The Fe i 4377 ÅLine as a Solar Faculae Indicator: Insights from Spectral Ratio Analysis

Abstract Faculae are a dominant source of stellar activity noise in radial velocity measurements, yet their low contrast and broad surface distribution make them difficult to track in disc-integrated observations. We apply Spectral Ratio Analysis (SRA) to HARPS-N Sun-as-a-star observations to isolate and characterize the spectral imprint of facular regions over rotational timescales. The resulting SRA spectra show coherent, line-dependent variability sensitive to surface magnetic activity, with the Fe i 4377 Å line exhibiting a particularly strong diagnostic response to facular coverage. We interpret the observed signatures using two complementary synthetic frameworks: composite PHOENIX spectra, from which we derive best-fit facular temperature contrasts in the range 200-400 K, and MPS-ATLAS spectra synthesized using MURaM simulations of the quiet Sun including a small-scale dynamo and magnetically-enhanced facular analogues with initial mean vertical magnetic fields of 100G, 200G, and 300G. Both approaches are benchmarked against facular filling factors measured from Solar Dynamics Observatory (SDO) disc-resolved images. We find good agreement between SDO-measured and SRA-inferred filling factors using the Fe i 4377 Å line, with Pearson R coefficients of 0.587-0.927 across models and timescales. The estimated filling factors track the solar activity cycle, rising from ∼ 1.5 % at lower activity to ∼ 5.5 % at higher activity, consistent with SDO-measured filling factors. These results demonstrate that SRA offers a means to reliably track surface magnetic activity in disc-resolved spectra, which is necessary for mitigating the effects of activity on RV characterization of exoplanet masses and atmospheres at modern precision.