  Recent observations of the line of sight velocity profile of elliptical
galaxies have furnished controversial results with some works favouring the
presence of a large amount of dark matter in the outer regions and others
arguing in favour of no dark matter at all. In order to shed new light on this
controversy, we propose here a new phenomenological description of the total
mass profile of galaxies. Under the hypothesis of spherical symmetry, we assume
a double power-law expression for the global M/L ratio Upsilon(r)=
Upsilon_0(r/r_0) ^{alpha}(1+r/r_0)^{beta}. In particular, Upsilon propto
r^{alpha} for r/r_0<<1 so that alpha=0 mimics a constant M/L ratio in the inner
regions, while, for (r/r_0>>1), Upsilon propto r^{alpha+beta} thus showing that
models with alpha+beta=0 have an asymptotically constant M/L ratio. A wide
range of possibilities is obtained by varying the slope parameters in the range
we determine on the basis of physical considerations. Choosing a general
expression for the luminosity density profile j(r), we work out an effective
galaxy model that accounts for all the phenomenology observed in real
elliptical galaxies. We derive the main dynamics and lensing properties of such
an effective model. We analyze a general class of models, able to take into
account different dynamical trends. We are able to obtain analytical
expressions for the main dynamical and lensing quantities. We show that
constraining the values of alpha+beta makes it possible to analyze the problem
of the dark matter in elliptical galaxies. Indeed, positive values of
alpha+beta would be a strong evidence for dark matter. Finally we indicate
possible future approaches in order to face the observational data, in
particular using velocity dispersion profiles and lensed quasar events.
