Black Hole Mass Measurements of Radio Galaxies NGC 315 and NGC 4261
  Using ALMA CO Observations
  We present Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 5 and
Cycle 6 observations of CO(2$-$1) and CO(3$-$2) emission at 0.2''$-$0.3''
resolution in two radio-bright, brightest group/cluster early-type galaxies,
NGC 315 and NGC 4261. The data resolve CO emission that extends within their
black hole (BH) spheres of influence ($r_\mathrm{g}$), tracing regular
Keplerian rotation down to just tens of parsecs from the BHs. The projected
molecular gas speeds in the highly inclined ($i>60^\circ$) disks rises at least
500 km s$^{-1}$ near their galaxy centers. We fit dynamical models of thin-disk
rotation directly to the ALMA data cubes, and account for the extended stellar
mass distributions by constructing galaxy surface brightness profiles corrected
for a range of plausible dust extinction values. The best-fit models yield
$(M_\mathrm{BH}/10^9\,M_\odot)=2.08\pm0.01(\mathrm{stat})^{+0.32}_{-0.14}(\mathrm{sys})$
for NGC 315 and
$(M_\mathrm{BH}/10^9\,M_\odot)=1.67\pm0.10(\mathrm{stat})^{+0.39}_{-0.24}(\mathrm{sys})$
for NGC 4261, the latter of which is larger than previous estimates by a factor
of $\sim$3. The BH masses are broadly consistent with the relations between BH
masses and host galaxy properties. These are among the first ALMA observations
to map dynamically cold gas kinematics well within the BH-dominated regions of
radio galaxies, resolving the respective $r_\mathrm{g}$ by factors of
$\sim$5$-$10. The observations demonstrate ALMA's ability to precisely measure
BH masses in active galaxies, which will enable more confident probes of
accretion physics for the most massive galaxies.
