The AURORA Survey: The Evolution of Multi-phase Electron Densities at High Redshift

We present an analysis of deep $\textit{JWST}$/NIRSpec spectra of star-forming galaxies at $z\simeq1.4-10$, observed as part of the AURORA survey. We infer median low-ionization electron densities of $268_{-49}^{+45}~\rm cm^{-3}$, $350_{-76}^{+140}~\rm cm^{-3}$, and $480_{-310}^{+390}~\rm cm^{-3}$ at redshifts z$=2.3$, $z=3.2$, and $z=5.3$, respectively, revealing an evolutionary trend following $(1+z)^{1.5\pm0.6}$. We identify weak positive correlations between electron density and star formation rate (SFR) as well as SFR surface density, but no significant trends with stellar mass or specific SFR. Correlations with rest-optical emission line ratios show densities increasing with $\rm [NeIII]\lambda3869/[OII]\lambda3727$ and, potentially, $\rm [OIII]\lambda5007/[OII]\lambda3727$, although variations in dust attenuation complicate the latter. Additionally, electron density is more strongly correlated with distance from the local BPT sequence than can be explained by simple photoionization models. We further derive electron densities from the CIII] doublet probing higher-ionization gas, and find a median value of $1.4_{-0.5}^{+0.7}\times10^4~\rm cm^{-3}$, $\sim30$ times higher than densities inferred from [SII]. This comparison suggests a consistent HII region structure across cosmic time with dense, high-ionization interiors surrounded by less dense, low-ionization gas. We compare measurements of AURORA galaxies to predictions from the SPHINX galaxy formations, highlighting the interplay between residual molecular cloud pressure in young galaxies and feedback from stellar winds and supernovae as galaxies mature.