adsabs/AstroCLIMB huggingface dataset:
Paper: Simulation of the 2010 September 9 Solar Energetic Particle Event by Using a Data-constrained Transport Model
Authors: Xinyi Tao, Fang Shen, Xueshang Feng, Wanyi Lian, Bofeng Tang, Yi Yang
Figure caption: (a): time–intensity profiles obtained from the simulated results (solid lines) and observational data (dashed–dotted lines) at the position of STA. The arrows indicate the time at which the energy spectra are performed. (b): energy spectra at different moments accessed from the simulations (lines) and measurements (diamonds).
Paper: Simulation of the 2010 September 9 Solar Energetic Particle Event by Using a Data-constrained Transport Model
Authors: Xinyi Tao, Fang Shen, Xueshang Feng, Wanyi Lian, Bofeng Tang, Yi Yang
Figure caption: Time–intensity profiles obtained from the simulated results (solid lines) and observational data (dashed–dotted lines) at the positions of (a) SOHO and (b) STB.
Paper: A Data-driven Approach for Star Formation Parameterization Using Symbolic Regression
Authors: Diane M. Salim, 美玲 林, Matthew E. Orr, Blakesley Burkhart, Rachel S. Somerville, Miles Cramner
Figure caption: Chart showing how data are manipulated and flow through our procedure. In all panels, filled green boxes represent a machine learning based method or algorithm that is utilized, and uncolored green outlined boxes represent a predictive model for our target variable, star formation rate surface density. The top panel shows how our initial raw data are prepared and filtered to determine the variables with which to run our experiments. The bottom-left panel depicts supervised training being applied to the filtered variable training set in order to attain predictive models for the target variable. The bottom-right panel shows how all the predictive models in this study are compared by being applied to the filtered variable test set.
Paper: A Data-driven Approach for Star Formation Parameterization Using Symbolic Regression
Authors: Diane M. Salim, 美玲 林, Matthew E. Orr, Blakesley Burkhart, Rachel S. Somerville, Miles Cramner
Figure caption: Star formation rate surface density (ΣSFR) maps of galaxy “m12b” at redshift z = 0 with 750 pc pixel size, averaged over 10 Myr (left panel) and 100 Myr (right panel).
Paper: Simulation of the 2010 September 9 Solar Energetic Particle Event by Using a Data-constrained Transport Model
Authors: Xinyi Tao, Fang Shen, Xueshang Feng, Wanyi Lian, Bofeng Tang, Yi Yang
Figure caption: Temporal evolution of speeds and radial distances of CME nose (dashed–dotted lines) and shock apex (solid lines). The arrows respectively indicate the moments of the first critical time τc1 and the second critical time τc2. The red vertical line refers to the moment when the shock arrives at 0.96 au.
Paper: Simulation of the 2010 September 9 Solar Energetic Particle Event by Using a Data-constrained Transport Model
Authors: Xinyi Tao, Fang Shen, Xueshang Feng, Wanyi Lian, Bofeng Tang, Yi Yang
Figure caption: Schematic of the shock front segmentation. The shock front is divided along the direction of longitude ϕ with an angular resolution of 5∘.
Paper: Changing-look Active Galactic Nuclei from the Dark Energy Spectroscopic Instrument. IV. Broad Emission-line Evolution Sequence among Hα, Mg II, and Hβ
Authors: Wei-Jian Guo, Victoria A. Fawcett, Małgorzata Siudek, Yan-Rong Li, Cheng Cheng, Swayamtrupta Panda, Zhiwei Pan, Shengxiu Sun, Claire L. Greenwell, David M. Alexander, John Moustakas, Shuo Zhai, Jun-Jie Jin, Huaqing Cheng, Jingwei Hu, Yong-Jie Chen, Zhi-Xiang Zhang, Jian-Min Wang
Figure caption: The relation between the broad emission-line luminosities and the continuum luminosity at 5100 Å (L5100) for four black hole mass bins. Each panel represents a different black hole mass: (a) ﹩{\mathrm{log}}({M}_{{\rm{BH}}}/{M}_{\odot })=7.08﹩, (b) ﹩{\mathrm{log}}({M}_{{\rm{BH}}}/{M}_{\odot })=7.50﹩, (c) ﹩{\mathrm{log}}({M}_{{\rm{BH}}}/{M}_{\odot })=7.92﹩, and (d) ﹩{\mathrm{log}}({M}_{{\rm{BH}}}/{M}_{\odot })=8.43﹩. The blue, cyan, and red points represent Hβ, Hα, and Mg II emission lines, respectively. Error bars in both x- and y-directions denote the measurement uncertainties.
Paper: Changing-look Active Galactic Nuclei from the Dark Energy Spectroscopic Instrument. IV. Broad Emission-line Evolution Sequence among Hα, Mg II, and Hβ
Authors: Wei-Jian Guo, Victoria A. Fawcett, Małgorzata Siudek, Yan-Rong Li, Cheng Cheng, Swayamtrupta Panda, Zhiwei Pan, Shengxiu Sun, Claire L. Greenwell, David M. Alexander, John Moustakas, Shuo Zhai, Jun-Jie Jin, Huaqing Cheng, Jingwei Hu, Yong-Jie Chen, Zhi-Xiang Zhang, Jian-Min Wang
Figure caption: Correlation between the broad emission-line luminosity (Lline) and the continuum luminosity for the CL-AGN parent sample (left panel) and CL-AGN core sample (right panel). Three broad lines—Hβ (dark blue), Hα (light blue), and Mg II (red)—and their linear regressions are plotted for individual objects.
Paper: Changing-look Active Galactic Nuclei from the Dark Energy Spectroscopic Instrument. IV. Broad Emission-line Evolution Sequence among Hα, Mg II, and Hβ
Authors: Wei-Jian Guo, Victoria A. Fawcett, Małgorzata Siudek, Yan-Rong Li, Cheng Cheng, Swayamtrupta Panda, Zhiwei Pan, Shengxiu Sun, Claire L. Greenwell, David M. Alexander, John Moustakas, Shuo Zhai, Jun-Jie Jin, Huaqing Cheng, Jingwei Hu, Yong-Jie Chen, Zhi-Xiang Zhang, Jian-Min Wang
Figure caption: Correlation between the line luminosity (Lline) and the continuum luminosity at 5100 Å (L5100) for quasars in four black hole mass (MBH) bins. Each panel represents one MBH bin, and data points correspond to the median luminosities of Hβ (dark blue circles), Hα (light blue triangles), and Mg II (red pentagons). Error bars denote the 16th–84th percentile range in each bin.
Paper: Changing-look Active Galactic Nuclei from the Dark Energy Spectroscopic Instrument. IV. Broad Emission-line Evolution Sequence among Hα, Mg II, and Hβ
Authors: Wei-Jian Guo, Victoria A. Fawcett, Małgorzata Siudek, Yan-Rong Li, Cheng Cheng, Swayamtrupta Panda, Zhiwei Pan, Shengxiu Sun, Claire L. Greenwell, David M. Alexander, John Moustakas, Shuo Zhai, Jun-Jie Jin, Huaqing Cheng, Jingwei Hu, Yong-Jie Chen, Zhi-Xiang Zhang, Jian-Min Wang
Figure caption: The relation between the broad emission-line luminosities and the Eddington ratios (﹩{\mathrm{log}}{\lambda }_{{\rm{Edd}}}﹩) for four black hole mass bins. Each panel represents a different black hole mass: (a) ﹩{\mathrm{log}}({M}_{{\rm{BH}}}/{M}_{\odot })=7.08﹩, (b) ﹩{\mathrm{log}}({M}_{{\rm{BH}}}/{M}_{\odot })=7.50﹩, (c) ﹩{\mathrm{log}}({M}_{{\rm{BH}}}/{M}_{\odot })=7.92﹩, and (d) ﹩{\mathrm{log}}({M}_{{\rm{BH}}}/{M}_{\odot })=8.43﹩. The blue, cyan, and red points represent Hβ, Hα, and Mg II emission lines, respectively. Error bars in both x- and y-directions denote the measurement uncertainties.
Paper: Changing-look Active Galactic Nuclei from the Dark Energy Spectroscopic Instrument. IV. Broad Emission-line Evolution Sequence among Hα, Mg II, and Hβ
Authors: Wei-Jian Guo, Victoria A. Fawcett, Małgorzata Siudek, Yan-Rong Li, Cheng Cheng, Swayamtrupta Panda, Zhiwei Pan, Shengxiu Sun, Claire L. Greenwell, David M. Alexander, John Moustakas, Shuo Zhai, Jun-Jie Jin, Huaqing Cheng, Jingwei Hu, Yong-Jie Chen, Zhi-Xiang Zhang, Jian-Min Wang
Figure caption: Correlation between broad emission-line luminosities (Lline) and the Eddington ratio (λEdd) for all CL-AGNs, binned by black hole mass (MBH). Each panel corresponds to a different MBH bin, as labeled. The emission lines Hβ (dark blue), Hα (light blue), and Mg II (red) are shown individually, with linear regression fits overplotted as dashed lines. Error bars are omitted here for clarity due to the large number of points.
Paper: Black-hole Shadows and Null Geodesics in Hamaus–Sutter–Wandelt Void Spacetimes with a Quintessential Field: Observational Signatures from EHT Data of M87∗ and Sgr A∗
Authors: A. Errehymy, S. Hansraj, C. Hansraj
Figure caption: The behavior of null geodesics in HSW void spacetimes with a quintessential field for the regular black hole is shown, with orange, green, and blue trajectories. In the left panel, δc is varied while keeping γ = 0.1 and ρs = 0.1 fixed. The middle panel illustrates the effect of changing γ with δc = 0.1 and ρs = 0.1. The right panel shows how variations in ρs influence f(r) with δc = 0.1 and γ = 0.1.
Paper: Black-hole Shadows and Null Geodesics in Hamaus–Sutter–Wandelt Void Spacetimes with a Quintessential Field: Observational Signatures from EHT Data of M87∗ and Sgr A∗
Authors: A. Errehymy, S. Hansraj, C. Hansraj
Figure caption: The behavior of the black-hole shadow radius (solid red line) in HSW void spacetimes with a quintessential field. In the left panel, δc is varied while keeping γ = 0.1 and ρs = 0.1 fixed. The middle panel illustrates the effect of changing γ with δc = 0.1 and ρs = 0.1, and the right panel shows how variations in ρs influence f(r) with δc = 0.1 and γ = 0.1. The orange and gray regions correspond to the EHT horizon-scale images of Sgr A∗ and M87∗ at 1σ, while the light blue and light green regions represent consistency at 2σ, respectively.
Paper: Black-hole Shadows and Null Geodesics in Hamaus–Sutter–Wandelt Void Spacetimes with a Quintessential Field: Observational Signatures from EHT Data of M87∗ and Sgr A∗
Authors: A. Errehymy, S. Hansraj, C. Hansraj
Figure caption: The phase portrait of ﹩\dot{r}﹩ versus r for different combinations of δc, γ, and ρs in HSW void spacetimes with a quintessential field for the regular black hole is shown, with the red dot indicating the location of the saddle (critical) point.
Paper: Black-hole Shadows and Null Geodesics in Hamaus–Sutter–Wandelt Void Spacetimes with a Quintessential Field: Observational Signatures from EHT Data of M87∗ and Sgr A∗
Authors: A. Errehymy, S. Hansraj, C. Hansraj
Figure caption: The behavior of the metric function f(r) as a function of radius r in HSW void spacetimes with a quintessential field. In the left panel, δc is varied while keeping γ = 0.1 and ρs = 0.1 fixed. The middle panel illustrates the effect of changing γ with δc = 0.1 and ρs = 0.1, and the right panel shows how variations in ρs influence f(r) with δc = 0.1 and γ = 0.1.
Paper: Black-hole Shadows and Null Geodesics in Hamaus–Sutter–Wandelt Void Spacetimes with a Quintessential Field: Observational Signatures from EHT Data of M87∗ and Sgr A∗
Authors: A. Errehymy, S. Hansraj, C. Hansraj
Figure caption: The behavior of the black-hole shadow and its dependence on the parameters in HSW void spacetimes with a quintessential field. In the left panel, δc is varied while keeping γ = 0.1 and ρs = 0.1 fixed. The middle panel illustrates the effect of changing γ with δc = 0.1 and ρs = 0.1, and the right panel shows how variations in ρs influence f(r) with δc = 0.1 and γ = 0.1.
Paper: Black-hole Shadows and Null Geodesics in Hamaus–Sutter–Wandelt Void Spacetimes with a Quintessential Field: Observational Signatures from EHT Data of M87∗ and Sgr A∗
Authors: A. Errehymy, S. Hansraj, C. Hansraj
Figure caption: The energy-emission rate is analyzed for different parameter choices in HSW void spacetimes with a quintessential field. In the left panel, δc is varied while keeping γ = 0.1 and ρs = 0.1 fixed. The middle panel highlights the impact of varying γ with δc = 0.1 and ρs = 0.1, while the right panel illustrates the influence of ρs on f(r) with δc = 0.1 and γ = 0.1.
Paper: Wind-AE: A Fast, Open-source 1D Photoevaporation Code with Metal and Multifrequency X-Ray Capabilities
Authors: Madelyn I. Broome, Ruth Murray-Clay, John R. McCann, James E. Owen
Figure caption: A. Gillet et al. (2023) secondary ionization profiles. We reproduce profiles from Figure 7 in A. Gillet et al. (2023) for a 0.05MJ, 0.55RJ planet at 0.045 au around a solar-type star for a pure-H outflow modeled using PLUTO with secondary ionizations enabled (black). Wind-AE profile for the same planet with the same solar spectrum plotted, but with bolometric heating and cooling and μ = 2.3mH for r < RXUV enabled (green) and without (yellow). Yellow boundary conditions at ﹩{R}_{{\rm{\min }}}﹩ = 1.1RP are matched to black (T = 1100K, ρ = 1.326 × 10−10 g s−1, P = 12 μbar), while green use Wind-AE's default lower BCs.
Paper: Wind-AE: A Fast, Open-source 1D Photoevaporation Code with Metal and Multifrequency X-Ray Capabilities
Authors: Madelyn I. Broome, Ruth Murray-Clay, John R. McCann, James E. Owen
Figure caption: Smoothing high escape velocity planet lower BC temperature oscillations—55 M⊕, 1.85 R⊕ at 0.05 au with Ftot = 1095 erg s−1 cm−2 temperature (right y-axis, solid) and velocity profiles (left y-axis, dashed). For a lower boundary pressure of 1 μbar, ﹩{R}_{{\rm{\min }}}=1.028{R}_{P}﹩, which does not capture the bolometrically heated/cooled region, so ﹩T({R}_{{\rm{\min }}}(1\mu {\rm{bar}}))\ne {T}_{{\rm{skin}}}=1324﹩ K (red) and results in an order-of-magnitude-higher mass loss than the ground truth (black). Averaging the temperature oscillations tells us the ﹩T({R}_{{\rm{\min }}}(1\mu {\rm{bar}}))=5486﹩ K (cyan), which puts the mass-loss rate within a factor of 2. Because neither of these solutions captures the molecular region, there is no higher mean molecular weight or bolometric heating/cooling included. To confirm the validity of this approximation, we lower (black) the base pressure to 1000 μbar (﹩{R}_{{\rm{\min }}}=1.016{R}_{P}﹩) to capture the photoionization base and molecular region, thus making ﹩T({R}_{{\rm{\min }}}(1000\mu {\rm{bar}}))={T}_{{\rm{skin}}}=1324﹩ K.
Paper: Wind-AE: A Fast, Open-source 1D Photoevaporation Code with Metal and Multifrequency X-Ray Capabilities
Authors: Madelyn I. Broome, Ruth Murray-Clay, John R. McCann, James E. Owen
Figure caption: Abundance-weighted ionization cross sections—photoionization cross sections for H I (olive) and O I (lime green) weighted by their fractional abundance (0.79332 and 0.00669, respectively) at 1× solar metallicity as a function of photon energy (bottom axis) and wavelength (top axis). Frequency-dependent cross sections are derived from coefficients and analytic equations in D. A. Verner & G. J. Ferland (1996) and I. M. Band et al. (1990).
Paper: Wind-AE: A Fast, Open-source 1D Photoevaporation Code with Metal and Multifrequency X-Ray Capabilities
Authors: Madelyn I. Broome, Ruth Murray-Clay, John R. McCann, James E. Owen
Figure caption: J. E. Owen & A. P. Jackson (2012) mass-loss grid. Solid lines are slices at 0.1MJ (black), 0.47MJ (dark cyan), and 1.08MJ (green) through the mass-loss grid for planets at 0.1 au irradiated by a 1 M⊙ star with X-ray luminosity LX = 1030 erg cm−2 from Figure 5 in J. E. Owen & A. P. Jackson (2012). Note that the radii in that figure are not optical transit radii but the approximate τ(1 keV) = 1 radius. Hence, we plot the log of geometrically averaged ﹩{\dot{M}}_{/3}﹩ in g s−1 as a function of τ(1 keV) = 1 for planets of the same masses (dashed). The dashed solutions do not extend to higher X-ray radii because planets with higher RP values enter the low escape velocity regime, in which the relaxation code is currently not well characterized (see Section 5.2).
Paper: Wind-AE: A Fast, Open-source 1D Photoevaporation Code with Metal and Multifrequency X-Ray Capabilities
Authors: Madelyn I. Broome, Ruth Murray-Clay, John R. McCann, James E. Owen
Figure caption: High-resolution scaled solar spectrum versus smoothed. Shown in blue are solutions using the FISM2 LISIRD solar spectrum scaled to an integrated flux of 1095 erg s−1 cm−2, and shown in orange are solutions using the smoothed spectrum normalized to the same integrated flux (as in Figure 2). Thicker, darker lines are the temperature profile, and thinner, lighter lines are the ionization fraction.
Paper: Wind-AE: A Fast, Open-source 1D Photoevaporation Code with Metal and Multifrequency X-Ray Capabilities
Authors: Madelyn I. Broome, Ruth Murray-Clay, John R. McCann, James E. Owen
Figure caption: Top: the colored lines show a comparison of our two-level atom model fits to the cooling rates (solid) against the numerically computed cooling rates (dashed) for the individual transitions of O II. The black lines show a comparison of the two-level model for the four most relevant lines compared to the full numerical cooling rate including all the energy levels and transitions (still under the assumption of a statistically collisional equilibrium). The lines are shown for an electron density of 5.4556 × 108 cm−3. Bottom: the relative error between the total cooling rate computed from our two-level atom approach and the total numerically computed cooling rate, demonstrating that our accuracy is at the 10%–30% level in the temperature range of interest.
Paper: Wind-AE: A Fast, Open-source 1D Photoevaporation Code with Metal and Multifrequency X-Ray Capabilities
Authors: Madelyn I. Broome, Ruth Murray-Clay, John R. McCann, James E. Owen
Figure caption: Mean weight complementary error function transition—the transition from mean molecular weight μ(r < RXUV) = 2.3mH to mean atomic weight as governed by Equation (14) for HD 209458 b. Here the erfc decays over 1 scale height at RXUV.
Paper: Spectropolarimetric Evolution Reveals Dual-axis Ejecta in the Atypical Magnetar-powered SN 2012au
Authors: Sabrina DeSoto, Jennifer L. Hoffman, G. Grant Williams, Christopher Bilinski, Douglas C. Leonard, Peter A. Milne, Christopher Pickens, Manisha Shrestha, Nathan Smith, Paul S. Smith
Figure caption: Polar plots of line polarization for SN 2012au throughout all (a) photospheric (days 0–90) and (b) transitional-nebular-phase (day 295) epochs. All polarization values have had continuum subtracted, except for those shown on day 295. For clarity, we plot PA +180° for different line regions as a function of blueshifted velocity (on the radial axes). The spread of the angle for each colored region is either 10° or the uncertainty in PA for that region, whichever is larger for legibility. The angle corresponding to the GCF slope (GCFθ; Section 5) has also been adjusted by +180° and is shown as a translucent gray wedge, spanning the width of the calculated PA uncertainty and stretched over the whole velocity space. The black, dashed semicircle represents the photospheric velocity (Section 3.2). Line polarization in regions for photospheric epochs (defined in Section 6) are shown for Fe II multiplet 42, He I λ5876, λ6678, λ7065, O I λ7774, and [O I] λλ 6300, 6330, as blocks with heights determined by a 15 Å bin size converted to velocity for the appropriate rest wavelength. Blocks corresponding to the peak polarization are solid filled and outlined in black. The peak polarization values for He I λ5876 and λ7065 at days 0–7 share the same PA and thus overlap in the first panel; we show only the He I λ5876 block. The plot for day 295 (b) shows a different subset of line polarization, including Mg I λ4571 and Na I λλ5980, 5986 for the wing regions described in Section 6.4, with the peak polarization of the red wing regions plotted as a single block with a red outline by taking the negative equivalent of the redward velocity shift where it appears. There is no continuum or photospheric velocity defined for this epoch.
Paper: Spectropolarimetric Evolution Reveals Dual-axis Ejecta in the Atypical Magnetar-powered SN 2012au
Authors: Sabrina DeSoto, Jennifer L. Hoffman, G. Grant Williams, Christopher Bilinski, Douglas C. Leonard, Peter A. Milne, Christopher Pickens, Manisha Shrestha, Nathan Smith, Paul S. Smith
Figure caption: Early photospheric-phase behavior in q−u space of the He I λ5876 (diamonds and green lines), potentially blended He I/Fe II λ5018 (squares and dark blue lines), He I λ6678 (triangles and purple lines), and He I λ7065 (circles and orange lines) absorption features in the velocity range of 0−18,000 km s−1 after continuum subtraction. Velocities are indicated by the point colors, referring to the color bar at right. The upper-limit ISP is plotted as a red circle on each panel, and average uncertainties for each line region are shown in the upper left of each panel. For calculated average uncertainties less than 0.05%, we display the upper-limit instrumental uncertainty of 0.05% (Section 2). The GCFs at each epoch are plotted in black for comparison (Section 5); because of the continuum subtraction, these lines are now offset from the data points.
Paper: Spectropolarimetric Evolution Reveals Dual-axis Ejecta in the Atypical Magnetar-powered SN 2012au
Authors: Sabrina DeSoto, Jennifer L. Hoffman, G. Grant Williams, Christopher Bilinski, Douglas C. Leonard, Peter A. Milne, Christopher Pickens, Manisha Shrestha, Nathan Smith, Paul S. Smith
Figure caption: Full-spectrum (3890–7855 Å, binned to 15 Å) Stokes q and u data for all epochs of SN 2012au, color coded by wavelength. Black diagonal lines represent the error-weighted best fit in each epoch to all the data excluding major line regions (He I λ5876, λ7065 and Fe II λλλ4924, 5018, 5169; Section 5). The error-weighted average of points for the blue continuum region (5120–5270 Å) is displayed as a black star and for the red continuum region (7250–7350 Å) as a black X, except for day 26, where it is designated by a gray X as it was calculated by other means (Section 6). Our adopted upper-limit ISP magnitude is plotted as a red circle around the origin. The average uncertainty over all points is displayed as a cross at the top left of each diagram.
Paper: Spectropolarimetric Evolution Reveals Dual-axis Ejecta in the Atypical Magnetar-powered SN 2012au
Authors: Sabrina DeSoto, Jennifer L. Hoffman, G. Grant Williams, Christopher Bilinski, Douglas C. Leonard, Peter A. Milne, Christopher Pickens, Manisha Shrestha, Nathan Smith, Paul S. Smith
Figure caption: Illustration of the possible SN 2012au explosion geometry on the sky for days 0–40 (top three panels) and day 295 (bottom panel). Arrows depict polarization vectors, with dashed lines representing those that cancel out and solid lines representing those contributing to the net polarization (“net P” arrows). At early times, an elongated (prolate ellipsoidal) photosphere creates a net continuum polarization (top panel). A nearly uniform distribution of iron over the photosphere (with a slight overdensity along the equatorial plane; second sketch) creates a large polarization magnitude and inverse P Cygni polarization profile in the Fe II triplet. Helium-rich material in the polar regions selectively blocks continuum light such that the remaining continuum creates the net polarization and rotated PA in the He I lines (third sketch). At later times (bottom), a highly asymmetric inner structure with a different PA reflects a newly oriented photosphere or excited heavy elements (purple). These sketches represent only one possible explanation for the observed signatures; other explosion configurations cannot be ruled out without further modeling.
Paper: Spectropolarimetric Evolution Reveals Dual-axis Ejecta in the Atypical Magnetar-powered SN 2012au
Authors: Sabrina DeSoto, Jennifer L. Hoffman, G. Grant Williams, Christopher Bilinski, Douglas C. Leonard, Peter A. Milne, Christopher Pickens, Manisha Shrestha, Nathan Smith, Paul S. Smith
Figure caption: Continuum polarization for SN 2012au by observation day. Error-weighted means of the total polarization for the narrow continuum regions defined in Section 5, tabulated as ﹩\overline{p}﹩ in Table 2, are displayed as the red squares (7250–7350 Å) and blue diamonds (5120–5270 Å). Corresponding exponential fits are shown as black-dashed lines with the corresponding exponent and residual sum of squares (RSS) displayed in black. For comparison, we also show power-law fits with gray-dotted lines and the power and RSS displayed in gray. Shaded regions around the data points represent the range of polarization magnitudes under different ISP assumptions (Section 5; Table 2). Exponential fits were not applied to these ISP-adjusted points because each point is calculated using a different ISP PA, dissolving any relation the points might have to one another over time.