Rapidly varying ionization features in a Quasi-periodic Eruption: a homologous expansion model for the spectroscopic evolution

Quasi-Periodic Eruptions (QPEs) are recurring bursts of soft X-ray emission from supermassive black holes (SMBHs), which a growing class of models explains via extreme mass-ratio inspirals (EMRIs). QPEs exhibit blackbody-like emission with significant temperature evolution, but the minimal information content of their almost pure-thermal spectra has limited physical constraints. Here we study the recently discovered QPEs in ZTF19acnskyy (``Ansky''), which show absorption-like features evolving dramatically within eruptions and correlating strongly with continuum temperature and luminosity, further probing the conditions underlying the emission surface. The absorption features are well-described by dense ionized plasma of column density $N_{\rm H}\gtrsim 10^{21}$ cm$^{-2}$, blueshift $0.06\lesssim v/c \lesssim 0.4$, and either collisional or photoionization equilibrium. With high-resolution spectra, we also detect ionized blueshifted emission lines suggesting a nitrogen over-abundance of $21.7^{+18.5}_{-11.0}\times$ solar. We interpret our results with orbiter-disk collisions in an EMRI system, in which each impact drives a shock that locally heats the disk and expels X-ray emitting debris undergoing radiation pressure-driven homologous expansion. We explore an analytical toy model that links the rapid change in absorption lines to the evolution of the ionization parameter and the photosphere radius, and suggest that $\sim 10^{-3}M_\odot$ ejected per eruption with expansion velocities up to $v_{\rm max}\sim 0.15c$, can reproduce the absorption features. With these assumptions, we show a P Cygni profile in a spherical expansion geometry qualitatively matches the observed line profiles. Our work takes a first step towards extending existing physical models for QPEs to address their implications for spectral line formation.