### 6. KINEMATICS AND DYNAMICS

Over the last two decades, several major kinematical studies have been carried out of both the ellipsoidal and the disk component of NC 5128. The kinematics of the ellipsoidal component have been traced by studies of the motions of stars (Wilkinson et al. 1986), globular clusters (Hesser, Harris & Hesser 1986; Harris, Harris & Hesser 1988) and planetary nebulae (Hui et al. 1985).

Stellar motions were fully mapped by Wilkinson et al. (1986) over 100" and supplemented by major axis data out to 400" (6.6 kpc). The ellipsoidal stellar component is rotating rather slowly at velocities not surpassing 40 km s-1 in the line of sight around an axis at position angle 135°, i.e. rotating only roughly perpendicular to the dust lane. The velocity dispersions range from 95 to 150 km s-1. The planetary nebula system, studied by Hui et al. (1995) out to 20', has a similar mean velocity dispersion of 110 km s-1. Major axis rotation increases to 100 km s-1 at 7 kpc and after that remains constant to at least 22 kpc. Minor axis rotation is less than 50 km s-1 out to the last observed radius of 10 kpc. The projected rotation axis is at position angle 165°, i.e. displaced from the photometric minor axis (and disk orientation) by about 40°; the line of zero rotation is not orthogonal to the line of maximum rotation. Such observations suggest that NGC 5128 has a triaxial potential. The kinematics of the globular cluster system again appear to be similar to those of the spheroidal stellar system (Hesser et al. 1986; Harris et al. 1988). In particular, the metal-rich globular clusters rotate very much like the planetary nebulae, whereas the metal-poor clusters appear to lack significant rotation (Hui et al. 1995).

The rich gas content of the dust lane (Sects. 4.1 and 4.2) has allowed detailed kinematical studies of the disk component to be performed in lines of ionized hydrogen (Bland, Taylor & Atherton 1987), neutral atomic hydrogen (van Gorkom et al. 1990; Schiminovich et al. 1994) and CO (Eckart et al. 1990a; Quillen et al. 1992; Wild et al. 1997). Optical and radio observations (Graham 1979; van Gorkom et al. 1990; Quillen et al. 1992) show the disk to be in rapid rotation with a rotation gradient of about 150 km s-1 kpc-1 close to the nucleus, in sharp contrast to the rather modest rotation of the elliptical component. Graham (1979) estimated the plane of rotation to be tilted by 73° with respect to the plane of the sky. Bland et al. (1987) mapped the ionized hydrogen gas at arcsec resolution over 7' × 5', with a moderate velocity resolution of 36 km s-1 similar to that obtained by Wilkinson et al. (1986); the neutral hydrogen observations have comparable velocity resolutions. Although the CO observations have high velocity resolutions of about 1 km s-1, that advantage is largely undone by their spatial resolution of 20"-40" causing significant beam-smearing which can only be partially undone by modelling.

The limited resolutions of the HI and CO data allow only relatively simple modelling of circular orbits in warped disks approximated by sets of variously tilted rings. Virtually all attempts to dynamically model the observed kinematics of the disk therefore rely largely or completely on the optical observations by Bland et al. (1987). Assuming circular motion consistent with an r1/4 law mass distribution, Nicholson, Bland-Hawthorn & Taylor (1992) confirmed Graham's (1979) conclusion that the gas and dust are in a highly inclined rotating disk, with an amplitude Vrot = 250 km s-1 at R = 2.0 kpc and a rotation gradient similar to the one derived by Graham (1979), eastern edge approaching. Projected onto the sky, the HII regions are confined to an envelope similar tothe form of a hysteresis loop, characteristic of a warped disk rather than a ring. They convincingly showed that the kinematical data can be represented by a class of models involving a thin warped disk geometry with a spatially averaged optical depth sufficiently low to allow emission from all positions of the disk to be seen. Double-peaked velocity profiles mark folds in the warped disk seen in projection. Quillen et al. (1992; 1993) confirmed that such an interpretation also applies to the dusty molecular disk.

Kinematical information is restricted to the distribution on the sky of radial velocities only. The large number of free parameters in combination with observational limitations such as finite resolution and extinction, renders the outcome of dynamical modelling very sensitive to initial assumptions (cf. Kormendy & Djorgovski 1989). It is therefore not surprising that the general agreement on kinematical (tilted ring) models describing the motion of the disk component is not matched by a similar convergence on a unique dynamical model. For a review of the methods and problems of determining structure and dynamics of elliptical galaxies in general the reader is referred to De Zeeuw & Franx (1991).

Wilkinson et al. (1986) found a ratio of maximum rotational velocity to peak nuclear velocity dispersion characteristic of a rotationally supported oblate system seen almost edge-on (Davies et al. 1983). Assuming the radio jet to mark the long axis, an effectively stationary rotating nearly oblate triaxial model with axis ratios 1:0.98:0.55 provided their best fit; our line of sight is then 30°-40°-40 from the plane defined by the two long axes. Dropping the requirement of identical jet direction and stellar symmetry axis, they also found a satisfactory fit to an effectively stationary prolate spheroidal model. Following earlier work by Tubbs (1980), a prolate model with clouds moving in circular orbits in a warped disk was favoured by Quillen et al. (1992) on the basis of their CO observations and the ionized gas kinematics determined by Bland et al. (1987). Quillen et al. (1993) presented a revised version of this model to reproduce the morphology of their near-infrared maps.

Assuming the planetary nebulae to form a relaxed system (implying a triaxial potential), a stationary galaxy figure, and the gas disk to be in the preferred plane defined by the long axis, Hui et al. (1995) derived a model with axial ratios of 1:0.92:0.79 where the short axis lies in the plane of the sky, and the intermediate axis is along the line of sight. Mathieu, Dejonghe & Hui (1996) used the planetary nebula system to construct triaxial models, assuming a spherical potential obtained by inverting the major axis photometry. Failing to obtain satisfactory fits with constant M/L ratios, they concluded to a significant presence of dark matter, causing a significant increase of the mass-to-light ratio with radius. They consider the kinematics and photometry of NGC 5128 to be well described by two kinematically distinct subsystems supporting the merger hypothesis. On the whole, there is substantial agreement that the inner parts of NGC 5128 have a roughly constant mass-to-light ratio M / LB 4 increasing with radius to the extent that the global ratio of NGC 5128 is M / LB = 10 (Hesser et al. 1984; van Gorkom et al. 1990; Hui et al. 1995; Mathieu et al. 1996). The total mass of the galaxy is M = 4 ± 1 × 1011 M, with typically half of it due to dark matter (Mathieu et al. 1996). The galaxy mass is thus between 2% and 10% of the NGC 5128 / NGC 5236 group mass.

Interpreting the dust band as a precessing warped structure, Nicholson et al. (1992) ruled out prolate models and concluded that its geometry is consistent with a near-polar gas disk in an oblate, almost spherical triaxial potential with its short axis likewise in the plane of the sky. In their models, the dust band is separated into an inner detached disk (r <1.7 kpc) and an outer extended annulus (1.7 kpc < r < 6.8 kpc). Sparke (1996) showed that, at least qualitatively, such models can explain not only the the observed disk features but also the broken HI ring observed by Schiminovich et al. (1994). An important factor is the variation in oblateness of the galaxy, which is taken to be nearly spherical at small radii and more flattened farther out. Sparke's (1986) model resembles that of Wilkinson et al. (1986) but is in contradiction to that of Hui et al. (1995). The discrepancy may be resolved if, in fact, the planetary nebulae do not represent a relaxed and well-mixed system (Sparke 1996).

Of particular interest is the shell system referred to in Sect. 4.1 and shown in Figs. 6 and 7. Malin et al. (1983) interpreted the shells as the signature of the collision between a dynamically cold system and a rigid potential well (Quinn, 1984; Hernquist & Quinn 1988, 1989) under the condition that the infalling system had a mass significantly less than that of the elliptical galaxy. The shells arise from phase-wrapping of the disk after it has been disrupted by the tidal field of the massive elliptical galaxy. In fact, this work, as well as that by Tubbs (1980) served to underpin the galactic-encounter interpretation of NGC 5128 first suggested by Baade & Minkowski (1954) and revived by Graham (1979). Malin et al. (1983) suggested that a late-type galaxy of mass a few times 1010 M, similar to e.g. M 33, merged with NGC 5128 a few hundred million years ago. Specific, more detailed merger scenarios were presented by Tubbs (1980) and Quillen et al. (1993).

If the gas dust disk would define a preferred plane in a triaxial system, its rotation should be retrograde with respect to the tumbling motion of the stellar ellipsoid (van Albada, Kotanyi & Schwarzschild 1982). However, Wilkinson et al. (1986) found that the disk has in fact prograde rotation, and suggested the warped disk to be due to incomplete settling of material into a symmetry plane of the potential. This is consistent with the conclusion by van Dokkum & Franx (1995) that dust disks in early-type galaxies, with a radius exceeding 250 pc, are generally not settled. The disk would thus be a transient phenomenon, unless it were stabilized by self-gravity (Nicholson et al. 1992; see also Sparke 1996).

A stable disk is required if the merger and dust band formation occurred some 109 years ago (Graham 1979; Nicholson et al. 1992). Quillen et al.'s (1992; 1993) "short" timescales of 1-2 × 108 years were criticized by Sparke (1996) who estimated three quarters of a gigayear as the time elapsed since capture of a companion galaxy from a polar orbit. The presence of an intermediate age stellar population in the halo of NGC 5128 prompted Soria et al. (1996) to suggest an even longer timescale of several gigayear, while intermediate scales of 2-8 × 108 years (and incomplete settling) have been suggested by Tubbs (1980) and Malin et al. (1983). All these timescales are, however, much longer than the age of the current burst of star formation in the disk which is typically a few times 107 years (van den Bergh 1976; Dufour et al. 1979)