Spectrally and spatially resolved (sub)millimeter HCN-to-HCO$^{+}$ flux ratios in nearby ultraluminous infrared galaxies

We present the results of our investigations of spectrally and spatially resolved (sub)millimeter HCN-to-HCO$^{+}$ flux ratios at J=2-1, J=3-2, and/or J=4-3 in 18 nearby ($z <$ 0.15) ultraluminous infrared galaxies (ULIRGs), using ALMA $\lesssim$0.2" ($\lesssim$500 pc) resolution data. The geometry of elevated HCN-to-HCO$^{+}$ flux ratios (with $>$3$\sigma$ detections for both molecular lines) in position-position-velocity (PPV) space is visually classified into (i) spherical shell (spectrally and spatially distinct), (ii) spectrally distinct and spatially compact, and (iii) filled (spectrally filled and spatially compact). These can naturally be explained by the elevation of the flux ratio due to (i) a spatially resolved outflow, (ii) an AGN and/or a spatially unresolved outflow with blueshifted and redshifted emission components, and (iii) an AGN and/or a spatially confined outflow with not clearly separated blueshifted and redshifted velocity components, respectively. Signatures of elevated HCN-to-HCO$^{+}$ flux ratios originated from (a) spatially resolved outflow and (b) AGN and/or spatially unresolved outflow are seen in seven and nine ULIRGs, respectively. In the former spatially resolved outflow-origin case, modest-velocity components relative to the maximum outflow velocity tend to be probed by spaxels with elevated HCN-to-HCO$^{+}$ flux ratios. The spectrally and spatially resolved HCN-to-HCO$^{+}$ flux ratios can provide additional information on the physical origin of the elevated flux ratios in nearby ULIRG nuclei, compared to previously conducted spatially integrated and/or velocity-integrated analyses.