An Empirical Model for Multiple Scattered Radiation in FUV

In this work, we present a systematic comparison of single- and multiple-scattering models for dust-scattered starlight across the UV sky and attempt to derive a simulation model of multiple-scattered radiation using the single-scattered radiation. Our new simulated multiple-scattering model uses a critical angle (θ c ) , which is dependent on optical depth (τ ), albedo (a), and phase function asymmetry (g), to replace the computationally intensive full Monte Carlo treatment. We find that multiple-scattering becomes increasingly important in almost all optical depths, depending on the scattering geometry. UV-bright stars show a peak scattering intensity near the stellar disk, dropping by an order of magnitude within 10–15 degrees and merging with the background at 40–50 degrees, whereas fainter or more distant stars require larger angular separations to reach the same relative reduction. We introduce a functional form, I θ = I 0 (1 − tanh(SP × θ)), to describe the radial decrease in scattered intensity, with the slope parameter declining systematically for more distant stars. Depending on a star’s position, multiple-scattered fluxes can exceed single-scattered fluxes by up to 200%, and both converge at a critical angle, θ c , which depends logarithmically on stellar distance and is governed by τ , a, and g. Notably, θ c remains independent of Galactic longitude or latitude, underscoring the robust, geometry-driven nature of the scattering process.