6 Conclusions

We have presented the results of a homogeneous dynamical analysis of a sample of 21 round galaxies (mostly E0-E1, four E2). The analysis is based on new extended kinematic data for eight ellipticals, reaching radii between $R_{\rm e}$ and $2R_{\rm e}$, and data from the literature for the remaining galaxies. All these data include line profile information.

For each galaxy we have constructed a sequence of non-parametric spherical models in different luminous plus dark matter potentials. Comparing with the data we have determined a "best'' potential model and a confidence range of models around it. From these we have determined circular velocity curves, mass-to-light ratio profiles, and anisotropy profiles for all galaxies, including error bands. We have done a variety of tests to investigate how the results are affected by details in the modelling and in how the data are treated, such as the choice of basis functions in the modelling (Sect. 5.3), treatment of systematic effects in the kinematic data (Sect. 4.2), colour gradients (Sect. 5.5), comparison of results from independent slit positions (Sect. 5.5), and small rotation (Sect. 5.1). From the statistics of apparent ellipticities the mean intrinsic short-to-long axis ratio for this sample of luminous ellipticals is 0.79. We have concluded that the derived mass-to-light ratios will typically be underestimated by about 10% due to flattening of our galaxies along the line-of-sight, and that embedded face-on disks of the sizes known from near edge-on boxy ellipticals affect the anisotropy profiles only inside $\simeq 0.2 R_{\rm e}$ (Sect. 5.1). We have also cross-checked both the data and the modelling results with a variety of other work.

The sample includes seven galaxies with kinematic data extending to $R>1.5R_{\rm e}$. Three of these show clear evidence for additional dark mass at these radii, in the sense that models based on luminous matter only are ruled out with $95\%$ confidence: NGC 2434, NGC 7507, and NGC 7626. One, NGC 1399, shows weak stellar-dynamical evidence for dark matter, two others, NGC 3379, NGC 6703 are consistent with constant M/L (revised analysis for NGC 6703). NGC 7145 is unclear because of a probable inner face-on disk. In addition, the less extended kinematics of NGC 315 also shows clear evidence for a radial increase in M/L.

Most of the galaxies with mass tracers other than stellar kinematics at larger radii (PNe, GCs, X-rays) also show evidence for dark matter: NGC 1399, 4472, 4486, 4636. In these cases the extrapolated dynamical models based on the stellar kinematic data match the independent models of the outer data very well. An exceptional case is NGC 3379, where also the outer PNe velocities are consistent with a constant M/L model.

For all galaxies, we determine improved mass-to-light ratios. Generally, the respective "best'' models show an outward increase of M/L. Although in many cases the data do not reach far enough to make this statistically significant, the agreement with additional outer data in the few cases cited above suggests that this may often be real.

The circular velocity curves (CVCs) resulting from our model fits are all consistent with being flat outside $R/R_{\rm e}\sim 0.3$ at the $\sim 10\%$ level. Extended flat rotation curves, however, can only be demonstrated for about eight of the galaxies. In some galaxies, e.g., NGC 1399, 3379, the CVC rises to a maximum at $R/R_{\rm e}\sim 0.3 \sim 10''$, before falling by about $10\%$ to reach the flat part at $R/R_{\rm e}\sim 1$. In others, e.g., NGC 2434, 7626, no such maximum is seen before the flat part of the CVC is reached.

The "best'' models for most galaxies are isotropic to slightly radially anisotropic, with typical $\beta\simeq 0.3$, in a few cases $\beta \mathrel{\hbox to 0pt{\lower 3pt\hbox{$\mathchar''218$ }\hss} \raise 2.0pt\hbox{$\mathchar''13C$ }}0.5$ at $R_{\rm e}/2$. Many then seem to turn back to nearly isotropic at larger radii. In their central regions, most of these galaxies also tend to become more isotropic. While the trend is significant, particularly in those galaxies where it starts at around 10'', the detailed structure in the innermost few arcsec is not resolved by the data.

In summary, these results suggest a surprising degree of uniformity in the dynamical properties of elliptical galaxies, with the dark matter halo setting in at radii slightly larger than the effective radius.

Acknowledgements

The authors would like to thank M. Carollo and H.-W. Rix for providing the kinematic and photometric data for NGC 2434 in electronic form, M. Kissler-Patig for the list of GC data on his web-page, and T. Fischbacher and the physics department of the University of Munich for allowing us to use their Linux-cluster and for their help. It is a pleasure to thank B. Binggeli and D. Merritt for advice and the anonymous referee for his constructive comments. This work is partly based on observations carried out at the European Southern Observatory, La Silla, Chile. The authors thank the staff of the Calar Alto and ESO (in Garching and La Silla) observatories for their effective support. Some image reduction was done using the IRAF package distributed by the National Optical Astronomy Observatories. AK and OG were supported by grant 20-50676.97 from the Schweizerischer Nationalfonds, RPS and RB acknowledge the support by DFG grant SFB 375.