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Scientific Report 2007-2009
Astronomy & Astrophysics
A4. Equilibrium and stability of relativistic stellar clusters and study
of properties of systems with anisotropic distribution of stars
velocities
The study of compact objects like relativistic stellar
clusters is considered one of the most important topics
in General Relativity, being the collapse of dense stellar
cluster one of the possible ways of formation of supermassive
black holes in quasars and galactic nuclei. The
structure and stability of such systems is strongly depending
on energy cutoff which takes into account the
evaporation of stars with large velocity. Also anisotropy
in momentum space may appear during the possible
rapid contraction of the cluster due to the preservation
of angular momentum. Strong anisotropy is expected
in dense clusters with a supermassive black hole at the
center, where in the vicinity of the last stable orbit only
stars with circular orbits can survive.
The study of the equilibrium configurations and their
dynamic and thermodynamic stability for clusters has
been systematically and deeply managed by constructing
non collisional selfgravitating models with spherical symmetry
and distribution function with a velocity cutoff.
Stability of isotropic clusters is analyzed by constructing
appropriate sequences of models by varying suitable
parameters. Results of this analysis lead to conclusion
that equilibrium configurations are dynamically stable in
Newtonian regime, independently from the choice of distribution
function while, in relativistic regime, a critical
density showing the appearance of dynamical instabilities
has been obtained. The general analysis of thermodynamical
and dynamical stability can be performed by
constructing a z c − T diagram of the equilibrium configuration
(see Figure 1).
of dynamical and thermodynamical instability for large
values of temperature T [2]. Perspectives of this research
is extending this analysis to anisotropic models. With
the study of the equilibrium models with anisotropic distribution
it is possible to see that these systems mantain
the spherical symmetry if the total angular momentum
is zero. The main characteristic of these models is the
appearance of a hollow structure for which the density
profile shows an increasing behavior at increasing values
of radius at sufficiently large level of anisotropy [1,3].
The study of thermodynamical instabilities of selfgravitating
systems is strictly connected with the problem of
gravothermal cathastrophe first introduced by the well
known paper of Lynden-Bell & Wood in 1968. In this
model, the effect of the presence of region at negative
thermal capacity leads the system towards the collapse of
the core. The rough picture introduced by Lynden-Bell
& Wood has been developed by constructing a selfconsistent
model in which regions at negative thermal capacity
coexists with positive ones (see Figure 2) on the basis of
the application of statistical mechanics in presence of
gravity. The general properties of these models are well
fitting the main characteristics of globular clusters, by
using the King distribution function, and give the possibility
to analyze the dynamical evolution of the systems
until the onset of the gravothermal catastrophe.
1
0.8
0.6
W0=5.0
0.4
W0=3.5
thermodynamic onset
dynamic onset
(Cv/Nk)r
W0=2.0
0.2
W0=1.35
10 1 with
dynamically
stable
configurations
unstable configurations
0
W0=0.8
-0.2
z c
10 0
thermodynamical
instability
-0.4
-0.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
r/R
stable configurations
10 -1
10 -2 10 -1 10 0 10 1
Figure 1: Regions of dynamical and thermodynamical stability
in the plane (T, z c).
The main result is the existence of dynamically stable
solutions for arbitrarily large values of the central
redshift z c for sufficiently small values of the temperature
T and the contemporary appearance of the onset
T
Figure 2: Values of thermal capacity in Nk units as a function
of relative radius r/R for selected values of central potential
W 0 .
References
1. G.S. Bisnovatyi-Kogan et al., ApJ 703, 628 (2009).
2. M. Merafina et al., AIP, 1206, 399 (2009).
3. G.S. Bisnovatyi-Kogan et al., ApJ,
Authors
M. Merafina
Sapienza Università di Roma 151 Dipartimento di Fisica