Linking Electron Density with Elevated Star Formation Activity from <i>z</i> = 0 to <i>z</i> = 10

Abstract 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 &lt; z &lt; 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mspace width="0.25em"/> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mspace width="0.1em"/> <mml:mtext>SFR</mml:mtext> <mml:mspace width="0.1em"/> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mspace width="0.1em"/> <mml:mtext>yr</mml:mtext> <mml:mspace width="0.1em"/> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mspace width="0.1em"/> <mml:mtext>kpc</mml:mtext> <mml:mspace width="0.1em"/> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≥</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1.46</mml:mn> </mml:math> , the relation follows <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mtext/> <mml:msub> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> <mml:mtext/> <mml:mo>=</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>233</mml:mn> <mml:mo>±</mml:mo> <mml:mn>13</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>×</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mspace width="0.1em"/> <mml:mtext>SFR</mml:mtext> <mml:mspace width="0.1em"/> </mml:mrow> <mml:mrow> <mml:mn>0.49</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.02</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . 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.