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The upper three panels show the dependency of the sheath electron density profiles (Ne(τ)) on the three parameters, ρe (panel (a)), dsheath (b), and dfront (c), while the other two parameters are fixed. The lower panels are the modeled Thomson-scattering brightness profiles I ′ (L) in mean solar brightness (B⊙), resulting from the given Ne(τ) in the same line-styles in the upper panels. Lines in solid, dotted, dashed, dash-dotted, dash-dot-dotted refers to the cases when ρe = (1.6, 3.1, 4.7, 6.2, 7.8) × 104, dsheath = 1 R⊙, and dfront = 0.25 R⊙ in panel (a); ρe = 6.2 × 104, dsheath = (0.6, 1.0, 1.4, 1.8, 8.0) R⊙, and dfront = 0.25 R⊙ in panel (b); and ρe = 6.2 × 104, dsheath = 1 R⊙, and (0.0, 0.1, 0.3, 0.4, 0.5) R⊙ in panel (c). Because the Gaussian tail is not zero even at large distances, Ne(τ < 0) is not exactly zero, if dfront ≠ 0. By definition, we simply set Ne(τ < 0) = 0. The 3D geometry of the shock used to calculate I′ is shown in Figure 1b.
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