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The origins of quasi-periodic eruptions (QPEs) are poorly understood,although most theoretical explanations invoke an accretion disk around asupermassive black hole. The gas and stellar environments in the galacticnuclei of these sources are also poorly constrained. In this paper, we presentan analysis of archival Hubble Space Telescope (HST) images to study thenarrow-line [O III] emission in the QPE source GSN 069. We find strong evidencefor a compact nuclear [O III] emission region of size $\lesssim 35$ pc,overlaid on top of extended [O III] emission up to 2 kpc away from the nucleus.The age of the accretion system is estimated to be between 10 and 100 yr. The[O III] luminosity of the compact region was measured to be $(2.1 \pm 0.3)\times 10^{40}\,\rm erg\,s^{-1}$. Based on CLOUDY simulations, we constrainthat the [O III] emitting gas has a hydrogen number density in the range $5\times 10^{3} < n_{\rm H} \lesssim 10^{8}\,\rm cm^{-3}$ and volume fillingfactor $f_{\rm V} < 2 \times 10^{-3}$. We suggest that the dense gas in thenuclear region of GSN 069 originates from molecular clouds (with total mass$\gtrsim 3 \times 10^{3}\,M_{\odot}$), which are freshly ionised by the softX-ray photons from the accretion disk. We predict possible evolution of thecompact narrow-line region on emission-line diagnostic diagrams, and hencefuture HST or integral-field unit observations can be used to further pin downthe age of this puzzling system.

Constraints on the narrow-line region of the X-ray quasi-periodic eruption source GSN 069