A DESI Calibration of the [O II]--[S II] Electron-density Offset in Integrated Star-forming Galaxies

The [O II]$\lambda \lambda 3726,3729$ and [S II]$\lambda \lambda 6716,6731$ doublets are widely used as low-ionization electron-density diagnostics in galaxy spectra and are often treated as interchangeable when only one of them is accessible. We test this assumption using the DESI DR1 Emission Line Catalog. For star-forming galaxies with fiducial emission lines, [O II] yields systematically higher electron densities than [S II], with a median offset of 0.228 dex. The binned median calibration is $\log n_e(\mathrm{O}\mathrm{I}\mathrm{I})=(0.752_{-0.097}^{+0.182})\log n_e(\mathrm{S}\mathrm{I}\mathrm{I})+(0.832_{-0.422}^{+0.231})$. The offset is larger in galaxies with higher stellar mass, H$\alpha$ star-formation rate, dust attenuation, and $N2\equiv \log ([\mathrm{N}\mathrm{I}\mathrm{I}]\lambda 6583\mathrm{/}\mathrm{H}\alpha )$, an empirical gas-phase metallicity proxy, and smaller in galaxies with higher $\log O_{32}\equiv \log \{[\mathrm{O}\mathrm{I}\mathrm{I}\mathrm{I}]\lambda 5007\mathrm{/}([\mathrm{O}\mathrm{I}\mathrm{I}]\lambda 3726+\lambda 3729)\}$, an ionization proxy; no significant trend is found with specific star-formation rate. These trends are consistent with [O II] and [S II] sampling different low-ionization gas phases in integrated spectra, with [S II] more strongly weighted toward lower-density diffuse or outer gas. Our results show that [O II]- and [S II]-based densities should not be mixed without empirical calibration in studies of ISM pressure, nebular density, and their evolution across galaxy samples and redshift.