## 4. ConclusionsWe have investigated the behaviour of the PME and VME when applied to a isotropic equilibrium system, and when partial sampling of this has been performed. We summarize our main conclusions as follows: -
The projected mass estimator (PME) and the virial mass estimator (VME) yield accurate results for the total mass of a gravitational system, provided that the whole system is sampled, is in equilibrium and has an isotropic velocity dispersion. Moreover, the VME can provide an accurate mass profile under the previous conditions without requiring the isotropy condition. -
The PME overestimates the mass if the sampled region is a small portion of the total system. The maximum error occurs around the total system's effective radius , and depends on the density profile. For realistic profiles this overestimate can be up to %. The VME yield similar errors when partial sampling of a complete system is made. This is because the summation in the VME (Eq. 17) does not includes all members of the system, but only those we can *observe*. -
A recently introduced correction term based on the surface pressure term of the continuous virial theorem is found to perform, for practical matters, as well as the VME under the same kind of hypotheses on the stellar system. In applications, e.g. to compute the mass distribution of clusters using galaxy data, however, the VME should be preferred here since it does not require any assumptions on the radial velocity dispersion of galaxies. Discrepancies found in the use of the VME, or the PME, in some *N*-body simulations are attributed to treating particles as test-particles and/or to anisotropies present in the numerical clusters.
© European Southern Observatory (ESO) 1999 Online publication: April 19, 1999 |