Correlation between star formation activity and electron density of ionized gas at z=2.5

In the redshift interval of $2<z<3$, the physical conditions of the inter-stellar medium (ISM) in star-forming galaxies are likely to be different from those in the local Universe because of lower gaseous metallicities, higher gas fractions, and higher star formation activities. In fact, observations suggest that higher electron densities, higher ionization parameters, and harder UV radiation fields are common. In this paper, based on the spectra of H$\alpha$-selected star-forming galaxies at $z=2.5$ taken with Multi-Object Spectrometer for InfraRed Exploration (MOSFIRE) on Keck-1 telescope, we measure electron densities ($n_e$) using the oxygen line ratio ( [OII]$\lambda\lambda$3726,3729), and investigate the relationships between the electron density of ionized gas and other physical properties. As a result, we find that the specific star formation rate (sSFR) and the surface density of SFR ($\Sigma_\mathrm{SFR}$) are correlated with the electron density at $z=2.5$ for the first time. The $\Sigma_\mathrm{SFR}-n_e$ relation is likely to be linked to the star formation law in HII regions (where star formation activity is regulated by interstellar pressure). Moreover, we discuss the mode of star formation in those galaxies. The correlation between sSFR and $\Sigma_\mathrm{SFR}$ suggests that highly star-forming galaxies (with high sSFR) tend to be characterized by higher surface densities of star formation ($\Sigma_\mathrm{SFR}$) and thus higher $n_e$ values as well.