JWST and ALMA Joint Analysis with [O <scp>II</scp> ] <i>λλ</i> 3726, 3729, [O <scp>III</scp> ] <i>λ</i> 4363, [O <scp>III</scp> ] 88 <i>μ</i> m, and [O <scp>III</scp> ] 52 <i>μ</i> m: Multizone Evolution of Electron Densities at <i>z</i>  ∼ 0–14 and

Abstract We present a JWST and Atacama Large Millimeter/submillimeter Array (ALMA) detailed study of the interstellar medium properties of high-redshift galaxies. Our JWST/NIRSpec integral field unit spectroscopy targeting three galaxies at z = 6–7 detects key rest-frame optical emission lines, allowing us to derive [O ii ] λλ 3726, 3729–based electron densities of n e ,optical ∼ 1000 cm −3 on average and [O iii ] λ 4363–based metallicities of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>12</mml:mn> <mml:mo>+</mml:mo> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">O</mml:mi> <mml:mo>/</mml:mo> <mml:mi mathvariant="normal">H</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>8.0</mml:mn> <mml:mo>-</mml:mo> <mml:mn>8.2</mml:mn> </mml:math> in two galaxies. New ALMA Band 9 and 10 observations detect the [O iii ] 52 μ m line in one galaxy but do not in the others, resulting in far-infrared (FIR)-based densities of n e ,FIR ≲ 500 cm −3 from the [O iii ] 52 μ m/[O iii ] 88 μ m ratio, systematically lower than the optical [O ii ]-based measurements. These low FIR-based densities are comparable to those at both z ∼ 0 and z &gt; 6 in the literature, including JADES-GS-z14-0 at z = 14.18, suggesting little evolution up to z ∼ 14, in contrast to the increasing trend of optical-based densities with redshift. By conducting a JWST and ALMA joint analysis using emission lines detected with both telescopes, we find that the observed FIR [O iii ] 52 and 88 μ m luminosities are too high to be explained by the optical-based densities at which they would be significantly collisionally de-excited. Instead, a two-zone model with distinct high- and low-density regions is required to reproduce all observed lines, indicating that FIR [O iii ] emission arises predominantly from low-density gas, while the optical [O iii ] and [O ii ] lines trace both regions. We further demonstrate that the direct- T e method can sometimes significantly underestimate metallicities up to 0.8 dex due to the presence of the low-density gas not fully traced by optical lines alone, highlighting the importance of combining optical and FIR lines to accurately determine gas-phase metallicities in the early Universe.