Recovering Ionizing Photon Escape and Galaxy Scaling Relations in the LzLCS via Si II and C II Absorption Lines and Mock Spectra from a Radiation-Hydrodynamic Simulation
In this work, we use a radiation-hydrodynamic simulation of a single $\sim10^9M_{\odot}$ virtual galaxy to study Si II and C II line profiles seen in stacked HST/COS spectra of 58 galaxies from the LzLCS+ sample. We compare stacks across three mass bins ($M_{\star} \leq 10^8M_{\odot}$, $10^8$-$10^9M_{\odot}$, and $M_{\star} \geq 10^9M_{\odot}$) and three stacking methods (mean, median, and weighted average) to a library of 22,500 mock spectra. We investigate whether the simulation can accurately mimic real gas features, reveal clear trends with galaxy properties, and provide indirect estimates of the ionizing escape fraction ($f_{\rm esc}$). We find reasonable agreement between simulated and observed profiles ($\chi^2 < 1$) across all mass regimes. Notably, extracting line properties such as EW and $R_f$ from best-fit mock profiles provides a robust alternative to direct empirical trends, particularly in the low-S/N regime where noise frequently biases results. The simulation-based LIS features, although derived from a single virtual object, exhibit clear correlations with $M_{\star}$, SFR, and $f_{\rm esc}$, mirroring established empirical scaling relations. We find that the best-matching mock spectra predominantly originate from simulation time steps corresponding to peak UV luminosity and intense starburst phases, suggesting that these active periods generate the ISM diversity observed in star-forming galaxies. Finally, simulation-based estimates ($f_{\rm esc}^{\rm virtual}$) reproduce the observed mass-dependent trends in $f_{\rm esc}$ and are in close agreement with the average $f_{\rm esc}$ of the generated stacks. This simulation-based framework establishes a relevant methodology for interpreting spectroscopic observations, including inferring $f_{\rm esc}$ and characterizing physical scaling relations, in high-redshift galaxies from the Epoch of Reionization.