We derive new self-consistent theoretical UV, optical, and IR diagnostics for the ISM pressure and electron density in the ionized nebulae of star-forming galaxies. Our UV diagnostics utilize the inter-combination, forbidden and resonance lines of silicon, carbon, aluminum, neon, and nitrogen. We also calibrate the optical and IR forbidden lines of oxygen, argon, nitrogen and sulfur. We show that line ratios used as ISM pressure diagnostics depend on the gas-phase metallicity with a residual dependence on the ionization parameter of the gas. In addition, the traditional electron density diagnostic [S II] {lambda}6731/[S II] {lambda}6717 is strongly dependent on the gas-phase metallicity. We show how different emission-line ratios are produced in different ionization zones in our theoretical nebulae. The [S II] and [O II] ratios are produced in different zones, and should not be used interchangeably to measure the electron density of the gas unless the electron temperature is known to be constant. We review the temperature and density distributions observed within H II regions and discuss the implications of these distributions on measuring the electron density of the gas. Many H II regions contain radial variations in density. We suggest that the ISM pressure is a more meaningful quantity to measure in H II regions or galaxies. Specific combinations of line ratios can cover the full range of ISM pressures (4 < log(P/k) < 9). As H II regions become resolved at increasingly high redshift through the next generation telescopes, we anticipate that these diagnostics will be important for understanding the conditions around the young, hot stars from the early universe to the present day.
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