Linking Electron Density with Elevated Star Formation Activity from z = 0 to z = 10

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The interstellar medium in high-redshift galaxies exhibits significantly higher electron densities ( n e ) than in the local Universe. To investigate the origin of this trend, we analyze a sample of 9590 centrally star-forming galaxies with stellar masses greater than 10 9 M ⊙ at redshifts 0.01 < z < 0.04, selected from the Dark Energy Spectroscopic Instrument Data Release 1. We derive n e from the [S ii ] λλ 6716, 6731 doublet, measuring values of n e = 30–400 cm −3 at z ≈ 0. We find a tight correlation between n e and the star formation rate surface density (Σ SFR ), which is well described by a broken power law. Above a threshold of log ( Σ SFR / M ⊙ yr − 1 kpc − 2 ) ≥ − 1.46 , the relation follows n e = ( 233 ± 13 ) × Σ SFR 0.49 ± 0.02 . Below this threshold, n e remains approximately at a constant value of 44 ± 3 cm −3 . Remarkably, this relation remains consistent with measurements of galaxies at z = 0.9–10.2. By converting the observed redshift evolution of Σ SFR into n e evolution through our n e –Σ SFR relation, we obtain n e = 40 × (1 + z ) 1.4 cm −3 , consistent with previous direct observations. The n e –Σ SFR relation arises likely because the high Σ SFR , fueled by dense cold gas or elevated efficiency, enhances radiative and mechanical feedback and produces dense ionized gas whose n e are further regulated by ambient pressure. We conclude that the redshift evolution of n e primarily reflects the evolution of the cold gas density and star formation activity over cosmic time.