Hydrostatic Gas Constraints on Supermassive Black Hole Masses:
  Implications for Hydrostatic Equilibrium and Dynamical Modelling in a Sample
  of Early-Type Galaxies
  We present new mass measurements for the supermassive black holes (SMBHs) in
the centres of three early-type galaxies. The gas pressure in the surrounding,
hot interstellar medium (ISM) is measured through spatially resolved
spectroscopy with the Chandra X-ray observatory, allowing the SMBH mass (Mbh)
to be inferred directly under the hydrostatic approximation. This technique
does not require calibration against other SMBH measurement methods and its
accuracy depends only on the ISM being close to hydrostatic, which is supported
by the smooth X-ray isophotes of the galaxies. Combined with results from our
recent study of the elliptical galaxy NGC4649, this brings to four the number
of galaxies with SMBHs measured in this way. Of these, three already have mass
determinations from the kinematics of either the stars or a central gas disc,
and hence join only a handful of galaxies with Mbh measured by more than one
technique. We find good agreement between the different methods, providing
support for the assumptions implicit in both the hydrostatic and the dynamical
models. The stellar mass-to-light ratios for each galaxy inferred by our
technique are in agreement with the predictions of stellar population synthesis
models assuming a Kroupa initial mass function (IMF). This concurrence implies
that no more than ~10-20% of the ISM pressure is nonthermal, unless there is a
conspiracy between the shape of the IMF and nonthermal pressure. Finally, we
compute Bondi accretion rates, finding that the two galaxies with the highest
rates exhibit little evidence of X-ray cavities, suggesting that the
correlation with the AGN jet power takes time to be established.
