Cross-checking SMBH mass estimates in NGC 6958 -- I: Stellar dynamics
  from adaptive optics-assisted MUSE observations
  Supermassive black hole masses (MBH) can dynamically be estimated with
various methods and using different kinematic tracers. Different methods have
only been cross-checked for a small number of galaxies and often show
discrepancies. To understand these discrepancies, detailed cross-comparisons of
additional galaxies are needed. We present the first part of our
cross-comparison between stellar- and gas-based MBH estimates in the nearby
fast-rotating early-type galaxy NGC 6958. The measurements presented here are
based on ground-layer adaptive optics-assisted Multi-Unit Spectroscopic
Explorer (MUSE) science verification data at around 0.6 arcsec spatial
resolution. The spatial resolution is a key ingredient for the measurement and
we provide a Gaussian parametrisation of the adaptive optics-assisted point
spread function (PSF) for various wavelengths. From the MUSE data, we extracted
the stellar kinematics and constructed dynamical models. Using an axisymmetric
Schwarzschild technique, we measured an MBH of (3.6+2.7-2.4)\times 10^8 Msun at
3\sigma significance taking kinematical and dynamical systematics
(e.g.,radially-varying mass-to-light ratio) into account. We also added a dark
halo, but our data does not allow to constrain the dark matter fraction. Adding
dark matter with an abundance matching prior results in a 25 per cent more
massive black hole. Jeans anisotropic models return MBH of (4.6+2.5-2.7) \times
10^8 Msun and (8.6+0.8-0.8) \times 10^8 Msun at 3\sigma confidence for
spherical and cylindrical alignment of the velocity ellipsoid, respectively. In
a follow-up study, we will compare the stellar-based MBH with those from cold
and warm gas tracers, which will provide additional constraints for the MBH for
NGC 6958, and insights into assumptions that lead to potential systematic
uncertainty.
