simulations.
Paper: Quijote-PNG: Quasi-maximum Likelihood Estimation of Primordial Non-Gaussianity in the Nonlinear Dark Matter Density Field
Authors: Gabriel Jung, Dionysios Karagiannis, Michele Liguori, Marco Baldi, William R. Coulton, Drew Jamieson, Licia Verde, Francisco Villaescusa-Navarro, Benjamin D. Wandelt
Figure caption: Cosmological and PNG amplitude parameters estimated from several sets of 10 N-body simulations for different ﹩{k}_{\max }﹩ with a different amount of local PNG in their initial conditions. The orange circles, green squares, and purple crosses correspond respectively to ﹩{f}_{\mathrm{NL}}^{\mathrm{local}}=40﹩, 0, and −40, and the vertical dashed lines are the expected standard errors on the average from 10 simulations. The horizontal dashed lines are the expected values of the different data sets. The vertical scale is linear around 0, and logarithmic close to the edges.
Paper: The Quantitative Relation of the Time Profiles of Intensities in the Well-connected Solar Energetic Particle Events
Authors: Yang Wang, Dan Lyu, Xinghui Wu, Gang Qin
Figure caption: From top to bottom: the SEP intensities (panels 1 to 4), magnetic field intensity (panel 5), and solar wind speed (panel 6) in the 2013 October 11 event. OMNI data are used instead of the plasma data observed by SOHO to improve the statistics.
Paper: Quijote-PNG: Quasi-maximum Likelihood Estimation of Primordial Non-Gaussianity in the Nonlinear Dark Matter Density Field
Authors: Gabriel Jung, Dionysios Karagiannis, Michele Liguori, Marco Baldi, William R. Coulton, Drew Jamieson, Licia Verde, Francisco Villaescusa-Navarro, Benjamin D. Wandelt
Figure caption: The error bars of the quasi-maximum likelihood estimator as a function of the number of realizations used to calculate the covariance matrix. We analyze the 8000 QUIJOTE simulations at z = 1, including both the power spectrum and the bispectrum, up to ﹩{k}_{\max }=0.5\,h\,{\mathrm{Mpc}}^{-1}﹩. All error bars are divided by their corresponding Fisher prediction, as described in Section 4.3.
Paper: Quijote-PNG: Quasi-maximum Likelihood Estimation of Primordial Non-Gaussianity in the Nonlinear Dark Matter Density Field
Authors: Gabriel Jung, Dionysios Karagiannis, Michele Liguori, Marco Baldi, William R. Coulton, Drew Jamieson, Licia Verde, Francisco Villaescusa-Navarro, Benjamin D. Wandelt
Figure caption: Impact of cosmological parameters on the matter bispectrum (ratio bispectrum with a modified parameter to fiducial, averaged from 500 N-body simulations).
Paper: The Quantitative Relation of the Time Profiles of Intensities in the Well-connected Solar Energetic Particle Events
Authors: Yang Wang, Dan Lyu, Xinghui Wu, Gang Qin
Figure caption: Locations of the two STEREO spacecraft and the Earth (SOHO) in the ecliptic plane between 2007 June and 2015 June.
Paper: The Quantitative Relation of the Time Profiles of Intensities in the Well-connected Solar Energetic Particle Events
Authors: Yang Wang, Dan Lyu, Xinghui Wu, Gang Qin
Figure caption: Variation of energetic particle intensity with time (dots) and fitting results (blue line) in the 2013 October 11 event. The red dots represent a varying background of the SEP intensity. The x-axis represents the time (day of the year) and the y-axis represents the logarithm of the intensity of 40–64 MeV protons.
Paper: Quijote-PNG: Quasi-maximum Likelihood Estimation of Primordial Non-Gaussianity in the Nonlinear Dark Matter Density Field
Authors: Gabriel Jung, Dionysios Karagiannis, Michele Liguori, Marco Baldi, William R. Coulton, Drew Jamieson, Licia Verde, Francisco Villaescusa-Navarro, Benjamin D. Wandelt
Figure caption: Impact of cosmological parameters on the matter power spectrum (averaged from 500 N-body simulations). Solid and dashed lines correspond respectively to values perturbed above and below the fiducial.
Paper: The Nonpotentiality of Steady-state Coronal Magnetic Field Derived with Time-relaxation Magnetohydrodynamics Simulations Using Helioseismic and Magnetic Imager Three-component Magnetic Field Data
Authors: Keiji Hayashi, Chin-Chun Wu, Kan Liou
Figure caption: The simulated coronal magnetic field lines, viewed from 90° Carrington longitude and 7° South: Clockwise from top left, those derived from (a) the first relaxation simulation where only the radial component B  r  is used as the boundary values, (b) the E-driven second relaxation simulation with boundary treatment BT3, (d) BT2 and (c) BT1 are shown. The cyan (orange) color on the field lines indicates the positive (negative) twist of the field lines, ﹩\alpha =\vec{B}\cdot ({\rm{\nabla }}\times \vec{B})/{B}^{2}﹩. The colors are truncated at α =± 2π/(10R ☉). The sign of α is overall unchanged along each field line. The blue (red) color on the solar surface sphere represents the positive (negative) values of the solar surface boundary B  r , truncated at ±10 G.
Paper: The Nonpotentiality of Steady-state Coronal Magnetic Field Derived with Time-relaxation Magnetohydrodynamics Simulations Using Helioseismic and Magnetic Imager Three-component Magnetic Field Data
Authors: Keiji Hayashi, Chin-Chun Wu, Kan Liou
Figure caption: The radially integrated current density from the bottom boundary (at r = 1.01 R ☉) to 1.3 R ☉, ﹩{\int }_{1.01{R}_{\odot }}^{1.3{R}_{\odot }}| \vec{J}| {dr}﹩. The polarity inversion lines (PILs) are drawn with thick dashed lines as the contour lines for B  r  = 0. The thin lines are the projection of the simulated field lines that do not reach 1.3 R ☉ or higher onto the longitude–latitude plane.
Paper: The Nonpotentiality of Steady-state Coronal Magnetic Field Derived with Time-relaxation Magnetohydrodynamics Simulations Using Helioseismic and Magnetic Imager Three-component Magnetic Field Data
Authors: Keiji Hayashi, Chin-Chun Wu, Kan Liou
Figure caption: The solar surface magnetic field for Carrington Rotation 2106. The three components of the bottom-boundary magnetic field in the first relaxed state are shown in the left column, (a–(c). In the right column, (d)–(f), the three components of the HMI synoptic map data smoothed with the Gaussian function are shown. The simulated boundary radial component is fixed all through the two simulation steps, hence its distribution is always identical to the observation data. In the second simulation step, the two horizontal components of the first time-relaxed state, (b) and (c), are altered to the observed values, (e) and (f), as ﹩\partial \vec{B}=-{\rm{\nabla }}\times \vec{E}﹩.
Paper: The Nonpotentiality of Steady-state Coronal Magnetic Field Derived with Time-relaxation Magnetohydrodynamics Simulations Using Helioseismic and Magnetic Imager Three-component Magnetic Field Data
Authors: Keiji Hayashi, Chin-Chun Wu, Kan Liou
Figure caption: Scatter plots of the magnetic field components given from observations and those in the time-relaxed states. From top to bottom, the simulated boundary ﹩\vec{B}﹩ components of the first relaxed state, and the three second relaxed states with boundary treatment BT3, BT2, and BT1 are compared with the smoothed synoptic map data from the HMI observations. In each column from left to right, the compared component is the radial (B  r ), colatitudinal (B  θ ), and longitudinal (B  ϕ ) component. The colors represent the area-weighted counts, in units of 10−6 of the whole sphere (﹩4\pi {R}_{\odot }^{2}﹩), sampled over a range from −10G to +10G at every 0.1G bin.
Paper: Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers
Authors: Raheem Beg, Alexander J. B. Russell, Gunnar Hornig
Figure caption: Comparison plot of different flux functions that can be used as a proxy to measure the reconnection rate. Dark blue: flux Φ1; light blue: modified flux Φ2; light green and (dashed) dark green: loss of poloidal fluxes Φ P  from the upper and lower laminar flux ropes; and pink and (dashed) purple: loss of toroidal fluxes Φ T  from the upper and lower laminar flux ropes, scaled down by the average flux ratio over t ∈ [2.4, 5.0] of Φ T /Φ P  ≈ 2.61. The vertical dotted lines indicate times of interest: (c) turbulent reconnection onset (t = 1.0); (e) SGTR onset (t = 2.4); and (f) “pure” SGTR onset (t = 3.0).
Paper: Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers
Authors: Raheem Beg, Alexander J. B. Russell, Gunnar Hornig
Figure caption: Mean profiles in the y-direction across the reconnection layer, over the SGTR phase t ∈ [2.4, 5.0] (after label (e) in Figure 2), using terms from the decomposition of the electric field component E  z . Purple (dashed): E  z ; blue: background EMF ﹩-{\left(\bar{{\boldsymbol{v}}}\times \bar{{\boldsymbol{B}}}\right)}_{z};﹩ light pink: turbulent EMF ﹩-{\left(\mathop{{\boldsymbol{v}}}\limits^{\sim }\times \mathop{{\boldsymbol{B}}}\limits^{\sim }\right)}_{z}﹩ (see Figure 11); and dark pink (dashed): resistive EMF η j  z .
Paper: Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers
Authors: Raheem Beg, Alexander J. B. Russell, Gunnar Hornig
Figure caption: Comparison of the aspect ratios 〈δ y〉/〈L〉 for various characteristic thicknesses 〈δ y〉 with the global reconnection rate V rec and mean inflow velocity 〈v in〉 over time. Dark red: current density strength j; yellow: outflow velocity ∣v  x ∣; pink (dotted): unsigned turbulent EMF ﹩\left|-{\left(\mathop{{\boldsymbol{v}}}\limits^{\sim }\times \mathop{{\boldsymbol{B}}}\limits^{\sim }\right)}_{z}\right|;﹩ purple (dotted): positive turbulent EMF ﹩\max \left\{-{\left(\mathop{{\boldsymbol{v}}}\limits^{\sim }\times \mathop{{\boldsymbol{B}}}\limits^{\sim }\right)}_{z},0\right\};﹩ dark green: squashing factor ﹩{Q}_{{z}_{0}}^{100}﹩ for z 0 = −0.5; turquoise: Poincaré section count ﹩{{ \mathcal N }}_{S}﹩ for n = 2000 iterations; black (dashed): global reconnection rate V rec; and gray (dashed): mean inflow velocity 〈v in〉. The vertical dotted lines mark times of interest: (c) turbulent reconnection onset (t = 1.0); (e) SGTR onset (t = 2.4); and (f) “pure” SGTR onset (t = 3.0).
Paper: Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers
Authors: Raheem Beg, Alexander J. B. Russell, Gunnar Hornig
Figure caption: Sample flux rope structures in the reconnection layer at t = 3.0. The forward (green) and backward (purple) FTLE ﹩{{\rm{\Lambda }}}_{z}^{\pm 1}﹩ maximizing ridges (50% of the maximum over the plane) are shown at z = −0.5 (see Figure 17). The stochastic separatrices (black), approximated using contours of the Poincaré section count ﹩{{ \mathcal N }}_{S}=0.5﹩ (for n = 2000), are provided on the z = −0.5 and z = −0.85 planes. The field line bundles (multicolored) are traced through selected low-pressure regions within the flux rope structure cross sections at z = −0.5. Here, flux rope structures are made up of field lines that are locally coherent about z = −0.5 before diverging at various rates in the positive and/or negative z-direction.
Paper: Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers
Authors: Raheem Beg, Alexander J. B. Russell, Gunnar Hornig
Figure caption: Comparison plots of the maximizing ridges of the forward and backward FTLE ﹩{{\rm{\Lambda }}}_{{z}_{0}}^{n}﹩. Samples over the bottom boundary z 0 = −0.5 at t = 3.0 for different iterations n are shown. The repelling ridges (forward n > 0 in green) and attracting ridges (backward n < 0 in purple) are regions where ﹩\left|{{\rm{\Lambda }}}_{{z}_{0}}^{n}\right|﹩ exceeds 50% of the maximum over the plane for a particular n. Top panel: n = ±0.1. Middle panel: n = ±0.25. Bottom panel: n = ±1.0.
Paper: Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers
Authors: Raheem Beg, Alexander J. B. Russell, Gunnar Hornig
Figure caption: Comparison of physical variables, flux rope structures, and stochastic separatrices within the reconnection layer over z = −0.5 at t = 3.0. The interior contours (black) of the Poincaré section count ﹩{{ \mathcal N }}_{S}=0.5﹩ (for n = 2000 iterations) are superimposed over each plot. Panel (a): maximizing ridges (50% of the maximum over the plane) of the forward (green) and backward (purple) FTLE ﹩{{\rm{\Lambda }}}_{z}^{\pm 1}﹩ (see Figures 17 and 18). Panel (b): outflow velocity v  x . Panel (c): current density strength j. Panel (d): vorticity strength ω. Panel (e): energy of the magnetic field fluctuations ﹩{\mathop{E}\limits^{\sim }}_{m}﹩. Panel (f): energy of the kinetic fluctuations ﹩{\mathop{E}\limits^{\sim }}_{k}﹩. Panel (g): turbulent EMF ﹩-{\left(\mathop{{\boldsymbol{v}}}\limits^{\sim }\times \mathop{{\boldsymbol{B}}}\limits^{\sim }\right)}_{z}﹩. Panel (h): pressure p.
Paper: Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers
Authors: Raheem Beg, Alexander J. B. Russell, Gunnar Hornig
Figure caption: Overlay plots of the v  x  (left panel) and v  y  (right panel) components with the laminar boundaries of the upper and lower flux ropes (black), i.e., stochastic separatrices, using a sample at z = 0.0, t = 4.0. The laminar boundaries are approximated using contours of the Poincaré section count ﹩{{ \mathcal N }}_{S}=0.5﹩ (for n = 2000 iterations). The mean inflow velocity 〈v in〉 is approximated within the interior of the laminar flux ropes. The common tangents of the laminar boundaries (dashed green) are used to approximate the mean length 〈L〉 of the reconnection layer.
Paper: Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers
Authors: Raheem Beg, Alexander J. B. Russell, Gunnar Hornig
Figure caption: Close-ups of the CFR at the bottom boundary z 0 = −0.5 during the 3D kink instability at t = 1.0 and t = 1.4. The CFR axis  x  axis (elliptic fixed point) is represented by the green circle (see Figure 4). The top row shows the open twist of field lines (with respect to the CFR axis) ﹩\mathop{{ \mathcal T }}\limits^{\sim }﹩ and the mean value about the CFR axis ﹩\langle \mathop{{ \mathcal T }}\limits^{\sim }\rangle ﹩. The middle row shows the alternative twist of field lines ﹩{ \mathcal T }﹩ and the CFR axis ﹩{{ \mathcal T }}_{\mathrm{axis}}﹩. The bottom row shows the open writhe of field lines ﹩\mathop{{ \mathcal W }}\limits^{\sim }﹩ and the CFR axis ﹩{\mathop{{ \mathcal W }}\limits^{\sim }}_{\mathrm{axis}}﹩.