2025MNRAS.541.1707T

We present an analysis of deep JWST/NIRSpec spectra of star-forming galaxies at $z\simeq 1.4{\!-\!}10$, observed as part of the Assembly of Ultra-deep Rest-optical Observations Revealing Astrophysics (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, which is best described by an evolutionary trend following $(1+z)^{1.5\pm 0.6}$. 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 $\rm [Ne\,{{\small III}}]\lambda 3869/[O\,{{\small II}}]\lambda 3727$ and, potentially, $\rm [O\,{{\small III}}]\lambda 5007/[O\,{{\small II}}]\lambda 3727$, although variations in dust attenuation complicate the latter. Additionally, electron density is more strongly correlated with distance from the local Baldwin, Phillips, and Terlevich (BPT) sequence than can be explained by simple photoionization models. We further derive electron densities from the [C III] doublet probing higher ionization gas, and find a median value of $1.4_{-0.5}^{+0.7}\times 10^4~\rm cm^{-3}$, ${\sim} 30$ times higher than densities inferred from [S II]. This comparison suggests a consistent H II 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.