adsabs/AstroCLIMB huggingface dataset:
Paper: Luminosity Distance Dispersion in Swiss-cheese Cosmology as a Function of the Hole Size Distribution
Authors: T. Cheunchitra, A. Melatos, R. L. Webster
Figure caption: Scaling of ﹩{\sigma }_{{D}_{{\rm{L}}}}﹩ as a function of ﹩{R}_{{\rm{\min }}}﹩ and γ. Top panel: ﹩{\sigma }_{{D}_{{\rm{L}}}}﹩ at ztarget = 1.1 for Swiss-cheese universes with ﹩-1\,\leqslant \,{\mathrm{log}}_{10}({R}_{{\rm{\min }}}/1\,{\rm{Mpc}})\,\leqslant \,1﹩. For each value of ﹩{\mathrm{log}}_{10}({R}_{{\rm{\min }}}/1\,{\rm{Mpc}})﹩, ﹩{\sigma }_{{D}_{{\rm{L}}}}﹩ is calculated for γ = 1.1, 2.1,  and 3.1 (blue circles, orange squares, and green triangles, respectively). The blue solid line, orange dashed line, and green dotted lines correspond to (30) with the best-fit parameters reported in Section 5. Bottom panel: as for top panel, but with ztarget = 2.1.
Paper: Luminosity Distance Dispersion in Swiss-cheese Cosmology as a Function of the Hole Size Distribution
Authors: T. Cheunchitra, A. Melatos, R. L. Webster
Figure caption: Schematic diagram showing continuity conditions between two adjacent Swiss-cheese holes. Darker shading corresponds to higher matter density. The geodesic (red arrow) exits hole ﹩{{ \mathcal H }}_{i}﹩ and enters hole ﹩{{ \mathcal H }}_{i+1}﹩ at point ﹩{ \mathcal O }﹩ (black dot), where the continuity conditions in Section 3.2 are applied. The holes overlap slightly by design.
Paper: Luminosity Distance Dispersion in Swiss-cheese Cosmology as a Function of the Hole Size Distribution
Authors: T. Cheunchitra, A. Melatos, R. L. Webster
Figure caption: As for Figure 6, but with ztarget = 2.0 (top panel), and ztarget = 5.0 (bottom panel), with the best-fit parameters reported in Section 7.
Paper: Luminosity Distance Dispersion in Swiss-cheese Cosmology as a Function of the Hole Size Distribution
Authors: T. Cheunchitra, A. Melatos, R. L. Webster
Figure caption: Schematic diagram of distance measures in cosmology of a source (galaxy) measured by the observer (telescope) and how they relate to the state variables of the beam. Top panel: angular diameter distance. Bottom panel: luminosity distance.
Paper: Dynamically Controlled Transport of GeV Cosmic Rays in Diverse Galactic Environments
Authors: Ronan N. Hix, Lucia Armillotta, Eve Ostriker, Chang-Goo Kim
Figure caption: Slices from a snapshot of the R8 Arm model. The top/bottom row represents vertical/horizontal slices through the center of the simulation box. The color maps represent scalar quantities: from left to right, these are gas temperature (T), hydrogen number density (nH), magnetic field strength (B), and scattering coefficient (σ∥). The superimposed streamlines show vectored quantities, with line width denoting magnitude. From left to right, these are the effective flux-transport speed (veff ≡ Fc/4Pc), the gas velocity (v), and the streaming velocity (vs). For clarity, the y-component of the arm rotation has been subtracted from both veff and v.
Paper: Dynamically Controlled Transport of GeV Cosmic Rays in Diverse Galactic Environments
Authors: Ronan N. Hix, Lucia Armillotta, Eve Ostriker, Chang-Goo Kim
Figure caption: CR pressure-weighted mean vertical dynamical velocity (vtot = vz + vs,z) as a function of temperature for all models (solid lines). Different colors correspond to different models: R2 (red), R4 (green), R8 (blue), and R8 Arm (purple). The arm and interarm regions of the R8 Arm model display no informative differences in this regime and are therefore combined for clarity. Horizontal dashed lines display the mean value of veff (defined via Equation (29)) corresponding to each model, with 1σ temporal variations shown with correspondingly colored dotted lines. These horizontal lines, as well as the black vertical lines that bound the variation ranges, are offset for legibility, rather than to imply any differences in their applicable temperature domain. The gray dashed curve represents a characteristic profile of the scattering coefficient, normalized for visual comparison. The good agreement between veff and vtot in the regime where scattering transitions from low to high values motivates Equation (30).
Paper: Dynamically Controlled Transport of GeV Cosmic Rays in Diverse Galactic Environments
Authors: Ronan N. Hix, Lucia Armillotta, Eve Ostriker, Chang-Goo Kim
Figure caption: Temporal medians of the median CR parallel scattering coefficient (σ∥) profiles as a function of temperature. The shaded regions represent the 16th–84th percentiles of temporal variation. The arm and interarm regions of the R8 Arm model displayed no meaningful variation, and are thus not differentiated for this figure.
Paper: Dynamically Controlled Transport of GeV Cosmic Rays in Diverse Galactic Environments
Authors: Ronan N. Hix, Lucia Armillotta, Eve Ostriker, Chang-Goo Kim
Figure caption: Comparative CR pressure profiles for the various models. The top panel shows the R-models, while the bottom panel shows the R8 Arm model, split into the arm and interarm regions. The shaded regions represent the 16th–84th percentiles of temporal variation. Exponential fits to the extraplanar distributions of each model are shown in dotted black, with solid black indicating the fitting domain.
Paper: Dynamically Controlled Transport of GeV Cosmic Rays in Diverse Galactic Environments
Authors: Ronan N. Hix, Lucia Armillotta, Eve Ostriker, Chang-Goo Kim
Figure caption: Comparisons between the normalized vertical CR pressure profiles obtained from the simulations (blue lines) and those predicted by the analytic model assuming dynamically controlled vertical CR transport (red lines; Equation (26)). The pressure profile is the temporal mean of unweighted horizontal-mean profiles, while the analytic model profile (computed from Equation (26)) uses the temporal mean of CR pressure-weighted horizontal-mean velocity profiles, to better capture the spatial regions most responsible for CR transport. The shaded regions represent the 16th–84th percentiles of temporal variation. Each panel refers to a different model. The R8 Arm model is shown both in its entirety and split into an arm and interarm region. The analytic models are normalized to the CR pressure at ∣z∣ = 0.75 kpc for R2 and R4, and ∣z∣ = 1.5 kpc in the R8 and R8 Arm models.
Paper: Dynamically Controlled Transport of GeV Cosmic Rays in Diverse Galactic Environments
Authors: Ronan N. Hix, Lucia Armillotta, Eve Ostriker, Chang-Goo Kim
Figure caption: Spatial and temporal median values of σ∥ (normalized by a specific combination of gas parameters motivated by the form of Equations (37) and (38)) as a function of local CR pressure. The left panel shows results for gas in the NLL regime and the right panel for gas in the IN regime. The black lines show predictions from our analytic prescriptions for each regime, for a range of input scale heights.
Paper: The b3Π–a3Δ and b3Π–X1Σ+ Band Systems of ZrO
Authors: Manish Bhusal, Peter F Bernath, Jacques Liévin, Léo Lavy
Figure caption: Overview emission spectrum of ZrO (red upward) and simulation (below) of Δv = 0 bands of b3Π–a3Δ transition of ZrO. The letters correspond to the listed band heads.
Paper: Dynamically Controlled Transport of GeV Cosmic Rays in Diverse Galactic Environments
Authors: Ronan N. Hix, Lucia Armillotta, Eve Ostriker, Chang-Goo Kim
Figure caption: Horizontally and temporally averaged profiles of the CR pressure in the R8 model, chosen as an example. Profiles are shown after the postprocessing step and after the MHD relaxation step. The shaded region again represents the 16th–84th percentiles of temporal variation. Note the minimal variation in these vertical profiles with and without the MHD step.
Paper: Fe Abundances of Early Galaxies at z = 9–12 Derived with Deep JWST Spectra
Authors: Minami Nakane, Masami Ouchi, Kimihiko Nakajima, Yoshiaki Ono, Yuichi Harikane, Yuki Isobe, Ken'ichi Nomoto, Miho N. Ishigaki, Hiroto Yanagisawa, Daichi Kashino, Nozomu Tominaga, Koh Takahashi, Moka Nishigaki, Yui Takeda, Kuria Watanabe
Figure caption: Same as Figure 13, but for the SN Ia models. The solid, dashed, and dotted lines present our SN Ia models with delay times of ﹩{t}_{\min }=100﹩, 50, and 30 Myr, respectively.
Paper: Molecular Observations of the Protoplanetary Nebula Frosty Leo: A Unique Window into Superoxygen Chemistry
Authors: K. R. Gold, L. M. Ziurys
Figure caption: (a) HST composite image (F606W in red and F814W in blue) of Frosty Leo (R. Sahai et al. 2000). Spatial scales are marked; north is up and east is left. The beam size (37″), corresponding to the H2S: JKa,Kc = 11,0 → 10,1, transition, is overlaid in white. (b) Spectra of the JKa,Kc = 11,0 → 10,1 transition of H2S (upper), ﹩{{{\rm{H}}}_{2}}^{33}{\rm{S}}﹩ (center), and ﹩{{{\rm{H}}}_{2}}^{34}{\rm{S}}﹩ (lower) observed toward Frosty Leo, obtained with the ARO 12 m antenna at 169 GHz. The temperature scale is ﹩{T}_{A}^{* }﹩ (mK). The spectra were simultaneously observed with 1.1 km s−1 resolution and smoothed to 5.6 km s−1. The integration time is 21.8 hr.
Paper: Molecular Observations of the Protoplanetary Nebula Frosty Leo: A Unique Window into Superoxygen Chemistry
Authors: K. R. Gold, L. M. Ziurys
Figure caption: Spectra of SO (left) and SO2 (right) observed toward the Frosty Leo Nebula, showing four transitions of SO and five transitions of SO2, obtained with the ARO 12 m antenna (2 and 3 mm); see Table 1. Transition quantum numbers are indicated on the figure. The temperature scale is ﹩{T}_{A}^{* }﹩ (mK). The spectra were observed with 1.1–1.9 km s−1 resolution and smoothed to 4.1–5.9 km s−1. Integration times for these spectra are in the range 8.0 to 46.6 hr, aside from the region around 165 GHz, which required 73.5 hr.
Paper: Molecular Observations of the Protoplanetary Nebula Frosty Leo: A Unique Window into Superoxygen Chemistry
Authors: K. R. Gold, L. M. Ziurys
Figure caption: The J = 1 → 0 and J = 2 → 1 spectra of CO and its 13C isotopologue (left); the CS: J = 2 → 1, J = 3 → 2, and J = 5 → 4 lines (top right) and the SiO: J = 2 → 1 and J = 3 → 2 transitions (lower right), observed toward the Frosty Leo Nebula, obtained with the ARO 12 m antenna (2 and 3 mm) and ARO SMT (1 mm); see Table 1. The temperature scale is ﹩{T}_{A}^{* }﹩ (mK). The spectra were observed with 1.3–2.2 (12 m) and 1.3–1.4 km s−1 (SMT) resolution and smoothed to 4.9–6.5 km s−1. Integration times for these spectra are in the range 6.2–38.6 hr, except for CO: J = 2 → 1 line (∼1 hr of integration time).
Paper: On the Fe XXII Emission in the X-Ray Spectrum of NGC 1068
Authors: M. Z. Buhariwalla, J. M. Miller, L. C. Gallo, J. Mao, J. Raymond, T. Kallman
Figure caption: Fe XXII diagnostic curves and line profiles generated using PION for different ionization (log ξ) and densities (n). The SED used is representative of NGC 1068. Top left panel: density vs. the ratio of line strengths, I(11.92 Å)/I(11.77 Å), at different ionizations. Higher values of log ξ are shown in darker red. Bottom left panel: the line profile of the Fe XXII doublet at different values of log ξ. Density is fixed at n = 1012 cm−3. The dotted black lines show the location of each of the diagnostic lines. Note that at this density, the presence of the 11.92 Å emission is ionization-dependent. The 11.92 Å emission is present at lower ionization when the density is higher (not shown here). Top right panel: ionization vs. I(11.92 Å)/I(11.77 Å) at different densities. Higher values of n are shown in darker blue. Bottom right panel: the Fe XXII doublet at different values of n with ionization fixed at log(ξ/erg cm s−1) = 3.7. At lower densities, the 11.77 Å line is very strong and the 11.92 Å line is relatively weak. At higher densities, the reverse is true.
Paper: On the Fe XXII Emission in the X-Ray Spectrum of NGC 1068
Authors: M. Z. Buhariwalla, J. M. Miller, L. C. Gallo, J. Mao, J. Raymond, T. Kallman
Figure caption: Energy level diagram for the Fe XXII doublet in photoionized equilibrium under best fit conditions. Each level is labeled with its electron configuration, term symbol, and energy level (e.g., the ground state is level 1, the first excited state is level 2, and so on). The 2s12p2 manifold contains levels 3–10, and the term symbols are neglected. They are treated as one energy state for simplicity. Blue solid lines indicate radiative decay, blue dotted lines indicate absorption, red dotted–dashed lines indicate the collisional excitation, and the red dashed line shows collisional de-excitation. The green dashed line is the combination of radiative recombination and cascades. The percentages listed provide information about the location and method by which an electron will transition from each level. The excitation energy between level 1 and level 2 is 14.7 eV (845.55 Å). The excitation energies from level 1 to levels 3–10 range between ∼50 and 125 eV (∼250–100 Å).
Paper: On the Fe XXII Emission in the X-Ray Spectrum of NGC 1068
Authors: M. Z. Buhariwalla, J. M. Miller, L. C. Gallo, J. Mao, J. Raymond, T. Kallman
Figure caption: Left panel: the four ionizing continua used to test the effects of SED on the Fe XXII diagnostic. The construction of each is described in the text. Middle panel: model ratio at 11.77 and 11.92 Å for each of the SEDs at ﹩{\rm{log}}(\xi /{\rm{erg}}\,{\rm{cm}}\,{{\rm{s}}}^{-1})=3.69﹩. Right panel: diagnostic curves for each SED at the best-fit ionization for each SED. The density of the High ionization component was constrained for each model and is shown in the shaded region.
Paper: On the Fe XXII Emission in the X-Ray Spectrum of NGC 1068
Authors: M. Z. Buhariwalla, J. M. Miller, L. C. Gallo, J. Mao, J. Raymond, T. Kallman
Figure caption: Density verse I(11.92 Å)/I(11.77 Å) for the best-fit PION component, log(ξ/erg cm s−1) = 3.69. The red horizontal line shows the measured ratio of the Fe XXII doublet from the data. The horizontal dotted lines are the 90% confidence interval on the measured ratio. The black vertical line shows the measured density from the High ionization PION component.
Paper: On the Fe XXII Emission in the X-Ray Spectrum of NGC 1068
Authors: M. Z. Buhariwalla, J. M. Miller, L. C. Gallo, J. Mao, J. Raymond, T. Kallman
Figure caption: Simulations of spectral variability. Top panel: the model spectra; the black solid line indicates the base model found in this work. Red indicates the spectrum with the High ionization component 25% brighter. The lower three panels show simulated data for Chandra HETG, XRISM Resolve (gate valve open), and Athena X-IFU, respectively, for both the base and 25% brighter cases. All data are simulated for a 100 ks exposure and all data are binned to three channels per bin.
Paper: On the Fe XXII Emission in the X-Ray Spectrum of NGC 1068
Authors: M. Z. Buhariwalla, J. M. Miller, L. C. Gallo, J. Mao, J. Raymond, T. Kallman
Figure caption: Best-fit PION model for NGC 1068. The data are shown in gray and presented without error bars for clarity. Note that the Fe XXII doublet is primarily fit by the High ionization component with limited contributions from the Mid ionization component. The black dotted vertical lines denote the location of the 11.77 and 11.92 Å lines. They have been corrected for the outflow velocity of the High ionization component.
Paper: On the Fe XXII Emission in the X-Ray Spectrum of NGC 1068
Authors: M. Z. Buhariwalla, J. M. Miller, L. C. Gallo, J. Mao, J. Raymond, T. Kallman
Figure caption: BAT 157 month light curve, the black solid line shows the mean of the 157 months light curve. The gray data are the individual months, while the blue data are the data binned into six months. The red data indicate months where the rate does not agree with zero.
Paper: On the Fe XXII Emission in the X-Ray Spectrum of NGC 1068
Authors: M. Z. Buhariwalla, J. M. Miller, L. C. Gallo, J. Mao, J. Raymond, T. Kallman
Figure caption: The SED used for PION in this work. The construction of the SED is described in the text.
Paper: On the Fe XXII Emission in the X-Ray Spectrum of NGC 1068
Authors: M. Z. Buhariwalla, J. M. Miller, L. C. Gallo, J. Mao, J. Raymond, T. Kallman
Figure caption: Change in fit statistic vs. density for each photoionized component. The C-stat is measured relative to the best-fit pion model.
Paper: Hybrid Strategy for Coordinated Interstellar Signaling: Linking the Galactic Center and Extragalactic Bursts
Authors: Naoki Seto
Figure caption: Schematic illustration of the hybrid scheme. The red curve represents the wave front of the burst signal at the moment it reaches the Galactic center G, where BG = BK = BKB. For the blue signaling line, the reference point and epoch are defined by the outward intersection K with the wave front. At a given time after the burst arrival, the search directions are symmetric around the burst direction.
Paper: Hybrid Strategy for Coordinated Interstellar Signaling: Linking the Galactic Center and Extragalactic Bursts
Authors: Naoki Seto
Figure caption: Schematic illustration of the signaling geometry. A set of civilizations (C−1, C0, C1, … ) are distributed along an oriented line. An astronomical event occurs at point A, with its closest point on the line denoted by P. At the location of civilization C0, the distance to the event is d, and the angular offset from the line is θ. Using the concurrent signaling scheme, the civilizations can coordinate their signaling activities without prior communication, relying solely on shared knowledge of event A.
Paper: Hybrid Strategy for Coordinated Interstellar Signaling: Linking the Galactic Center and Extragalactic Bursts
Authors: Naoki Seto
Figure caption: Target offset angles given in Equations (2) and (13) from the burst direction as a function of the nondimensional times x and y. For q = 1, we have a solution for θ only with ﹩-2\leqslant x\leqslant \sqrt{2}-1﹩.
Paper: Hybrid Strategy for Coordinated Interstellar Signaling: Linking the Galactic Center and Extragalactic Bursts
Authors: Naoki Seto
Figure caption: The opening angle β for the search ring around the three representative extragalactic bursts. The horizontal axis shows the time τ since the observation of each burst.
Paper: Hybrid Strategy for Coordinated Interstellar Signaling: Linking the Galactic Center and Extragalactic Bursts
Authors: Naoki Seto
Figure caption: Accessible volume V(θB, τ) as a function of θB, shown for elapsed times τ = 1, 10, and 100 yr. Note that V(θB, τ) is approximately proportional to τ.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: Examples fit of the Poynting flux luminosity with a power law 〈L〉 ∝ Ωp. Top row: (left) the case with α1 = 0°, α2 = 0°, and λ = −1. (Right) The case with α1 = 45°, α2 = 0°, and λ = 10 demonstrates that, although the power law cannot describe the periodic fluctuations, it captures well the trend of the luminosity. Bottom row: (left) the case with α1 = 90°, α2 = 90°, λ = −1, and ΔΦ = 0° highlights that, although the flux can vary significantly, dropping to very low values and affecting the flux dependence on Ω the power law still describes quite well the averaged trend. (Right) The case with α1 = 0°, α2 = 0°, and λ = 100, which consists of an example of not that accurate description of the Poynting flux luminosity’s evolution with the power law. In all the cases, the dotted line indicates the moving average for comparison.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: The distribution of the Poynting flux across a spherical surface of radius 13r⋆, integrated over the last 7.7 ms of the inspiral. White lines indicate the areas containing 50% and 90% of the total (integrated over the entire surface) flux. (Left) The two stars have antialigned magnetic moments ↑ ↓, with magnetic moment ratios λ = −1, −10, −100 from top to bottom, respectively. (Right) Cases with λ = −10 and α1 = 45°, α2 = 0° (↗ ↓), α1 = 90°, α2 = 0°(→ ↓) and α1 = 90°, α2 = 90°, ΔΦ = 0°(→ ←) from top to bottom, respectively.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: Scatter plot showing the power p derived from the power-law fitting 〈L〉 ∝ Ωp for the different simulated cases. On x-axis is λ in logarithmic scale while the color and the size of each point indicate the two inclination angles α1 and α2 according to the legends. The circles are cases with λ > 0, while the triangles are with λ < 0. The different values of the exponent p for the same α1, α2, and λ combinations is due different ΔΦ angles.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: Histogram of the power-law index p obtained from fitting of the relation 〈L〉 ∝ Ωp shown in gray for all data points and in red only for the peak values. The distribution of p spans a wide range from ∼1 to >6, in contrast to the p ≡ 4 value for an isolated dipolar pulsar.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: Two schematic snapshots of the BNS system on the corotating frame during its evolution, illustrating the forces exerted along the z-axis on each star. The plotted forces indicate the development of an EM torque. As shown, the magnitude of the forces increases between the two snapshots while their direction reverses, demonstrating that the torque amplitude grows over time and changes sign every half an orbital period. This periodic behavior suggests a cumulative effect that could influence the orbital motion of the system.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: A snapshot of the forces that develop at each star for the case with α1 = 0°,  α2 = 45°, and λ = 1 (↑ ↗). The color scale indicates the quantity K (see section 3.2.1).
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: The total Poynting flux crossing a spherical surface radius 13r⋆ throughout the system’s evolution for cases with α1 = α2 = 0 and λ < 0 (↑ ↓) and progressively increasing ∣λ∣ values.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: The time evolution ensemble average of Poynting flux from all simulated cases with varying ∣λ∣ (solid line of different colors) in comparison with the calculated ﹩\overline{\langle L\rangle }﹩ from the scaling law of the Equation (15) for the same value of λ (dotted).
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: Histogram of emission anisotropy, showing the distribution of the sky area fraction that contains 50% of the total flux across the explored parameter combinations.