Astron. Astrophys. 345, 439-447 (1999)
We 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