The E3 giant elliptical galaxy ( catalog IC~1459 ) is the prototypical galaxy with a fast counterrotating stellar core .
We obtained one HST/STIS long-slit spectrum along the major axis of this galaxy and CTIO spectra along five position angles .
The signal-to-noise ( S / N ) of the ground-based data is such that also the higher order Gauss-Hermite moments ( h _ { 3 } – h _ { 6 } ) can be extracted reliably .
We present self-consistent three-integral axisymmetric models of the stellar kinematics , obtained with Schwarzschild ’ s numerical orbit superposition method .
The available data allow us to study the dynamics of the kinematically decoupled core ( KDC ) in IC 1459 and we find it consists of stars that are well-separated from the rest of the galaxy in phase space .
In particular , our study indicates that the stars in the KDC counterrotate in a disk on orbits that are close to circular .
We estimate that the KDC mass is \approx 0.5 % of the total galaxy mass or \approx 3 \times 10 ^ { 9 } M _ { \odot } .

We estimate the central black hole mass M _ { \bullet } of IC 1459 independently from both its stellar and its gaseous kinematics .
Although both tracers rule out models without a central black hole , neither yields a particularly accurate determination of the black hole mass .
The main problem for the stellar dynamical modeling is the fact that the modest S / N of the STIS spectrum and the presence of strong gas emission lines preclude measuring the full line-of-sight velocity distribution ( LOSVD ) at HST resolution .
The main problem for the gas dynamical modeling is that there is evidence that the gas motions are disturbed , possibly due to non-gravitational forces acting on the gas .
These complications probably explain why we find rather discrepant BH masses with the different methods .
The stellar kinematics suggest that M _ { \bullet } = ( 2.6 \pm 1.1 ) \times 10 ^ { 9 } M _ { \odot } ( 3 \sigma error ) .
The gas kinematics suggests that M _ { \bullet } \approx 3.5 \times 10 ^ { 8 } M _ { \odot } if the gas is assumed to rotate at the circular velocity in a thin disk .
If the observed velocity dispersion of the gas is assumed to be gravitational , then M _ { \bullet } could be as high as \sim 1.0 \times 10 ^ { 9 } M _ { \odot } .
These different estimates bracket the value M _ { \bullet } = ( 1.1 \pm 0.3 ) \times 10 ^ { 9 } M _ { \odot } predicted by the M _ { \bullet } - \sigma relation .
It will be an important goal for future studies to attempt comparisons of black hole mass determinations from stellar and gaseous kinematics for other galaxies .
This will assess the reliability of black hole mass determinations with either technique .
This is essential if one wants to interpret the correlation between the BH mass and other global galaxy parameters ( e.g .
velocity dispersion ) and in particular the scatter in these correlations ( believed to be only \sim 0.3 dex ) .