The density of the warm ionized gas in high-redshift galaxies is known to be higher than what is typical in local galaxies on similar scales .
At the same time , the mean global properties of the high- and low-redshift galaxies are quite different .
Here , we present a detailed differential analysis of the ionization parameters of 14 star-forming galaxies at redshift 2.6–3.4 , compiled from the literature .
For each of those high-redshift galaxies , we construct a comparison sample of low-redshift galaxies closely matched in specific star formation rate ( sSFR ) and stellar mass , thus ensuring that their global physical conditions are similar to the high-redshift galaxy .
We find that the median \log [ { \mathrm { O } } \textsc { iii } ] \ > 5007 / [ { \mathrm { O } } \textsc { ii } ] \ > 3727 line ratio of the high-redshift galaxies is 0.5 dex higher than their local counterparts .
We construct a new calibration between the [ { \mathrm { O } } \textsc { iii } ] \ > 5007 / [ { \mathrm { O } } \textsc { ii } ] \ > 3727 emission line ratio and ionization parameter to estimate the difference between the ionization parameters in the high and low-redshift samples .
Using this , we show that the typical density of the warm ionized gas in star-forming regions decreases by a median factor of 7.1 ^ { +10.2 } _ { -5.4 } from z \sim 3.3 to z \sim 0 at fixed mass and sSFR .
We show that metallicity differences can not explain the observed density differences .
Because the high- and low-redshift samples are comparable in size , we infer that the relationship between star formation rate density and gas density must have been significantly less efficient at z \sim 2 - 3 than what is observed in nearby galaxies with similar levels of star formation activity .