We combine Hubble Space Telescope spectroscopy and ground-based integral-field data from the SAURON and OASIS instruments to study the central black hole in the nearby elliptical galaxy NGC 3379. From these data, we obtain kinematics of both the stars and the nuclear gaseous component. Axisymmetric three-integral models of the stellar kinematics find a black hole of mass 1.4 (+2.6 / -1.0) x 10^8 M_sun (3 sigma errors). These models also probe the velocity distribution in the immediate vicinity of the black hole and reveal a nearly isotropic velocity distribution throughout the galaxy and down to the black hole sphere of influence R_BH. The morphology of the nuclear gas disc suggests that it is not in the equatorial plane; however the core of NGC 3379 is nearly spherical. Inclined thin-disc models of the gas find a nominal black hole of mass 2.0 (+/- 0.1) x 10^8 M_sun (3 sigma errors), but the model is a poor fit to the kinematics. The data are better fit by introducing a twist in the gas kinematics (with the black hole mass assumed to be 2.0 x 10^8 M_sun), although the constraints on the nature and shape of this perturbation are insufficient for more detailed modelling. Given the apparent regularity of the gas discs appearance, the presence of such strong non-circular motion indicates that caution must be used when measuring black hole masses with gas dynamical methods alone.
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