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We present 0$.\!\!^{\prime\prime}22$-resolution Atacama LargeMillimeter/submillimeter Array (ALMA) observations of CO(2$-$1) emission fromthe circumnuclear gas disk in the red nugget relic galaxy PGC 11179. The diskshows regular rotation, with projected velocities near the center of 400 kms$^{-1}$. We assume the CO emission originates from a dynamically cold, thindisk and fit gas-dynamical models directly to the ALMA data. In addition, weexplore systematic uncertainties by testing the impacts of various modelassumptions on our results. The supermassive black hole (BH) mass($M_\mathrm{BH}$) is measured to be $M_\mathrm{BH} = (1.91\pm0.04$ [$1\sigma$statistical] $^{+0.11}_{-0.51}$ [systematic])$\times 10^9$ $M_\odot$, and the$H$-band stellar mass-to-light ratio $M/L_H=1.620\pm0.004$ [$1\sigma$statistical] $^{+0.211}_{-0.107}$ [systematic] $M_\odot/L_\odot$. This$M_\mathrm{BH}$ is consistent with the BH mass$-$stellar velocity dispersionrelation but over-massive compared to the BH mass$-$bulge luminosity relationby a factor of 3.7. PGC 11179 is part of a sample of local compact early-typegalaxies that are plausible relics of $z\sim2$ red nuggets, and its behaviorrelative to the scaling relations echoes that of three relic galaxy BHspreviously measured with stellar dynamics. These over-massive BHs could suggestBHs gain most of their mass before their host galaxies do. However, our resultscould also be explained by greater intrinsic scatter at the high-mass end ofthe scaling relations, or by systematic differences in gas- andstellar-dynamical methods. Additional $M_\mathrm{BH}$ measurements in thesample, including independent cross-checks between molecular gas- andstellar-dynamical methods, will advance our understanding of the co-evolutionof BHs and their host galaxies.

ALMA gas-dynamical mass measurement of the supermassive black hole in the red nugget relic galaxy PGC 11179