Time evolution of far-field neutrino luminosities, ﹩{L}_{{\nu }_{l}}^{\mathrm{Euler}}﹩, observed by an Eulerian observer at a distance of 500 km from a collapsing 20 M _⊙ star. Dashed lines and solid lines correspond to the results with the advanced set (I) and (II) interactions (i.e., Adv.I and Adv.II), respectively. Dashed–dotted lines, loosely dotted lines, and dotted lines correspond to the results of Adv.II with cutoff density values for ﹩{\nu }_{e}{\bar{\nu }}_{e}﹩ pair annihilation of ρ _cut = 10¹¹ g cm⁻³, ρ _cut = 10^12.5 g cm⁻³, and ρ _cut = 0 without the conservation treatment in Equation (70), respectively.