High [O III]/[C II] surface brightness ratios trace early starburst galaxies

We study the impact of deviations from the Kennicutt-Schmidt relation (quantified by the 'burstiness' parameter κ_s), gas metallicity (Z), and density (n) on the observed [O III]88 μm/[C II]158 μm surface brightness ratios (Σ_{[O III]}/Σ_{[C II]}) in nine galaxies at z ≈ 6-9. We first discuss possible biases in the measured Σ_{[O III]}/Σ_{[C II]} ratios by comparing the data with zoom-in cosmological simulations and then use a Markov Chain Monte Carlo algorithm to derive the best-fitting values of (κ_s, Z, n). We find that (i) the strongest dependence of Σ_{[O III]}/Σ_{[C II]} is on κ_s; (ii) high ratios identify starburst galaxies with short gas depletion times ($t_{\rm dep}=6-49\, \rm Myr$); (iii) a secondary dependence on density is found, with Σ_{[O III]}/Σ_{[C II]} anticorrelating with n as a result of the lower [O III] critical density; and (iv) the ratio weakly depends only on Z. The nine galaxies are significantly enriched (Z = 0.2-0.5 Z_⊙) and dense n ≈ 10^1-3 cm^-3. This lends further support to the starburst scenario in which a rapid enrichment of the interstellar medium is expected.