Dependence of EKNR abundance on surrounding density and mass distribution. Top: $\frac{\mathrm{d}{N}_{\mathrm{obs}}}{\mathrm{dlog}t}$ for EKNRs taking a distribution of external densities n₀ with $n_{0,\max }=1{\mathrm{cm}}^{-3}$ and varying n_0, min and a (Eq. (30)) shown by different line styles. In green, we consider a distribution over both density and ejecta mass but not over ejecta energy. For reference, we show our fiducial case of EKNR as in Fig. 3 in solid blue lines. Bottom: Areal density for the same cases as in the top panel. We also show the KNR case from Fig. 3, which is a factor of about 10² − 10³ smaller than the EKNR cases. We have used the results of Anderson et al. 2020, Murphy et al. 2021, Mooley et al. 2022 as upper limits, because these authors do not detect a KNR.