20 40 Radius along Major lii: (nrcloc)

Fig. 8. Tangential velocities on the short axis (full dots) and long axis (open dots) of the elliptical orbits in the plane of the polar ring (upper) and lenticular disk (lower), compared with the circular approximation of Figs. 5 and 6 (long-dash:circular velocities)

polar ring. This is due to the matter deficiency or “hole” in the centre of the wide polar annulus, the only region where the potential is not axisymmetric.

Mass-to-light ratios — The results of the modelling give us a mass-to-light ratio M/LB = 4 for the S0 disk and 5 for the stellar PR. The similarities between the M/L ratios in the two components could have been caused by 1) dust obscuration in the PR, and 2) star formation in the S0 and PR. As the polar ring formed via an accretion/merging event, the gas at small radii must have fallen onto the S0 leading to a burst of star formation in the S0 disk itself at the same epoch as in the polar ring. Evidence for starburst activity in the host galaxy of a polar ring system is observed in the UV spectrum of AM 2020-504 (Arnaboldi et al. 1993b).

4.3. The dark matter component

From the previous model, we can conclude that no dark matter is needed to reproduce the lenticular observed velocities. The luminous-mass model accounts also for the observed velocities in the polar ring out to 30" (5 kpc, the outer radius of the lenticular galaxy). But the still-rising rotation curve of the polar ring does require some dark matter outside this region. This result is amplified by the HI velocities. Without dark matter, the rotation curve in the polar ring plane falls down after 60", and it is not possible to account for the apparently flat HI-velocity profile (cf. Fig. 6).

If it is clear that some dark matter is needed outside the main galaxy disk, it is quite difficult to constrain the shape of its distribution. Also the total amount of dark matter is determined

Fig. Particle plots of the 3D simulation of the S0 and the polar ring system: a x-y projection, b sky projection, c projection and d velocity vectors projected on the sky plane (z-y). The HI gas component is not included here

with uncertainties, which are mainly related to the varying inclination and orientation of the polar ring. The observed velocities are not affected by the sin(i) corrections, which are at most 2% for a tilt of 10° from edge-on, but they are modified by the lineof-sight integration, that samples different regions of the polar ring. Fig. 6 shows the predicted HI velocities in the two extreme hypothesis of a constant inclination of 90° and 85°. The real HI disk should fall in between these two curves, the inclination being 85° in the centre, then 90° in the outer parts.For the stellar polar ring, an inclination of 85° was used at all radii.

There are several possibilities for the shape of the dark halo. Until now; only oblate components with short axis coincident with that of the main SO disk have been considered. We have also analysed such model, with various halo flattening q, as defined in Sect. 3.2. Reasonable fit were obtained for different value of

the q parameter, from q 1 to q = 0.2, and the model for q 0.2 is shown in Fig. 10. The core radius of the dark component is chosen to be rh = 6 kpc, and the asymptotic rotational velocity is 150 km/s. Only the outer parts of the stellar polar ring are not well reproduced, but this could be caused by the polar ring geometry, becoming edge-on there, while we used a constant 85° inclination (see the effect of inclination in Fig. 10b). As shown by S94, once the correction for the Warp in the PR are taken into account, the “over-the-pole” speeds are reduced by 10 km/s, which solves already most of the discrepancy.

We note however that more dark matter is needed when the flattening is increased, since the orbits of the HI gas in the polar ring are becoming more elliptical, with lower velocities on the

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