Possible explanation for the PD discrepancy between POLAR and AstroSAT. (a) The PD distribution for the emission from different local fluid elements, relative to the light of sight. Note that Γ = 100, θ_c, Γ = 0.01, θ_v = 0.015, and p = 4 were adopted. The solid red line represents the polarization degree of each fluid element with θ_LOS, without considering the influence of the azimuthal angle ϕ_LOS (see Equation (5)). The blue boxes illustrate the integrated polarization degree for specific θ_LOS intervals, considering the influence of the azimuthal angle. The polarization degree obviously rises rapidly, peaks at around θ_LOS ∼ 1/Γ, and then drops down quickly. The high polarization is almost within ∼1.5/Γ or ∼2/Γ. The dashed green line marks the total polarization degree for 0 ≤ θ_LOS ≤ 0.1. (b) The comparison of the spectra emitted from 0 ≤ θ_LOS ≤ 1.5/Γ and 1.5/Γ ≤ θ_LOS ≤ 5/Γ (Γ = 200, Γ ⋅ θ_c, Γ = 1, and θ_v = 1.5/Γ were adopted). Obviously, the spectrum from the inner region (0 ≤ θ_LOS ≤ 1.5/Γ) has higher energy and a higher PD (as can be seen in the left panel). This may contribute to the larger PD of AstroSAT (100–600 keV), due to its higher band energy and narrower bandwidth than POLAR (50–500 keV). The narrow bandwidth of ∼6 times ultimately enables only the detection of the high-energy component from the inner region (the right portion of the blue line).