10 20 Rudlua along llqlor a210 (arcane)

Fig. 10a. Same as Fig. 5, but with an oblate dark matter component included, with the same short axis as the lenticular, and a flattening

q 0.2

50 100 Ring Radium (u-cone)

Fig. 10b. Same as Fig. 6, but with the flattened (q = 0.2) oblate dark component

PR major axis. For example, the amount of dark matter required in the q 0.2 (E8) model is 63 - 109 M9 within 150" = 25 kpc, which is much larger than the lenticular total stellar mass. The corresponding dark mass inside 60" = 10 kpc is 14 - 109 M9. S94 models predict a total mass of 40- 109 MG inside 60’ for an

F. Combes & M. Arnaboldiz The dark halo of polar-ring galaxy NGC 4650a

E8 flattened halolz our model requires a lower amount of dark mass to fit the data, because we have maximized the visible mass contribution within the optical disk.

Since dark matter is only needed to account for the PR kinematics, the smallest amount of mass is required when the dark component is flattened with the same axes as the polar ring itself. In this model, the dark distribution is intimately related to the HI gas of the NGC 4650a system, which corresponds to what is derived from galaxy rotation curves in spiral galaxies. In spirals there is a roughly constant ratio between dark matter and the HI surface densities (e. g. Bosma 1981, Freeman 1993), and the HI rich dwarf irregulars, dominated by dark matter, extend this relation (e.g. Carignan & Freeman 1988). Moreover, a recent study of the B,R,K broad band photometry for a sample of polar ring galaxies (Arnaboldi et al. 1995) has indicated several similarities between the integrated colours of polar ring galaxies and those of spirals. The main results concern the wide polar annuli around S0, which show i) a colour gradient towards bluer colours at larger radii, a behaviour similar to the one observed for the optical-infrared colours of the late-type disks (Kent 1992, de Jong & van der Kruit 1994); and ii) the integrated colours B-R, of PR are very similar to those of spirals.

Therefore the hypothesis that the dark matter is linked to the gaseous component, here the polar ring itself, is to be considered. We have tried a very simple model, where the HI mass has been multiplied by 5: i.e. the dark matter has exactly the same radial distribution of the HI gas with the same flattening. The predicted velocities for the optical and HI polar ring are perfectly compatible with the observations (the fit is even better than for models flattened the other way around, cf. Fig. ll). The acceptable ratio between the dark matter and HI surface densities is found to be in the range from 5 to 10.

4.4. Comparison with previous work

We would like to compare in more details our proposed models with previous ones: in particular, we would like to discuss why Sackett et al. (1994) have ruled out a spherical dark halo, while we present it here as a possible solution.

This fact is related to our finding that no dark matter is needed to reproduce the observed kinematics inside a radius of 100” 17 kpc, and only the HI velocities at larger radii than the optical polar ring require a significant amount of dark matter. We find M/LBs for the stellar S0 disk and the polar ring (4 and 5) which are twice as large as those found in previous works ( M/LBS 2 for both in S94). In previous works (SS, S94) the maximum disk hypothesis was used for the S0 disk, and it was claimed that the polar rotation curve tightly constrains the maximum disk mass. For the expected velocity in the polar ring already just exceeds the observed one at 1' 12" (see Fig. 6 of S94), which explains why no higher was tried. However, due to the presence of elliptical orbits, a higher

1 They give 8 - 109 MG in their Table 3 for the E8 model, but because of an extra q in their formula (4) to estimate the mass, this has to be multiplied by 1 / q 5.

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