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Congresso del Dipartimento di Fisica Highlights in Physics 2005 11–14 October 2005, Dipartimento di Fisica, Università di Milano Structure, formation and dynamical evolution of elliptical galaxies S.E. Arena * , G. Bertin * , L. Ciotti † , T.V. Liseikina ^,# , F. Pegoraro $ , M. Trenti & ,
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Highlights in Physics 2005
11–14 October 2005, Dipartimento di Fisica, Università di Milano
Structure, formation and dynamical evolution of
S.E. Arena*, G. Bertin*, L. Ciotti†, T.V. Liseikina^,#, F. Pegoraro$, M. Trenti&,
and T.S. van Albada+
* Dipartimento di Fisica, Università di Milano
† Dipartimento di Astronomia, Università di Bologna
^ Ruhr-Universitaet, Bochum, Germania
# Institute of Computational Technologies, Novosibirsk, Russia
$ Dipartimento di Fisica, Università di Pisa
+ Kapteyn Astronomical Institute, Groningen, Olanda
Elliptical galaxies may be imagined to have formed from collisionless collapse, reaching dynamical equilibrium by incomplete violent relaxation. We have tested this picture by showing that analytical models constructed under the above scenario and general statistical considerations, the so-called f(n) models, not only match the basic structure of elliptical galaxies (for a constant mass-to-light ratio), but are able to fit the density profiles (over nine orders of magnitude; with relative error within
10%) and the phase space properties (predicting the pressure anisotropy profile
focusing on the slow evolution induced by dynamical friction of a host galaxy
finding in general that (i) The role of collective effects and of inhomogeneities is important; (ii) The density distribution of the host galaxy tends to relax to a broader profile, in contrast with the expectations of adiabatic models; (iii) Satellites spiraling in on quasi-circular orbits tend to heat the stellar system preferentially in the tangential directions. Finally, we are opening the way to the construction of models characterized by a significantly non-spherical geometry .
on a minority component of “satellites”, in a laboratory of N-body simulations. The basic mechanisms have been modeled long ago by Chandrasekhar (1943), but are not understood under realistic conditions. After a first study  of the evolution of an n=3 isotropic polytrope, we now address a sequence of realistic galaxy models (the f(n) models mentioned above),
with mean error of 5%) of the results of collisionless collapse in a variety of N-body simulations . To our knowledge, this is the first time that an analytically simple model constructed from physical arguments is matched successfully to the results of N-body experiments of galaxy formation. We have then addressed the issue of the dynamical evolution of such stellar systems,
1. STRUCTURE AND FORMATION: f() MODELS
of the total energy and of an additional third quantity Q, defined as:
As shown in (Stiavelli & Bertin 1987), this leads to the following distribution function:
where a, A, d and are positive real constants.
The two-parameter family of models, constructed by solving the Poisson equation, is described by the parameter and the concentration parameter =-a(0), the dimensionless depth of the central potential well.
1.B Comparaison with the products of collisionless collapse
The end products of
high resolution simulations of
where incomplete violent relaxation
of a \'\'gravitational plasma"
results from a collisionless collapse process, are well and in detail
described by the f() models, in spite of their simplicity and
of their spherical symmetry.
2. DYNAMICAL EVOLUTION: EFFECTS OF DYNAMICAL FRICTION
(Chandrasekhar 1943): is not suited to describe real systems, characterized by inhomogeneities and complex orbits. No simple analytical theory exists able to incorporate these effects. Great help in understanding the physical processes then derives from numerical simulations.
It is the same code as in box 1, but with the addition of one or more particles to represent one satellite or a spherical shell of satellites.
These additional particles interact directly with the galaxy particles and among them; they are modeled as Plummer spheres with radius Rs and mass Ms.
Initial conditions are: an f(n) galaxy, with given n and Y, and one satellite (or a shell of satellites), with given Rs and Ms, in circular orbit around the galaxy centre at initial distance r0 (or a range of distances).
Most simulations have been carried out with 2.5 105 particles for the galaxy and 1, 20, or 100 satellites. From such initial conditions the satellite (or shell of satellites) slowly sinks toward the centre of the galaxy, because of dynamical friction.
The fall of the satellites is significantly modified by the collective effects and inhomegeneities associated with the host galaxy,which, in turn, evolves by decreasing its density concentration and bychanging the pressure anisotropy in the tangential directions.
3. GALAXY MODELS WITH NON-SPHERICAL GEOMETRY
There are no systematic procedures to construct galaxy models with triaxial geometry. Only a few triaxial density-potential pairs are known, one example is that of the stratified homeoids.
To generate new models we have found it useful to consider an elementary property of the asymptotic expansion for small flattening of the homeoidal density-potential pairs.
Surprisingly, this offers a device to construct, in a systematic way, new density-potential pairs with finite deviations from spherical symmetry.
An application of this method is given in figures 10 and 11, where are illustrated the isodensity (rR2/ra, a>0) and the isopotential (F) for two toroidal models.