There is no single density: star-forming regions and galaxies hold more dense ionized gas than long assumed
Ionized gas fills star-forming regions and galaxies, and nearly everything we know about its temperature, pressure, mass, and composition is inferred from its emission lines [1-3]. The electron density is needed for all of these, yet a longstanding puzzle has resisted explanation: different density-sensitive lines, applied to the same gas, return values that disagree by up to two orders of magnitude. This is usually attributed either to each line tracing a physically distinct ionization zone or to imperfect atomic data [4-7]. Here we show that the disagreement is neither a flaw in the atomic data nor an ionization-stratification effect, but something more fundamental. Each diagnostic is tuned to a particular density, and when a nebula contains gas across a wide range of densities, as real nebulae do, each line reports the part of that range it is most sensitive to. The diagnostics do not measure a representative average density; they respond to different parts of a broad density distribution. This resolves the discrepancy with a simple relation between the density each line returns and the density it is most sensitive to, a relation that holds from individual H II regions to whole galaxies, near and far, and reveals that ionized nebulae contain far more dense gas than any one diagnostic implies. A nebula has no single electron density to measure, but a broad density distribution, and the masses, pressures, abundances and energetics built on the single-density assumption must be reconsidered, from nearby star-forming regions to galaxies across cosmic time.