Results for the radiating sphere test at t = 10⁴. Left panels show energy-integrated number densities (top panel) and energy densities (bottom panel) multiplied by r² vs. radius. In each of these panels we show the comoving- and Eulerian-frame number and energy densities, and results have been scaled to values at the outer radial boundary. In the top left panel, we plot the comoving-frame number density ﹩[{D}_{\nu }(r)/{D}_{\nu }(r=1{0}^{4})]\times {(r/1{0}^{4})}^{2}﹩ (dotted black) and the Eulerian-frame number density ﹩[{N}_{\nu }(r)/{N}_{\nu }(r=1{0}^{4})]\times {(r/1{0}^{4})}^{2}﹩ (dotted blue). In the bottom-left panel, we plot the comoving-frame energy density ﹩[{J}_{\nu }(r)/{J}_{\nu }(r=1{0}^{4})]\times {(r/1{0}^{4})}^{2}﹩ (dotted black) and the Eulerian-frame energy density ﹩[{E}_{\nu }(r)/{E}_{\nu }(r=1{0}^{4})]\times {(r/1{0}^{4})}^{2}﹩ (dotted blue). In both of these panels, the analytical solution, obtained using Equation (149), is plotted for the comoving-frame quantity (solid black). In the right panel, spectral particle distributions are plotted for various radii. Analytic spectra are plotted for r = 10¹ (solid black) and r = 1.5 × 10² (solid blue). Numerically obtained spectra are plotted for r = 10¹ (black circles), r = 1.5 × 10² (blue circles), and r = 10⁴ (red crosses).