Signatures of Inflowing Gas in Red Geyser Galaxies Hosting Radio Active Galactic Nuclei

We study cool neutral gas traced by NaD absorption in 140 local ($\rm z<0.1)$ early-type ``red geyser'' galaxies. These galaxies show unique signatures spatially-resolved strong-line emission maps that have been interpreted as large-scale active galactic nuclei driven ionized winds. To investigate the possible fuel source for these winds, we examine abundance and kinematics of T \sim 100-1000 K$) inferred from Na I D red geysers matched control samples drawn SDSS-IV MaNGA. find host greater amounts NaD-associated material. Substantial components are detected more than $\rm 50 \%$ (compared to 25\% sample) going up 78$\%$ radio-detected geysers. Our key result is predominantly infalling. Among our 30 geysers, 86$\%$ receding velocities (with respect systemic velocity) between 40 - 50~km~s^{-1}$. verify this stacking profiles across each sample which confirms presence infalling within ( $\sim\rm 40~km~s^{-1}$) with no velocity offsets samples. Interpreting observations inflowing clouds, derive an approximate mass inflow rate \dot{M}_{in} 0.1 M_{\odot} yr^{-1}$, similar expected minor merging internal recycling. Some much higher rates 5 yr^{-1}$) may indicate ongoing accretion event.