5. The Dynamics and Dark Matter Halos of Elliptical Galaxies

5.1. Results from Dynamical Analysis of Absorption Line Profiles

Giant ellipticals with L L_* are typically fit best by dynamical models that have near-isotropic to modestly radially anisotropic velocity dispersions at intermediate radii, 0.5 - 1R_e [4, 27, 31]. This is based on spherical and axisymmetric three-integral models of about two dozen ellipticals. In ellipticals less luminous than M_B = - 19.5 rotation is important and, moreover, these galaxies become rotation-dominated (v / ~ 2) at 1 - 2R_e, similar to disk-dominated S0 galaxies [32].

Most of the results on dark matter halos in ellipticals obtained from ALS data to 2R_e are based on spherical models for round ellipticals. [4, 31] analyzed the line-profile shapes of a sample of 21 mostly luminous, slowly rotating, and nearly round elliptical galaxies in a uniform way, using spherical DF models. Intrinsic deviations from sphericity and embedded, near-face-on disks can play a role in only a small number of these bright galaxies. Nevertheless, a similar study using three-integral axisymmetric models of near-edge-on galaxies avoiding these issues will be very worthwhile. For these reasons the three-integral models of Matthias & Gerhard for the boxy E4 elliptical galaxy NGC 1600 provide some of the strongest evidence for radial anisotropy, because this galaxy must must be viewed nearly edge-on [27].

The sample of Kronawitter et al. [4] includes a subsample with mostly new extended kinematic data, reaching to ~ 2R_e, and a subsample based on the less extended older data of [28]. Based on these data and on photometry, non-parametric spherical models were constructed from which circular velocity curves, anisotropy profiles, and radial profiles of M / L were derived, including confidence ranges. The circular velocity curve (CVC) for test particles on circular orbits of varying radius is a convenient measure of the potential, even though luminous elliptical galaxies do not rotate rapidly. The CVCs of the elliptical galaxies analysed by [4, 31] are flat to within 10% for R 0.2R_e to R 2R_e, independent of luminosity (Fig. 2). This argues against strong luminosity segregation in the dark halo potential.

Figure 2. "Best model" circular velocity curves of all galaxies from the sample of [4], plotted as a function of radius scaled by the effective radius Re, and normalized by the maximum circular velocity. The upper panel shows the galaxies from the extended kinematics subsample, the lower panel the galaxies from the subsample with older data from [28]. (Figure from [31].)

The dynamical models imply small to modest amounts of dark matter within 2R_e [4, 31]. However, constant M / L models can be ruled out only for 7/21 ellipticals in this sample, at the 2 level. There are ellipticals in this sample which are very well represented by constant M / L models, and no indication for dark matter within 2R_e, and others where the best dynamical models result in local M / L_Bs of 15-30 at 2R_e. Likewise, Magorrian & Ballantyne [25] find evidence for additional dark matter only in a subset of their galaxies, using constant-anisotropy spherical modelling. I.e., despite the uniformly flat CVCs, there is a spread in the ratio of the CVCs from luminous and dark matter. As in spiral galaxies, the combined rotation curve of the luminous and dark matter is flatter than those for the individual components ("conspiracy").

In the models with maximum stellar mass, the dark matter contributes ~ 10 - 40% of the mass within R_e. The flat CVC models, when extrapolated beyond the range of kinematic data, predict equal interior mass of dark and luminous matter at ~ 2 - 4R_e, consistent with results from X-ray analyses. Even in maximum stellar mass models, the implied halo core densities and phase-space densities are at least ~ 25 times larger and the halo core radii ~ 4 times smaller than in maximum disk spiral galaxies with the same circular velocity [33]. This could imply that some elliptical galaxy halos collapsed at high redshifts or perhaps even that some of their dark matter might be baryonic.

Dust and Scattered Light?   Baes & Dejonghe have argued that scattered light from a high-velocity nucleus might give rise to broad wings in the LOSVD at large radii, in such a way as to mimic a dark matter halo in dynamical analysis [34]. This requires an optical depth 1, i.e., that elliptical galaxies are on the verge of opaqueness. No such effect on the surface density of background galaxies is known to this author. A direct test is moreover possible when velocity measurements are available simultaneously from ALS data and from PNe, as the PN velocities are unaffected (e.g., NGC 4697 above), or when mass determinations are possible with independent techniques (e.g., NGC 1399 below). Also, the effect should be absent when the dispersion profile is constant; one such case in the sample of [4] is NGC 7626.