The images are well fitted by an axisymmetric model with the gas and dust in a disc of 1.5 arcsec radius (340 pc) in the equatorial plane of the stellar body, viewed at inclination i=70 degrees. The flux distribution of the ionized gas is very centrally concentrated, and is unresolved inside the seeing radius. The central cusp-steepness alpha of the stellar luminosity density (j = cst x r^alpha for r ---> 0) is not well constrained by the observed surface brightness distribution, because of the dust absorption.
We model the gas kinematics with the gas on circular orbits in the equatorial plane, with a local velocity dispersion due to turbulence (or otherwise non-gravitational motion). The circular velocity is calculated from the combined gravitational potential of the stars and a possible nuclear black hole. The observed gas rotation curve is well fitted by a model with alpha = -1.3, either with or without a black hole. Turbulent velocities > 300 km/s must be present at radii < 0.5 arcsec to fit the observed nuclear line widths. Seeing convolution of a Keplerian rotation curve around a 10^9 solar mass black hole can fit the observed widths without turbulence, but such a model predicts nuclear emission line shapes with pronounced peaks at v = +/- 300 km/s, which are not observed. Models with both a black hole and gas turbulence can fit the data well, but the black hole is not required by the data, and, if present, its mass must be < 5 x 10^8 solar masses.
Although this upper limit is not very stringent, it is already 5 times
smaller than the black hole mass inferred for M87 from HST data. We
show that HST observations of NGC 7052 should improve significantly
the constraints on the mass of any possible black hole. Kinematic
observations of nuclear gas discs are likely to become a widely used
tool in the search for massive black holes in galactic nuclei. The
modelling and analysis techniques presented here will be useful for
the interpretation of such data.