Dynamical and gravitational lensing properties of a new phenomenological model of elliptical galaxies
1
Dipartimento di Scienze Fisiche, Università di Napoli Federico II, Compl. Univ. Monte S. Angelo, 80126 Napoli, Italy e-mail: ctortora@na.infn.it
2
Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, 80131 Napoli, Italy
3
INFN – Sezione di Napoli
4
Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, via S. Allende, 84081 Baronissi (Salerno), Italy
Received:
5
May
2006
Accepted:
13
November
2006
Aims.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.
Methods.Under the hypothesis of spherical symmetry, we assume a double power-law expression
for the global mass-to-light (hereafter 
) ratio
with 
scaling parameters and 
determining the inner and outer slope of the ratio. In particular, 
for
so that 
mimics a constant ratio in
the inner regions, while, for 
, 
thus showing that models with 
have an asymptotically constant 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 
, we work out an effective galaxy model that accounts for all the phenomenology observed in real elliptical galaxies. We derive the
main dynamics and gravitational lensing properties of such an effective model.
Results.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 
makes it possible to analyze the problem of the dark matter
in elliptical galaxies. Indeed, positive values of would be a strong evidence for dark matter.
Conclusions.Finally we indicate possible future approaches in order to face the observational data, in particular using velocity dispersion profiles and lensed quasar events.
Key words: dark matter / gravitational lensing / galaxies: elliptical and lenticular, cD
© ESO, 2007