A comparative study of two X2.2 and X9.3 solar flares observed with HARPS-N. Reconciling Sun-as-a-star spectroscopy and high-spatial resolution solar observations in the context of the solar-stellar connection

Context. Stellar flares cannot be spatially resolved, which complicates ascertaining the physical processes behind particular spectral signatures. Due to their proximity to Earth, solar flares can serve as a stepping stone for understanding their stellar counterparts, especially when using a Sun-as-a-star instrument and in combination with spatially resolved observations.
Aims: We aim to understand the disk-integrated spectral behaviors of a confined X2.2 flare and its eruptive X9.3 successor, which had energies of 2.2 × 10³¹ erg and 9.3 × 10³¹ erg, respectively, as measured by Sun-as-a-star observations with the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N).
Methods: The behavior of multiple photospheric (Na D₁ & D₂, Mg I at 5173 Å, Fe I at 6173 Å, and Mn I at 4031 Å) and chromospheric (Ca II H & K, Hα, Hβ, and He ID₃) spectral lines were investigated by means of activity indices and contrast profiles. A number of different photospheric lines were also investigated by means of equivalent widths, and radial velocity measures, which were then related to physical processes directly observed in high-resolution observations made with the Swedish 1-m Solar Telescope (SST) and the Atmospheric Imaging Assembly (AIA) on board of the Solar Dynamics Observatory (SDO).
Results: Our findings suggest a relationship between the evolving shapes of contrast profile time and the flare locations, which assists in constraining flare locations in disk-integrated observations. In addition, an upward bias was found in flare statistics based on activity indices derived from the Ca II H & K lines. In this case, much smaller flares cause a similar increase in the activity index as that produced by larger flares. Hα-based activity indices do not show this bias and are therefore less susceptible to activity jitter. Sodium line profiles show a strongly asymmetric response during flare activity, which is best captured with a newly defined asymmetrical sodium activity index. A strong flare response was detected in Mn I line profiles, which is unexpected and calls for further exploration. Intensity increases in Hα, Hβ, and certain spectral windows of AIA before the flare onset suggest their potential use as short-term flare predictors.