adsabs/AstroCLIMB huggingface dataset:
Paper: Collapse of Rotating Massive Stars Leading to Black Hole Formation and Energetic Supernovae
Authors: Sho Fujibayashi, Yuichiro Sekiguchi, Masaru Shibata, Shinya Wanajo
Figure caption: Mass histograms as a function of the electron fraction (top), entropy per baryon (middle), and expansion timescale (r/v  r ;  bottom) at T = 5 GK of the tracer particles that experience temperature higher than 5 GK.
Paper: Collapse of Rotating Massive Stars Leading to Black Hole Formation and Energetic Supernovae
Authors: Sho Fujibayashi, Yuichiro Sekiguchi, Masaru Shibata, Shinya Wanajo
Figure caption: Time evolution of ejecta mass (top) and explosion energy (bottom) as functions of post-explosion time ﹩t-{t}_{\exp }﹩. The dashed and solid curves are the values calculated with r ext = 1 × 109 cm and 2 × 109 cm, respectively. The values in the legend denote the mass (in units of solar mass) and binding energy (in units of 1051 erg) above the extraction radius when the shock wave reaches these radii (see Section 2.3).
Paper: Collapse of Rotating Massive Stars Leading to Black Hole Formation and Energetic Supernovae
Authors: Sho Fujibayashi, Yuichiro Sekiguchi, Masaru Shibata, Shinya Wanajo
Figure caption: Isobaric mass fraction for our models. Nuclei at A = 12 and 16 are, respectively, predominantly unprocessed 12C and 16O in the progenitor stars.
Paper: Collapse of Rotating Massive Stars Leading to Black Hole Formation and Energetic Supernovae
Authors: Sho Fujibayashi, Yuichiro Sekiguchi, Masaru Shibata, Shinya Wanajo
Figure caption: Masses (top) and dimensionless spins (bottom) of black holes for our models as functions of post-bounce time.
Paper: Standardized Luminosity of the Tip of the Red Giant Branch Utilizing Multiple Fields in NGC 4258 and the CATs Algorithm
Authors: Siyang Li, Adam G. Riess, Daniel Scolnic, Gagandeep S. Anand, Jiaxi Wu, Stefano Casertano, Wenlong Yuan, Rachael Beaton, Richard I. Anderson
Figure caption: Tip measurements as a function of contrast ratio using the CATs algorithm on simulated populations of single ages (3–12 Gyr) and metallicities ([Fe/H]; −2 to −0.7) generated with ArtPop with the selection shown in Figure 6. We then apply the CATs algorithm to this grid of simulated populations with a grid of noise (0.02, 0.05, and 0.10 mag) and smoothing values (0.05, 0.10, and 0.15). Noise values are added using the exponential model of σ = Ae  Bm , where the coefficients are provided in Section 5. We restrict and fit each subplot to contrast ratios between 3 and 12. We also restrict the tips to be fainter than −4.1 mag as we find tips brighter than this often correspond to the tip of the AGB rather than TRGB. We show the points that have ages and metallicities that lie inside the ellipse from Figure 6 as large, solid black dots and points with ages and metallicities that lie outside the ellipse as smaller, fainter dots. Linear least squares fits and their slopes are shown in red (large dots) and blue (all dots including large and small). The fits are unweighted.
Paper: Standardized Luminosity of the Tip of the Red Giant Branch Utilizing Multiple Fields in NGC 4258 and the CATs Algorithm
Authors: Siyang Li, Adam G. Riess, Daniel Scolnic, Gagandeep S. Anand, Jiaxi Wu, Stefano Casertano, Wenlong Yuan, Rachael Beaton, Richard I. Anderson
Figure caption: Grid of ages (3–12 Gyr) and metallicities ([Fe/H]; −2 to −0.7) used to simulate stellar populations for Figure 7. To approximate an old, metal-poor to young, metal-rich trend, we draw an ellipse along this axis on the plot. Points that fall inside this ellipse are shown as large, solid dots while points that lie outside this ellipse are shown as smaller fainter dots.
Paper: Standardized Luminosity of the Tip of the Red Giant Branch Utilizing Multiple Fields in NGC 4258 and the CATs Algorithm
Authors: Siyang Li, Adam G. Riess, Daniel Scolnic, Gagandeep S. Anand, Jiaxi Wu, Stefano Casertano, Wenlong Yuan, Rachael Beaton, Richard I. Anderson
Figure caption: CMDs after applying quality and spatial cuts for the fields analyzed in this study are shown in the left panels of each subplot. Internal and external extinction corrections have not yet been applied in this plot. Diagonal blue lines in the left panels for each subplot indicate the optimized color band determined with the CATs algorithm, and the orange lines in the right panels for each subplot show the Sobel response generated with the CATs algorithm with a smoothing parameter of 0.1 and stars within the blue color bands.
Paper: Standardized Luminosity of the Tip of the Red Giant Branch Utilizing Multiple Fields in NGC 4258 and the CATs Algorithm
Authors: Siyang Li, Adam G. Riess, Daniel Scolnic, Gagandeep S. Anand, Jiaxi Wu, Stefano Casertano, Wenlong Yuan, Rachael Beaton, Richard I. Anderson
Figure caption: Normalized Sobel responses for all fields described in Section 2 overlaid for comparison. The plotted lines here are identical to the orange lines in Figure 2 and produced using the CATs algorithm. We measure these Sobel responses for each field using the CATs algorithm by first applying spatial clipping, optimizing a color band selection, applying 0.1 smoothing to the LF, and evaluate the Sobel response using the same procedure from Wu et al. (2023). The Sobel responses shown here have not yet been corrected for internal or external extinction. We mark the locations of the measured TRGB from these Sobel responses with tick marks colored with their corresponding Sobel response curve at the top of the figure.
Paper: Standardized Luminosity of the Tip of the Red Giant Branch Utilizing Multiple Fields in NGC 4258 and the CATs Algorithm
Authors: Siyang Li, Adam G. Riess, Daniel Scolnic, Gagandeep S. Anand, Jiaxi Wu, Stefano Casertano, Wenlong Yuan, Rachael Beaton, Richard I. Anderson
Figure caption: Measured tips as a function of contrast ratio using the CATs algorithm described in Wu et al. (2023) using the NGC 4258 fields from Figure 1 and Table 1 (top) and the GHOSTS fields (Radburn-Smith et al. 2011; bottom). An approximated tip–contrast ratio pair from Figure 10 in Jang et al. (2021) is added in the top panel in blue for comparison purposes only. We note that their measurement setup would likely produce a TCR different from the one calibrated here.
Paper: Standardized Luminosity of the Tip of the Red Giant Branch Utilizing Multiple Fields in NGC 4258 and the CATs Algorithm
Authors: Siyang Li, Adam G. Riess, Daniel Scolnic, Gagandeep S. Anand, Jiaxi Wu, Stefano Casertano, Wenlong Yuan, Rachael Beaton, Richard I. Anderson
Figure caption: Footprints for the 10 fields (blue) and locations of stars that made it past the CATs spatial clipping algorithm (green). Field numbers are labeled in orange. The background image was created by combining gri images from the Sloan Digital Sky Survey (Alam et al. 2015). In this image, north and east correspond to the upward and leftward directions, respectively.
Paper: Standardized Luminosity of the Tip of the Red Giant Branch Utilizing Multiple Fields in NGC 4258 and the CATs Algorithm
Authors: Siyang Li, Adam G. Riess, Daniel Scolnic, Gagandeep S. Anand, Jiaxi Wu, Stefano Casertano, Wenlong Yuan, Rachael Beaton, Richard I. Anderson
Figure caption: Left: locations of the 10 fields analyzed in this study overplotted on an H I density map from Heald et al. (2011). Right: TCR-corrected tips from Table 2 as a function of the mean H I column density. We do not find a significant trend between the corrected tips and H I column densities.
Paper: Evolution of Planetary Obliquity: The Eccentric Kozai–Lidov Mechanism Coupled with Tide
Authors: Xiumin Huang, Jianghui Ji, Shangfei Liu, Ruobing Dong, Su Wang
Figure caption: Evolution of the planetary obliquity of S-type terrestrials with a mass of 1 M ⊕ and a semimajor axis smaller than 0.2 au, whose other initial conditions are set to m 0 = 0.1 M ⊙, m 1 = 1 M ⊕, m 2 = 0.1 M ⊙, a 1 = [0.02, 0.04, 0.045, 0.05, 0.1, 0.12, 0.14, 0.2] au, a 2 = 5 au, e 1 = 0.4, e 2 = 0.2, i 1 = 50°, and i 2 = 0°. The obliquity can be triggered to retrograde and the time to reach the obliquity equilibrium state is much sensitive to the planetary initial position.
Paper: Evolution of Planetary Obliquity: The Eccentric Kozai–Lidov Mechanism Coupled with Tide
Authors: Xiumin Huang, Jianghui Ji, Shangfei Liu, Ruobing Dong, Su Wang
Figure caption: The relationship between t  I  and t kl obtained from the theoretical equations. In panels (a)–(b), m 1 = 0.2 M ⊕, and in (c)–(d), m 1 = 1 M ⊕. The eccentricity e 2 is set to 0.2 in panels (a) and (c) and e 2 = 0.4 in (b) and (d). “Dotted” lines are the comprehensive evolution timescale of the planetary obliquity during the first output step of the simulations. The comprehensive evolution timescale of the obliquity locally decreases when t  I  > t kl for a 2 > 10 au and a 1 = 0.02–0.08 au under EKL.
Paper: Evolution of Planetary Obliquity: The Eccentric Kozai–Lidov Mechanism Coupled with Tide
Authors: Xiumin Huang, Jianghui Ji, Shangfei Liu, Ruobing Dong, Su Wang
Figure caption: Geometry of the hierarchical system. ﹩{\overrightarrow{{\boldsymbol{G}}}}_{1}﹩ and ﹩{\overrightarrow{{\boldsymbol{G}}}}_{2}﹩ are the angular momentum vectors of the inner and outer orbits. ﹩\overrightarrow{{\boldsymbol{G}}}﹩ is the total angular momentum vector of the orbital motion. ﹩{\overrightarrow{{\boldsymbol{N}}}}_{p}﹩ is the rotation angular momentum.
Paper: Evolution of Planetary Obliquity: The Eccentric Kozai–Lidov Mechanism Coupled with Tide
Authors: Xiumin Huang, Jianghui Ji, Shangfei Liu, Ruobing Dong, Su Wang
Figure caption: Evolution of the eccentricity and inclination for S-type terrestrials with a mass of 1 M ⊕ and a semimajor axis smaller than 0.1 au, whose other initials are the same as those in Figure 4. The eccentricity can be excited to 0.7 and the inclination decreases to below 40° when a 1 = 0.1 au. The oscillation amplitudes of e 1 and i 1 increase with a 1. When a 1 > 0.1 au, the upper- and lower-limit e 1 and i 1 in the evolution are not sensitive to a 1 anymore.
Paper: Evolution of Planetary Obliquity: The Eccentric Kozai–Lidov Mechanism Coupled with Tide
Authors: Xiumin Huang, Jianghui Ji, Shangfei Liu, Ruobing Dong, Su Wang
Figure caption: Three examples of Hamiltonian level curves for the spin evolution of terrestrial planets around an M-dwarf. The planetary semimajor axis ranges from 0.05 au to 0.1 au, and the precession frequency ratio noted as η by Su & Lai (2020) is selected as [0.12, 0.45, 1.2]. The different Cassini states are marked out with labels I, II, and III.
Paper: The Disk Reverberation Mapping of X-Ray Weak Quasars: A Case Study of SDSS J153913.47+395423.4
Authors: Marcin Marculewicz, Mouyuan Sun, Jianfeng Wu, Zhixiang Zhang
Figure caption: Left panel: the SDSS DR16 spectrum (black curve) of SDSS J1539+3954 and the Zwicky Transient Facility (ZTF) g- and r-filter response curves, in blue and green, respectively. Major broad emission lines, i.e., C IV, C III], and Mg II, are marked. C IV and C III] are exceptionally weak in SDSS J1539+3954. Right panel: the X-ray to UV power-law slope α OX versus the rest-frame monochromatic luminosity L 2500. Gray dots are X-ray-selected type 1 AGN samples by Lusso et al. (2010). The solid line represents the best-fitting line obtained by Lusso et al. (2010). The green point represents the X-ray normal state of our target in 2019, well consistent with the relation of Lusso et al. (2010). Red and black points are the 90% confidence upper limits for our X-ray-weak quasar SDSS J1539+3954 (Ni et al. 2020). Its 2013 and 2020 data points are slightly horizontally shifted for better visibility. SDSS J1539+3954 has a significantly lower value of α OX in 2013 and 2020 (Ni et al. 2020) than in typical type 1 sources.
Paper: On the Effectiveness of the Planetary Infrared Excess (PIE) Technique to Retrieve the Parameters of Multiplanet Systems around M Dwarfs: A Case Study on the TRAPPIST-1 System
Authors: L. C. Mayorga, J. Lustig-Yaeger, K. B. Stevenson
Figure caption: Posterior distribution and residuals for the star-only models retrieved with the best known parameters in 2015 from Filippazzo et al. (2015) as Gaussian priors. Top: 2D posterior distributions for the stellar parameters. The zoomed insets show the correlation between temperature and radius more clearly. In the noiseless case here, the best-fit parameters are extremely precise. Bottom: the residuals of the best fit vs. the original model. In the “Planet-Free” case, we fit a data set of only TRAPPIST-1A. In “System–Star Only,” the data set includes all planets. Thus, the PIE technique can distinguish between a solitary star and one hosting planets.
Paper: The Disk Reverberation Mapping of X-Ray Weak Quasars: A Case Study of SDSS J153913.47+395423.4
Authors: Marcin Marculewicz, Mouyuan Sun, Jianfeng Wu, Zhixiang Zhang
Figure caption: The radius–luminosity relation at 5100 Å. The best linear fit (red dotted line) applies to all sources with a typical luminosity uncertainty of 0.05 dex. The black solid and dashed lines correspond to the relations in Netzer (2022) and Guo et al. (2022a). SDSS J1539+3954 helps to extend the radius–luminosity relation to the higher end of L 5100. Given its weak-line nature, one would expect that SDSS J1539+3954 falls below the radius–luminosity relation if the diffuse continuum is the only mechanism that accounted for this relation. This expectation is inconsistent with our observation.
Paper: On the Effectiveness of the Planetary Infrared Excess (PIE) Technique to Retrieve the Parameters of Multiplanet Systems around M Dwarfs: A Case Study on the TRAPPIST-1 System
Authors: L. C. Mayorga, J. Lustig-Yaeger, K. B. Stevenson
Figure caption: Best-fit system in each modeling scenario compared to the true TRAPPIST-1 system using only Filippazzo et al. (2015) priors. The symbol size corresponds to the planet size, and the color indicates albedo. Horizontal bars indicate the uncertainty on a planet’s semimajor axis. Each modeling scenario is labeled with the number of planets included, the computed evidence, and its significance against the best-fit model. We use transparency to demonstrate which models are ruled out by >3σ confidence. The vertical dashed lines indicate the limits of our semimajor axis bounds.
Paper: The Disk Reverberation Mapping of X-Ray Weak Quasars: A Case Study of SDSS J153913.47+395423.4
Authors: Marcin Marculewicz, Mouyuan Sun, Jianfeng Wu, Zhixiang Zhang
Figure caption: The g-, r-, and i-band light curves of the SDSS J1539+3954 from ZTF. The green solid and red dashed curves are the best-fitting second-order polynomial curves for g and r, respectively. Due to the limited coverage of the i band, we will not analyze the i-band light curves. For the sake of completeness, we have included it in the plot.
Paper: The Disk Reverberation Mapping of X-Ray Weak Quasars: A Case Study of SDSS J153913.47+395423.4
Authors: Marcin Marculewicz, Mouyuan Sun, Jianfeng Wu, Zhixiang Zhang
Figure caption: Top panel: the observed-frame time lag between g and r bands in days vs. correlation coefficient for the second-order polynomial approach. This approach is based on subtracting the second-order polynomial linear least-squares fit (with equal weight given to all data points) from the original light curves. Bottom panel: the g vs.  r time delay (τ gr,obs) centroid distribution (from the flux randomization/random-subset selection method) for the second-order polynomial approach. The red dashed line indicates the median value.
Paper: On the Effectiveness of the Planetary Infrared Excess (PIE) Technique to Retrieve the Parameters of Multiplanet Systems around M Dwarfs: A Case Study on the TRAPPIST-1 System
Authors: L. C. Mayorga, J. Lustig-Yaeger, K. B. Stevenson
Figure caption: Same as Figure 3 but using the information gained from Gillon et al. (2016). Despite the fact that the eight-planet case is within 3σ, the planets “e” and “f” are trying to compensate for each other and thus fundamentally show little difference from the seven-planet model.
Paper: On the Effectiveness of the Planetary Infrared Excess (PIE) Technique to Retrieve the Parameters of Multiplanet Systems around M Dwarfs: A Case Study on the TRAPPIST-1 System
Authors: L. C. Mayorga, J. Lustig-Yaeger, K. B. Stevenson
Figure caption: The PIE technique exemplified on the TRAPPIST-1 system assuming all objects in the system are blackbodies. We scale up the planet flux by 106 for demonstration purposes and overlay the wavelength coverage of present and proposed IR missions.
Paper: Quantifying Poynting Flux in the Quiet Sun Photosphere
Authors: Dennis Tilipman, Maria Kazachenko, Benoit Tremblay, Ivan Milić, Valentin Martínez Pillet, Matthias Rempel
Figure caption: Average Poynting flux in MURaM simulations as a function of optical depth. The red curve shows the transverse Poynting flux. The x-axis corresponds to a vertical range of ∼0.35 Mm. The black curves (gray diamonds) correspond to vertical Poynting flux computed on geometrical (optical) surfaces and spatially averaged over subsets of pixels with varying magnetic field strengths. The dotted curve represents the emergence term (﹩{v}_{z}{B}_{h}^{2}﹩) of the vertical Poynting flux averaged over all pixels on geometrical surfaces. The blue curve represents the response function of the Fe I 5250.2 Å line in IGLs in arbitrary units. Its peak is at ﹩\overline{\tau }=3\times {10}^{-3}﹩, which is slightly below 400 km. The horizontal and vertical orange lines in the inset represent S  z,thr from Withbroe & Noyes (1977; see Section 5) and the ﹩\overline{\tau }=1﹩ surface, respectively.
Paper: Quantifying Poynting Flux in the Quiet Sun Photosphere
Authors: Dennis Tilipman, Maria Kazachenko, Benoit Tremblay, Ivan Milić, Valentin Martínez Pillet, Matthias Rempel
Figure caption: Left panel: temporal evolution of the average Poynting flux, computed using the ideal MHD assumption and DeepVel velocities. The dashed green lines represent Poynting flux computed in the same sets of pixels as the solid lines, but using random azimuths instead of azimuths obtained via the Poynting flux optimization procedure. Right panel: Poynting flux computed via PDFI_SS and DeepVel velocities and averaged over pixels above the threshold  B -field value (see Section 3.2.2), using random azimuths (orange line), optimized azimuths (red line), and azimuths obtained from the potential-field acute-angle method (solid black line) and from imposing ∣∇ ·  B  = 0∣ (dashed black line). Note the different y-axis limits.
Paper: Quantifying Poynting Flux in the Quiet Sun Photosphere
Authors: Dennis Tilipman, Maria Kazachenko, Benoit Tremblay, Ivan Milić, Valentin Martínez Pillet, Matthias Rempel
Figure caption: Vertical Poynting flux computed on optical surface τ = 1 (left panel) and geometrical surface z = 0 Mm, where the spatially averaged optical depth is ﹩\overline{\tau }=1.1﹩ (center panel). Notice the concentration of both positive and negative S  z  in the IGLs. On the right panel is a 2D histogram comparing pixel-by-pixel S  z  values computed on optical and geometrical surfaces. Note the different scales for the axes.
Paper: Quantifying Poynting Flux in the Quiet Sun Photosphere
Authors: Dennis Tilipman, Maria Kazachenko, Benoit Tremblay, Ivan Milić, Valentin Martínez Pillet, Matthias Rempel
Figure caption: Scatterplots comparing the velocities inferred by the DeepVel neural network to the STAGGER simulation (reference) velocities: (a) v  x , (b) v  y , (c) ∇ h  ·  v   h , and (d) ω  z  = [∇ ×  v ] z . Statistical metrics are provided in the legend to each panel. MAE stands for mean absolute error.
Paper: Quantifying Poynting Flux in the Quiet Sun Photosphere
Authors: Dennis Tilipman, Maria Kazachenko, Benoit Tremblay, Ivan Milić, Valentin Martínez Pillet, Matthias Rempel
Figure caption: Comparison between the velocity fields computed by the STAGGER simulation (left; reference) and those predicted by the DeepVel (center) and FLCT (right) velocity tracking methods. Both the FLCT and DeepVel velocity fields are obtained using STAGGER-simulated QS intensities, which serve as a background for the figure. Note the different scale for the FLCT vector arrows.
Paper: Quantifying Poynting Flux in the Quiet Sun Photosphere
Authors: Dennis Tilipman, Maria Kazachenko, Benoit Tremblay, Ivan Milić, Valentin Martínez Pillet, Matthias Rempel
Figure caption: Histograms of the spatially averaged Poynting flux within the FOV at t = 1430 s. The computations are performed using the ideal MHD method with 5000 realizations of randomized azimuth disambiguation. The vertical red line corresponds to the value of the emergence term of S  z  (see Section 4).
Paper: Quantifying Poynting Flux in the Quiet Sun Photosphere
Authors: Dennis Tilipman, Maria Kazachenko, Benoit Tremblay, Ivan Milić, Valentin Martínez Pillet, Matthias Rempel
Figure caption: Same as Figure 10, but for the optical depth τ = 0.1 and geometrical surface z = 0.128 Mm with spatially averaged optical depth ﹩\overline{\tau }=0.11﹩.
Paper: High-energy Neutrinos from the Inner Circumnuclear Region of NGC 1068
Authors: Ke Fang, Enrique Lopez Rodriguez, Francis Halzen, John S. Gallagher
Figure caption: The multiwavelength emission of the central 180 × 180 pc2 region of NGC 1068. The total intensity maps at 0.25 μm from HST/FOC (left; Kishimoto 1999; T. Barnouin 2023, in preparation), 8.7 μm from CanariCam/GTC (middle; Lopez-Rodriguez et al. 2016), and 860 μm from ALMA (right; Lopez-Rodriguez et al. 2020) are shown. The contours start at 3σ and increase as 1.5 n  σ, where n = 1, 1.5, 2, 2.5, ... , and σ is the noise of the background regions of each observation. The circles show the aperture size of 0.″3 (18 pc) used to compute the photometry of the “S1” (yellow), “C” (orange), and “NE” (green) knots.
Paper: High-energy Neutrinos from the Inner Circumnuclear Region of NGC 1068
Authors: Ke Fang, Enrique Lopez Rodriguez, Francis Halzen, John S. Gallagher
Figure caption: Inelastic optical depth to protons due to pp interaction (black solid curve), photopion production (colored dashed curves), and Bethe–Heitler process (colored dashed–dotted curves) as a function of the proton energy assuming R = 0.1 pc, n gas = 105 cm−3, and β sh = 10−3 for S1 (light blue) and C (dark blue) knots, respectively. For reference, the thin dotted line shows τ = 1.
Paper: High-energy Neutrinos from the Inner Circumnuclear Region of NGC 1068
Authors: Ke Fang, Enrique Lopez Rodriguez, Francis Halzen, John S. Gallagher
Figure caption: Optical depth to γ-rays due to pair (solid curves) and double pair production (dashed curves) as a function of the γ-ray energy assuming R = 0.1 pc for S1 (light blue) and C (dark blue) knots, respectively. As in the previous plot, the thin dotted line corresponds to τ = 1.
Paper: Implications of Narrow Spectra of Fast Radio Bursts
Authors: Yuan-Pei Yang
Figure caption: The cumulative distribution of the linear (top panels) and circular (bottom panels) polarization degrees for the radiation by multiple particles with γ ψ ≫ 1. Notice that the cumulative distribution of the circular polarization degrees is N( > Π V  = 0) = 1 at Π V  = 0 and decreases significantly once Π V  > 0. The component of N( > Π V  = 0) = 1 at Π V  = 0 is not shown in the bottom panels. The distribution function of the viewing direction is assumed to satisfy Equation (A19). In the left panels: the solid, dashed, and dotted lines correspond to η  c  = 10, 100, and 1000, respectively, for ﹩\hat{\omega }=1﹩ and γΘ j  = 10. In the middle panels: the solid, dashed, and dotted lines correspond to γΘ j  = 3, 10, and 100, respectively, for ﹩\hat{\omega }=1﹩ and η  c  = 100. In the right panels: the solid, dashed, and dotted lines correspond to ﹩\hat{\omega }=0.1,1,\,\mathrm{and}\,3﹩, respectively, for γΘ j  = 10 and η  c  = 100.