Does galaxy-scale compactness regulate nebular electron density? A cross-scale test with DESI

Abstract: Nebular electron density, $n_e$, traces ionized gas in small-scale H\,{\sc ii} regions and diffuse ionized structures, whereas galaxy stellar surface density, $Σ<em>\star$, measures compactness on kpc scales. Whether these quantities are correlated is therefore a cross-scale question rather than a geometrical identity. We test whether nebular electron density varies systematically with galaxy-scale stellar compactness after controlling for the correlated effects of stellar mass and star-formation rate (SFR). We use DESI DR 1 spectra to test this cross-scale connection in AGN-clean star-forming galaxies at $0.10<z<0.44$. We divide each redshift interval into tertiles of $Σ</em>\star=M_\star/(2πR_e<sup>2)$. We construct one controlled sample in which the $M_\star$ distributions are matched across the three compactness tertiles, and a second in which their joint $M_\star$--SFR distributions are matched, thereby minimizing the influence of these correlated galaxy properties. For each compactness tertile, we stack the galaxy spectra with equal weight and use the stacked spectrum to measure the average $n_e$ of the galaxies in that sample. The average $n_e$ increases systematically toward higher stellar surface density in all redshift intervals. This is the first controlled population-level evidence for a correlation between kpc-scale galaxy stellar surface density (compactness) and the average $n_e$ of ionized gas on subgalactic scales. Its persistence after matching both $M_\star$ and SFR suggests that a more compact stellar configuration may promote higher gas pressure and/or stronger confinement of ionized gas, linking galaxy-scale structure to nebular conditions.