What is the reason for the lack of cool evolved stars near the center of the Galaxy?
The observed deficit of bright late-type giants in the central parsec of the Milky Way remains an open problem. We investigate whether repeated passages of red giants (RGs) through a past jet from Sgr$~$A$^*$ can modify their envelopes and apparent spectral types. Three-dimensional hydrodynamical simulations follow a $1\,M_\odot$, $100\,R_\odot$ RG through up to ten jet crossings at $10^{-3}\,\text{pc}$, using jet kinetic luminosities of $10^{42}$, $10^{44}$, and $10^{48}\,\text{erg}\,\text{s}^{-1}$. Each passage produces shocks, envelope ablation, and an asymmetric downstream tail. For jet luminosities up to $10^{44}\,\text{erg}\,\text{s}^{-1}$, the cumulative ablated mass evolves approximately as $ΔM\propto t^{1/2}$ and reaches about $10^{-4}\,M_\odot$ over a $10^5\,\text{yr}$ active phase. Repeated heating also raises the surface temperature from about $3600$ to $8500\,\text{K}$ during the first ten passages, potentially making an M-type giant appear as an A-type source. Jet feedback may therefore contribute to the apparent depletion of cool giants and the excess of hot stars in galactic nuclei (GN).