adsabs/AstroCLIMB huggingface dataset:
Paper: TIC 5724661: A Long-period Binary with a Pulsating sdB Star and δ Scuti Variable
Authors: Rahul Jayaraman, Saul A. Rappaport, Lorne Nelson, Donald W. Kurtz, George Dufresne, Gerald Handler, Abdel Senhadji, David W. Latham, George Zhou, Allyson Bieryla, George R. Ricker
Figure caption: The top panel shows the Fourier amplitude spectrum to 1000 day−1 from the Sector 29 light curve; there are no significant peaks between 1000 day−1 and the Nyquist frequency, 2160 day−1. The second panel zooms into a cluster of peaks in the δ Sct frequency range between 20 and 55 day−1, along with a single, high-frequency peak at 523.99 day−1 (6.065 mHz). The third panel shows the δ Scuti and high-frequency pulsations observed in Sector 42; the peak at 579.85 day−1 (6.711 mHz) increases in prominence between Sectors 29 and 42. The bottom panel shows the Fourier spectrum of the residuals after a nonlinear least-squares fit of the 13 highest-amplitude δ Sct peaks and the peak at 523.99 day−1 (from the sdB star) has been subtracted from the data.
Paper: TIC 5724661: A Long-period Binary with a Pulsating sdB Star and δ Scuti Variable
Authors: Rahul Jayaraman, Saul A. Rappaport, Lorne Nelson, Donald W. Kurtz, George Dufresne, Gerald Handler, Abdel Senhadji, David W. Latham, George Zhou, Allyson Bieryla, George R. Ricker
Figure caption: Left: a plot of the optimal aperture for TIC 5724661, marked with shading indicating flux, along with the positions and Gaia magnitudes of nearby stars in the Gaia catalog. It is evident that none of the nearby stars is bright or hot enough to produce a pulsational signal at the observed frequencies. Right: a 4 × 4 subarray of the Fourier transforms of the time series at the pixel level. The result for each pixel has been obtained by convolution with a 3 × 3 boxcar filter to enhance the statistics, at the cost of decreased spatial resolution (see text for details). The four pixels displaying the highest pulsational signals correspond to exactly the four central pixels of the optimal aperture shown in the left panel. This clearly demonstrates that both the δ Scuti pulsations and the 524 day−1 pulsation arise from within the optimal aperture and that none of the other stars in the TPF cause them. The location of the high-frequency pulsation (from the putative sdB star) is marked with an arrow.
Paper: TIC 5724661: A Long-period Binary with a Pulsating sdB Star and δ Scuti Variable
Authors: Rahul Jayaraman, Saul A. Rappaport, Lorne Nelson, Donald W. Kurtz, George Dufresne, Gerald Handler, Abdel Senhadji, David W. Latham, George Zhou, Allyson Bieryla, George R. Ricker
Figure caption: Upper limits on the mass of a potential companion to a 2 M ⊙ star that are derived from our RV measurements for a range of assumed orbital inclinations. The shaded red region indicates the range of masses of the sdBs that resulted from the modeling of various evolutionary scenarios (described in Section 6). It is clear that the derived constraints are more stringent for periods ≲35 days. There exist islands of marginally acceptable binary periods between 35 and ∼60 days, especially for lower inclinations; more probable periods lie near 200 and ∼300 days. The mass is essentially unconstrained above 500 days. Spikes represent locations where we do not possess any information on the mass of a potential companion, as a result of our observing cadence. The narrow spikes below 3 days are aliases of the 1 day observing windows.
Paper: TIC 5724661: A Long-period Binary with a Pulsating sdB Star and δ Scuti Variable
Authors: Rahul Jayaraman, Saul A. Rappaport, Lorne Nelson, Donald W. Kurtz, George Dufresne, Gerald Handler, Abdel Senhadji, David W. Latham, George Zhou, Allyson Bieryla, George R. Ricker
Figure caption: The light curve of TIC 5724661 obtained in 20 s cadence in TESS Sectors 29 and 42 after processing with the SPOC pipeline (Jenkins et al. 2016). The pulsations are too rapid and too low in amplitude to discern visually in this compressed figure. Its purposes are (i) to show the two gaps in the data, which affect the spectral window, and (ii) to show the noise level in the 20 s data points. The scale of the abscissa is barycentric Julian date – 2,400,000.0.
Paper: Testing Model-determined Temperatures in the Hyades: A Bayesian Approach
Authors: Elizabeth J. Jeffery, Benjamin J. Taylor, Michael D. Joner
Figure caption: Apparent V (left panel) and absolute V (middle and right panels) vs. V–K CMDs of our sample of Hyades stars. We note that the scatter in the apparent CMD is largely due to the depth of the cluster, and has been corrected for in the middle and right CMDs. Stars in the middle panel plotted as open circles are suspected binaries, and were cross-checked to confirm binarity and cluster membership. Stars plotted as blue triangles near the MSTO were also cross-checked, due to their importance in the isochrone fits. The stars plotted as green squares are single stars, but are known variable stars, and therefore were discarded from our analysis. Red diamonds represent stars with larger parallax errors in Gaia eDR3 compared to DR2 causing them to scatter off the MS; in this case, DR2 parallaxes were used. The absolute V vs. V–K CMD in the right panel is the cleaned set of Hyades single stars used in our analysis.
Paper: Testing Model-determined Temperatures in the Hyades: A Bayesian Approach
Authors: Elizabeth J. Jeffery, Benjamin J. Taylor, Michael D. Joner
Figure caption: Box-and-whisker plots for posterior distributions of cluster-wide parameters recovered by each model set. On the age plot (upper left), the dotted and dashed lines represent an age of 625 Myr (log(Age) = 8.796, Perryman et al. 1998) and 794 Myr (log(Age) = 8.9, Gaia collaboration 2018b), respectively. On the remaining plots, the solid and dotted lines are the mean and standard deviation of the prior probability distribution, respectively.
Paper: Diagnosing FU Ori-like Sources: The Parameter Space of Viscously Heated Disks in the Optical and Near-infrared
Authors: Hanpu Liu, Gregory J. Herczeg, Doug Johnstone, Carlos Contreras-Peña, Jeong-Eun Lee, Haifeng Yang, Xingyu Zhou, Sung-Yong Yoon, Ho-Gyu Lee, Masanobu Kunitomo, Jessy Jose
Figure caption: The midplane and surface gravity versus radial distance in the viscous disk region. The temperature profile is also included. Dusty regions outside the range of this plot, where we assume blackbody emission, is not affected by gravity. Fiducial disk properties are adopted.
Paper: Diagnosing FU Ori-like Sources: The Parameter Space of Viscously Heated Disks in the Optical and Near-infrared
Authors: Hanpu Liu, Gregory J. Herczeg, Doug Johnstone, Carlos Contreras-Peña, Jeong-Eun Lee, Haifeng Yang, Xingyu Zhou, Sung-Yong Yoon, Ho-Gyu Lee, Masanobu Kunitomo, Jessy Jose
Figure caption: Model and observed spectral lines of FU Ori (top) and differences between the models and observations (bottom), for the uniform gravity model (orange lines) and the varying gravity model (blue lines).
Paper: Testing Model-determined Temperatures in the Hyades: A Bayesian Approach
Authors: Elizabeth J. Jeffery, Benjamin J. Taylor, Michael D. Joner
Figure caption: Left: absolute B/U–B CMD with isochrones overlaid, generated for each model set using the means of the respective posterior distributions (see Table 2). The panels to the right of the CMD show the difference between observed color and model color for stars below the MSTO for each isochrone. Right: same as the left panel, but for the absolute V/B–V CMD.
Paper: Testing Model-determined Temperatures in the Hyades: A Bayesian Approach
Authors: Elizabeth J. Jeffery, Benjamin J. Taylor, Michael D. Joner
Figure caption: Left: same as Figure 3, but for the absolute V/V – K CMD. Right: same as Figure 3, but for the Gaia absolute G/G BP−G  RP  CMD.
Paper: Testing Model-determined Temperatures in the Hyades: A Bayesian Approach
Authors: Elizabeth J. Jeffery, Benjamin J. Taylor, Michael D. Joner
Figure caption: Examples of posterior distributions of effective temperature for four stars covering a range of spectral types, as indicated. Results are from the MIST models (with no rotation).
Paper: Testing Model-determined Temperatures in the Hyades: A Bayesian Approach
Authors: Elizabeth J. Jeffery, Benjamin J. Taylor, Michael D. Joner
Figure caption: Correlations among cluster-wide parameters for MIST models with no rotation. Other models show similar results. Such a plot allows us to explore and understand how different cluster-wide parameters relate to each other. See the text for a full discussion.
Paper: The Core Population and Kinematics of a Massive Clump at Early Stages: An Atacama Large Millimeter/submillimeter Array View
Authors: Elena Redaelli, Stefano Bovino, Patricio Sanhueza, Kaho Morii, Giovanni Sabatini, Paola Caselli, Andrea Giannetti, Shanghuo Li
Figure caption: Left panel: The color scale shows the integrated intensity of the isolated N2H+ hyperfine component F 1 = 0–1. The white contours show the cores identified in o‐H2D+ (labeled with numbers), and the star symbols the positions of the protostars (labeled in bold face). The scale bar is indicated in the bottom-right corner. The white ellipse shows the beam size of the N2H+ data, while the smaller gray ellipse represents the o‐H2D+ beam size. Right panel: position–velocity plot from the results of ACORNS. The plot is the projection in R.A.–velocity space of the 3D plot shown in Figure 9. Right-ascension values are given as offsets with respect to the center of the FoV (position: R.A. = 18h17m22.ˢ05, decl. = −16°25′01.″7). The four main trees identified by ACORNS are shown with distinct colors, and the color scale is determined by the peak intensity of the line, stretching linearly between 0 K and 90% of the maximum T peak in each tree. The positions of the prestellar and the protostellar cores are shown with the black circles and the yellow stars, respectively. Labels correspond to those in the left panel.
Paper: The Core Population and Kinematics of a Massive Clump at Early Stages: An Atacama Large Millimeter/submillimeter Array View
Authors: Elena Redaelli, Stefano Bovino, Patricio Sanhueza, Kaho Morii, Giovanni Sabatini, Paola Caselli, Andrea Giannetti, Shanghuo Li
Figure caption: Left panel: The color scale shows the peak intensity of the N2H+ components associated with tree G, and the white contour shows the mask (corresponding to T peak > 2.5 K) used to identify the filament studied in Section 3.2. The black contours show the continuum emission at 1.34 mm, at levels [0.5,1.0,1.7,2.5,4.2,5.9] mJy beam−1 (from Sanhueza et al. 2019). The red box indicates the position of the zoomed area shown in the right panel. Right panel: V lsr map of tree G within the white contour of the left panel, with CO emission overlaid in contours (from Li et al. 2020). The contours are computed in the velocity indicated in the bottom-right corner, at levels: for the blue component, [1.08, 1.62, 2.16, 2.7 , 3.78, 4.32, 4.86] Jy beam−1 km s−1; for the red component, [1.33, 1.995, 2.66, 3.99, 5.32, 6.65, 9.31, 10.64, 11.97] Jy beam−1 km s−1. The positions of protostars p2 and p3 are shown with yellow stars in both panels.
Paper: The Core Population and Kinematics of a Massive Clump at Early Stages: An Atacama Large Millimeter/submillimeter Array View
Authors: Elena Redaelli, Stefano Bovino, Patricio Sanhueza, Kaho Morii, Giovanni Sabatini, Paola Caselli, Andrea Giannetti, Shanghuo Li
Figure caption: Composite maps obtained showing together the results of MCWEEDS fit on the o‐H2D+ spectra for all the cores. Panel (a): molecular column density, with contours of the 0.8 mm continuum emission overlaid (levels from 2 to 11σ, in steps of 3σ); Panel (b): V lsr map, with the o‐H2D+-identified cores shown in black contours, and numeric labels; Panel (c): velocity dispersion σv map; Panel (d): one-dimensional turbulent Mach number. Note that in case of core overlapping, the maps show the results of only one of them. For the complete sets of maps of each individual core we refer to Appendix. B. The beam size and scale bar are indicated in the bottom left and right corners, respectively, of panel (d).
Paper: The Core Population and Kinematics of a Massive Clump at Early Stages: An Atacama Large Millimeter/submillimeter Array View
Authors: Elena Redaelli, Stefano Bovino, Patricio Sanhueza, Kaho Morii, Giovanni Sabatini, Paola Caselli, Andrea Giannetti, Shanghuo Li
Figure caption: In black we show the average o‐H2D+(11,0–11,1) spectra obtained in each core (labeled at the top-right corner of each panel). The red histogram shows the best-fit obtained with MCWEEDS. The corresponding best-fit parameters are recorded in Table 2. Cores that overlap by at least 5% of their extension with another core are marked with a blue asterisk in the top-left corner of the panel.
Paper: The Core Population and Kinematics of a Massive Clump at Early Stages: An Atacama Large Millimeter/submillimeter Array View
Authors: Elena Redaelli, Stefano Bovino, Patricio Sanhueza, Kaho Morii, Giovanni Sabatini, Paola Caselli, Andrea Giannetti, Shanghuo Li
Figure caption: The green color scale shows the normalized kernel density distribution of σv and N col in AG14, with the contour levels set on [0.1, 0.3, 0.5, 0.7, 0.9]. The same data are shown for AG351 with the dashed contours and for AG354 with solid contours (taken from Redaelli et al. 2021; the N col values have been corrected by a factor ﹩\sqrt{\pi }﹩; see text for details). The horizontal blue solid and red dashed–dotted lines represent the sound speed and the thermal broadening of o‐H2D+, respectively, both at 10 K.
Paper: The Core Population and Kinematics of a Massive Clump at Early Stages: An Atacama Large Millimeter/submillimeter Array View
Authors: Elena Redaelli, Stefano Bovino, Patricio Sanhueza, Kaho Morii, Giovanni Sabatini, Paola Caselli, Andrea Giannetti, Shanghuo Li
Figure caption: The cores identified in o‐H2D+ by SCIMES are shown as white contours, on top of the continuum emission. They are labeled in order of decreasing right-ascension. The star symbols show the position of the protostellar cores identified by Li et al. (2020), labeled in bold face. The beam size and scale bar are indicated in the bottom left and right corners, respectively.
Paper: The Core Population and Kinematics of a Massive Clump at Early Stages: An Atacama Large Millimeter/submillimeter Array View
Authors: Elena Redaelli, Stefano Bovino, Patricio Sanhueza, Kaho Morii, Giovanni Sabatini, Paola Caselli, Andrea Giannetti, Shanghuo Li
Figure caption: Core masses vs. sizes in AG351 (blue triangles), AG354 (green squares), and AG14 (red circles). The thresholds for high-mass star formation described by Krumholz & McKee (2008), Kauffmann & Pillai (2010), and Baldeschi et al. (2017) are shown with the dashed–dotted black curve, the dashed blue curve, and the solid red line, respectively. For the last two relations we also indicated uncertainties with shaded blue and red areas, which reflect differences in the dust opacity values used here and in those works. The uncertainties on M core are 30% (AG351 and AG354) and 38% (AG14).
Paper: The Core Population and Kinematics of a Massive Clump at Early Stages: An Atacama Large Millimeter/submillimeter Array View
Authors: Elena Redaelli, Stefano Bovino, Patricio Sanhueza, Kaho Morii, Giovanni Sabatini, Paola Caselli, Andrea Giannetti, Shanghuo Li
Figure caption: Comparison of the N2H+ (1–0), in blue, and the o‐H2D+(11,0–11,1) spectra, in black, at the core positions. The spectra are taken at the position of the peak of o‐H2D+ integrated intensity. The red curves show the best model obtained by fitting the N2H+ data with three Gaussian components. The centroid velocity of the o‐H2D+ is shown with the vertical dashed line in each panel.
Paper: Lyα Emitting Galaxies (LAEs) at Cosmic Dawn: Implications and Predictions
Authors: Eduard Salvador-Solé, Alberto Manrique, J. Miguel Mas-Hesse, Cristina Cabello, Jesús Gallego, José Miguel Rodríguez-Espinosa, Rafael Guzman
Figure caption: H I (solid lines) and He II (dashed lines) reionization histories expressed through their volume filling factors Q HII = 1 − 〈x HI〉 and Q HeIII = 1 − 〈x HeII〉 − 〈x HI〉 in single reionization (left panel) and double reionization (right panel) compatible with current global data on galaxies and AGN and the CMB radiation (SS+17). Thick lines give the best solutions of each kind, while thin lines bracket their acceptability range. The vertical dashed black lines mark z = 7 where Q HII is found to be ∼0.7.
Paper: Lyα Emitting Galaxies (LAEs) at Cosmic Dawn: Implications and Predictions
Authors: Eduard Salvador-Solé, Alberto Manrique, J. Miguel Mas-Hesse, Cristina Cabello, Jesús Gallego, José Miguel Rodríguez-Espinosa, Rafael Guzman
Figure caption: Differential stellar MFs of all galaxies (black lines) and LAEs (colored lines) predicted by AMIGA at z = 9 in the two reionization scenarios. Specifically, the galaxy MF in single (double) reionization is the lower (upper) black curve, and the corresponding LAE MF is the red (blue) curve. Black symbols give the observational estimates by different authors of the galaxy stellar MF drawn from the observed UV LF. (A color version of this figure is available in the online journal.)
Paper: Lyα Emitting Galaxies (LAEs) at Cosmic Dawn: Implications and Predictions
Authors: Eduard Salvador-Solé, Alberto Manrique, J. Miguel Mas-Hesse, Cristina Cabello, Jesús Gallego, José Miguel Rodríguez-Espinosa, Rafael Guzman
Figure caption: Evolution of the differential intrinsic Lyα LFs (colored solid lines) in single (left panel) and double (right panel) reionization. At z > 7.5, the growth of LAEs of intermediate L Lyα  in single reionization is somewhat delayed with respect to that in double reionization. The horizontal thin black lines bracket the ordinate range covered by current observations at high z. (A color version of this figure is available in the online journal.)
Paper: Lyα Emitting Galaxies (LAEs) at Cosmic Dawn: Implications and Predictions
Authors: Eduard Salvador-Solé, Alberto Manrique, J. Miguel Mas-Hesse, Cristina Cabello, Jesús Gallego, José Miguel Rodríguez-Espinosa, Rafael Guzman
Figure caption: Contribution from LAEs of different stellar masses (colored lines) to the cumulative intrinsic Lyα LF predicted at z = 9 in single and double reionization. The lower curves of each color correspond most often to the case of single reionization, as expected from the slight difference between the global LAE abundances in the two reionization scenarios (see Figure 2). (A color version of this figure is available in the online journal.)
Paper: Lyα Emitting Galaxies (LAEs) at Cosmic Dawn: Implications and Predictions
Authors: Eduard Salvador-Solé, Alberto Manrique, J. Miguel Mas-Hesse, Cristina Cabello, Jesús Gallego, José Miguel Rodríguez-Espinosa, Rafael Guzman
Figure caption: Differential Lyα LFs predicted at z = 5.7 after correction for ISM absorption in single (red lines) and double (blue lines) reionization compared to observations (dots with error bars). (A color version of this figure is available in the online journal.)
Paper: Star Formation Activity beyond the Outer Arm. II. Distribution and Properties of Star Formation
Authors: Natsuko Izumi, Naoto Kobayashi, Chikako Yasui, Masao Saito, Satoshi Hamano, Patrick M. Koch
Figure caption: Locations of BKP clouds overplotted on H I channel maps from the Canadian Galactic Plane Survey (Taylor et al. 2003). Black open circles show clouds without associated star-forming regions. Red circles and yellow squares show clouds with associated candidate star-forming regions with respective contamination rates of their parental clouds of <30% (reliable) and ≥30% (less reliable).
Paper: Star Formation Activity beyond the Outer Arm. II. Distribution and Properties of Star Formation
Authors: Natsuko Izumi, Naoto Kobayashi, Chikako Yasui, Masao Saito, Satoshi Hamano, Patrick M. Koch
Figure caption: Identical to Figure 23, but for the threshold values W-3 and F-3.
Paper: Star Formation Activity beyond the Outer Arm. II. Distribution and Properties of Star Formation
Authors: Natsuko Izumi, Naoto Kobayashi, Chikako Yasui, Masao Saito, Satoshi Hamano, Patrick M. Koch
Figure caption: Identical to Figure 23, but for the threshold values W-3 and F-2.
Paper: Modeling the Hα and He 10830 Transmission Spectrum of WASP-52b
Authors: Dongdong Yan, Kwang-il Seon, Jianheng Guo, Guo Chen, Lifang Li
Figure caption: (a–b) Density profiles of helium in models with different H/He ratios but with the same F XUV = F 0 and β  m  = 0.22. (c) Source and sink terms related to the population of He(23 S) for the model with H/He = 99.5/0.5, F XUV = F 0, and β  m  = 0.22. The source terms plotted with the black dashed and dotted lines are in units of cm−3 s−1, and the sink terms plotted with the solid lines are in units of s−1. (d) Similar to panel (c), but additionally showing the advection term of He(23 S) with the yellow dashed–dotted line. Here both the source and sink terms are shown in units of cm−3 s−1, unlike in panel (c).
Paper: Modeling the Hα and He 10830 Transmission Spectrum of WASP-52b
Authors: Dongdong Yan, Kwang-il Seon, Jianheng Guo, Guo Chen, Lifang Li
Figure caption:  χ 2 contours for Hα transmission spectrum, obtained by comparing the model spectrum with the observation data in the wavelength range of [6562.05, 6563.55] Å. Panels (a)–(d) show the χ 2 contours for various hydrogen-to-helium abundance ratios. Note that the χ 2 contour levels in color bars are shown in logarithm scale.
Paper: Modeling the Hα and He 10830 Transmission Spectrum of WASP-52b
Authors: Dongdong Yan, Kwang-il Seon, Jianheng Guo, Guo Chen, Lifang Li
Figure caption: H(2) number density for various models. (a) H/He = 92/8, F XUV = F 0, β  m  = 0.22; (b) H/He = 92/8, F XUV = 8F 0, β  m  = 0.22; (c) H/He = 92/8, F XUV = F 0, β  m  = 0.5; (d) H/He = 99.5/0.5, F XUV = F 0, β  m  = 0.22.
Paper: Modeling the Hα and He 10830 Transmission Spectrum of WASP-52b
Authors: Dongdong Yan, Kwang-il Seon, Jianheng Guo, Guo Chen, Lifang Li
Figure caption: EW contours of the Hα line, calculated in the passband of [6562.05, 6563.55] Å, as a function of F XUV and β  m . The panels show the EW contours for various hydrogen-to-helium abundance ratios.
Paper: Modeling the Hα and He 10830 Transmission Spectrum of WASP-52b
Authors: Dongdong Yan, Kwang-il Seon, Jianheng Guo, Guo Chen, Lifang Li
Figure caption: (a–d) Atmosphere structures for helium of models with different F XUV but with the same H/He = 98/2, β  m  = 0.22. (e–f) Atmosphere structures for helium of models with different F XUV but with the same H/He = 99/1, β  m  = 0.22.
Paper: Modeling the Hα and He 10830 Transmission Spectrum of WASP-52b
Authors: Dongdong Yan, Kwang-il Seon, Jianheng Guo, Guo Chen, Lifang Li
Figure caption: Atmosphere structures for helium of models with different β  m  but with the same H/He = 98/2, F XUV = F 0.
Paper: Modeling the Hα and He 10830 Transmission Spectrum of WASP-52b
Authors: Dongdong Yan, Kwang-il Seon, Jianheng Guo, Guo Chen, Lifang Li
Figure caption: Hα transmission spectra of the models that predict C(Hα) between 0.73% and 0.99%. The gray scatters with error bars are the observed data from Chen et al. (2020). The blue dashed lines are the best-fit Gaussian to the data. In panels (a)–(d), the H/He ratio is 92/8, 98/2, 99/1, and 99.5/0.5, respectively.
Paper: Modeling the Hα and He 10830 Transmission Spectrum of WASP-52b
Authors: Dongdong Yan, Kwang-il Seon, Jianheng Guo, Guo Chen, Lifang Li
Figure caption: Absorption depth at the Hα line center as a function of F XUV and β  m  for various H/He ratios.
Paper: Modeling the Hα and He 10830 Transmission Spectrum of WASP-52b
Authors: Dongdong Yan, Kwang-il Seon, Jianheng Guo, Guo Chen, Lifang Li
Figure caption: (a–c) χ 2 contours for He 10830 transmission spectrum, obtained by comparing the model spectrum with the observation data in the wavelength range of [10828.2, 10831.8] Å. (d–f) EW contours of He 10830 line. The χ 2 and EW contours were calculated for three hydrogen-to-helium abundance ratios.
Paper: Slow Diffusion is Necessary to Explain the γ-Ray Pulsar Halos
Authors: Li-Zhuo Bao, Kun Fang, Xiao-Jun Bi, Sheng-Hao Wang
Figure caption: Left: sketch map for the geometric parameters. Right: small-angle diffusion approximation M as a function of α for different x.