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7.2 Stellar Velocity Dispersions

The use of stellar velocity dispersions to investigate the presence and distribution of DM in ellipticals has recently experienced a revival. This technique uses observed velocity dispersion profiles in conjunction with the Jeans equation (equation (2.1) above). Self-consistent solutions with either an assumed mass distribution or distribution function are then obtained (for a detailed discussion see de Zeeuw 1992).

Such a study was carried out by Binney, Davies and Illingworth (1990) who found that all the ellipticals in their sample had velocity dispersion profiles consistent with a constant mass-to-light ratio (that is, no radial gradient in M/L). An extension of this work reached the same conclusions (van der Marel, Binney and Davies 1990). These authors concluded that the galaxies showed no evidence for DM within the inner regions. It should be noted, however, that a constant mass-to-light ratio does not exclude the presence of a dark halo. If the DM has the same profile as the stars, for instance, the derived M/L will remain constant with radius, although it will be higher than that produced by the stars alone. A halo that is more extended than the stars produces an increase in M/L with radius.

It is well-known that the surface brightness profiles of the vast majority of elliptical galaxies can be fit by the R1/4 law (de Vaucouleurs 1948; Binney and Tremaine 1987). If one accepts the hypothesis that ellipticals contain DM, this result is, at first glance, suprising. One would expect that variations in the amount and distribution of DM from one elliptical to another would lead to distortions of the R1/4 law in many galaxies (Bertin, Saglia and Stiavelli 1989). Perhaps the physical significance of the R1/4 has been overinterpreted (cf. Makino, Akiyama and Sugimoto 1990). Irrespective of the reason for this finding, it seems likely that if DM is present in the inner regions of ellipticals it will require a cunning method to detect it unequivocally.

Bertin, Saglia and Stiavelli (1992) attacked the problem by constructing self-consistent solutions of the two-component Vlasov-Poisson equations for elliptical galaxies embedded in dark halos. They then derived density limits on the amount and distribution of DM inside the effective radius Re of the R1/4 profile through the Jeans equation and the virial theorem. They found the surprising result that in a wide range of their models the R1/4 surface brightness profile was reproduced even with substantial amounts of DM inside Re.

Saglia, Bertin and Stiavelli (1992) have applied these techniques to 10 bright ellipticals. They compared the photometric and kinematic profiles of these galaxies to their models to obtain best-fit solutions and hence constraints on possible dark halos. Saglia et al. (1992) find that inside Re the amount of DM is not large, but is nevertheless present. Typically, the DM mass is comparable to the mass in visible material. Within Re, characteristic values are M/LB) ~ 7 for the stellar component, compared to a total dynamical value of M/LB ~ 12. Their models also allow the calculation of a global mass-to-light ratio which is much larger than the values in the inner regions of the galaxies. For one of their galaxies a mass estimate based on the kinematics of globular clusters is available and agrees well with their best-fit model.

Ford et al. (1989) used the radial velocities of planetary nebulae in the halo of NGC 5128 to study the halo kinematics. They also derived preliminary mass distributions which showed an increase in (M/LB) from 2.4 to 10.1 over the radial range from 1.3 to 20.8 kpc. However, de Zeeuw (1992) summarizes other observations which suggest a more modest increase in this galaxy.

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