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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 inspatially-resolved strong-line emission maps that have been interpreted aslarge-scale active galactic nuclei driven ionized winds. To investigate thepossible fuel source for these winds, we examine the abundance and kinematicsof cool gas ($\rm T \sim 100-1000 K$) inferred from Na I D absorption in redgeysers and matched control samples drawn from SDSS-IV MaNGA. We find that redgeysers host greater amounts of NaD-associated material. Substantial cool gascomponents are detected in more than $\rm 50 \%$ of red geysers (compared to25\% of the control sample) going up to 78$\%$ for radio-detected red geysers.Our key result is that cool gas in red geysers is predominantly infalling.Among our 30 radio-detected red geysers, 86$\%$ show receding NaD absorptionvelocities (with respect to the systemic velocity) between $\rm 40 -50~km~s^{-1}$. We verify this result by stacking NaD profiles across eachsample which confirms the presence of infalling NaD velocities within redgeysers ( $\sim\rm 40~km~s^{-1}$) with no velocity offsets detected in thecontrol samples. Interpreting our observations as signatures of inflowing coolneutral clouds, we derive an approximate mass inflow rate of $\rm \dot{M}_{in}\sim 0.1 M_{\odot} yr^{-1}$, similar to that expected from minor merging andinternal recycling. Some red geysers show much higher rates ($\rm \dot{M}_{in}\sim 5 M_{\odot} yr^{-1}$) that may indicate an ongoing accretion event.

Signatures of inflowing gas in red geyser galaxies hosting radio-AGN