An ALMA Gas-dynamical Mass Measurement of the Supermassive Black Hole in
  the Local Compact Galaxy UGC 2698
  We present 0\farcs{14}-resolution Atacama Large Millimeter/submillimeter
Array (ALMA) CO(2$-$1) observations of the circumnuclear gas disk in UGC 2698,
a local compact galaxy. The disk exhibits regular rotation with projected
velocities rising to 450 km s$^{-1}$ near the galaxy center. We fit
gas-dynamical models to the ALMA data cube, assuming the CO emission originates
from a dynamically cold, thin disk, and measured the mass of the supermassive
black hole (BH) in UGC 2698 to be $M_{\mathrm{BH}} = (2.46 \pm{0.07}$
[$1\sigma$ stat] $^{+0.70}_{-0.78}$ [sys])$\times 10^9$ $M_\odot$. UGC 2698 is
part of a sample of nearby early-type galaxies that are plausible $z\sim2$ red
nugget relics. Previous stellar-dynamical modeling for three galaxies in the
sample found BH masses consistent with the BH mass$-$stellar velocity
dispersion ($M_{\mathrm{BH}}-\sigma_\star$) relation but over-massive relative
to the BH mass$-$bulge luminosity ($M_{\mathrm{BH}}-L_{\mathrm{bul}}$)
correlation, suggesting that BHs may gain the majority of their mass before
their host galaxies. However, UGC 2698 is consistent with both
$M_{\mathrm{BH}}-\sigma_\star$ and $M_{\mathrm{BH}}-L_{\mathrm{bul}}$. As UGC
2698 has the largest stellar mass and effective radius in the local compact
galaxy sample, it may have undergone more recent mergers that brought it in
line with the BH scaling relations. Alternatively, given that the three
previously-measured compact galaxies are outliers from
$M_{\mathrm{BH}}-L_{\mathrm{bul}}$, while UGC 2698 is not, there may be
significant scatter at the poorly sampled high-mass end of the relation.
Additional gas-dynamical $M_{\mathrm{BH}}$ measurements for the compact galaxy
sample will improve our understanding of BH$-$galaxy co-evolution.
