Breaking the degeneracy between anisotropy and mass: the dark halo of the E0 galaxy NGC 6703

We have measured line-of-sight velocity profiles (VPs) in the E0 galaxy NGC 6703 out to 2.6Re. Comparing these with the VPs predicted from spherical distribution functions (DFs), we constrain the mass distribution and the anisotropy of the stellar orbits in this galaxy. We have developed a non-parametric technique to determine the DF f(E, L2) directly from the kinematic data. We test this technique on Monte Carlo simulated data with the spatial extent, sampling, and error bars of the NGC 6703 data. We find that smooth underlying DFs can be recovered to an rms accuracy of 12 per cent inside three times the radius of the last kinematic data point, and the anisotropy parameter β(r) can be recovered to an accuracy of 0.1, in a known potential. These uncertainties can be reduced with improved data. By comparing such best-estimate, regularized models in different potentials, we can derive constraints on the mass distribution and anisotropy. Tests show that, with presently available data, an asymptotically constant halo circular velocity v0 can be determined with an accuracy of A±≲50 km s−1. This formal range often includes high-v0 models with implausibly large gradients across the data boundary. However, even with extremely high quality data some uncertainty on the detailed shape of the underlying circular velocity curve remains. In the case of NGC 6703, we thus determine the true circular velocity at 2.6Re to be 250±40 km s−1 at 95 per cent confidence, corresponding to a total mass in NGC 6703 inside 78 arcsec (13.5 h−150 kpc, where h50≡H0/50 km s−1 Mpc−1) of 1.6–2.6A–1011h−150 M⊙. No model without dark matter will fit the data; however, a maximum stellar mass model in which the luminous component provides nearly all the mass in the centre will. In such a model, the total luminous mass inside 78 arcsec is 9A–1010 M⊙ and the integrated B-band mass-to-light ratio out to this radius is ΥB=5.3–10, corresponding to a rise from the centre by at least a factor of 1.6. The anisotropy of the stellar distribution function in NGC 6703 changes from near-isotropic at the centre to slightly radially anisotropic (β=0.3–0.4 at 30 arcsec, β=0.2–0.4 at 60 arcsec) and is not well-constrained at the outer edge of the data, where β=−0.5 to +0.4, depending on variations of the potential in the allowed range. Our results suggest that also elliptical galaxies begin to be dominated by dark matter at radii of ∼10 kpc.