Tuesday, February 21, 2017  h 15:30
at
ICRANet Pescara
Piazza della Repubblica 10, 65122  Pescara (Italy)
ICRANet Seminars
Speaker: Prof. Marco Merafina
Institution: Department of Physics, University of Rome La Sapienza, Italy
Title: "GRAVITY AND THERMODYNAMICS: A NEW
POINT OF VIEW IN THE ANALYSIS OF EQUILIBRIUM AND DYNAMICAL
EVOLUTION OF GLOBULAR CLUSTERS"
Abstract:
In the analysis of the evolution of globular clusters, stellar
encounters strongly contribute in phase
space mixing of stellar orbits. In this scenario, thermodynamics
plays a central role in the gravitational
equilibrium and stability of the clusters, being binary
relaxation time shorter than the age of such systems.
On the other hand, the observations of luminosity profiles of
globular clusters, at different values of the
central gravitational potential, show self similar curves that
suggested a unique sequence of models with
the same distribution function and different parameters during
the dynamical evolution [1].
This feature was also confirmed by several numerical simulations
of globular clusters
existing in literature. This means that the evolution of
globular clusters can be studied by considering
small thermodynamic transformations which keep constant the
functional form of the velocity
distribution of stars like in the framework of the Boltzmann
statistical mechanics. Here we construct
models with a different approach by applying thermodynamic
principles to a Boltzmann distribution
function with an Hamiltonian function which contains an
effective potential depending on the kinetic
energy of the stars, due to the effect of tidal interactions
induced by the hosting galaxy. This particular
form of the Hamiltonian function derives from solving the
FokkerPlanck equation in a different way
with respect to the King approach. The distribution obtained
also corresponds to a maximum of the
entropy, and therefore implies a thermodynamical equilibrium
based on collisions among stars in the
FokkerPlanck approximation. This result is a real breakthrough
point in the analysis of dynamical
evolution of globular clusters. We obtain new relations for the
thermodynamical equilibrium in presence
of a gravitational potential, a different form of the virial
theorem, and introduce the concept of
thermodynamic and kinetic temperature, pressure and chemical
potential (the intensive quantities).
In addition, we can show that a globular cluster can be
described as a model containing regions with
positive and negative specific heat producing thermodynamic
instabilities which drive the systems towards
the gravothermal catastrophe, without the necessity of an
external thermal bath. The influence
of the effective potential on the virial theorem will be
described, together with the related consequences
on the gravothermal stability limit for star clusters through
the analysis of the caloric curve
and its critical points. This new limit is different from one
obtained by Katz in 1978 [2] and now is
in complete accordance with the value related to the maximum of
cluster distribution constructed by
data from Harris Catalogue for globular clusters [3], solving
the unexplained discrepancy evidenced
since forty years. This agreement between theory and
observations is obtained also for small clusters,
giving the conditions for the disruption of clusters, never
obtained from the theoretical point of view,
but observed in several clusters. Finally, new developments on
Nbody simulations for glubular clusters
are presented. The results confirm the presence and the
predicted form of the effective potential
arising from tidal interactions between the cluster and the
hosting galaxy, as well the possibility to
verify this effect by complete observations of transverse and
radial velocities of stars of a globular
cluster even in one single shell at given radius.
References
1. I.R. King, AJ, 71, 64 (1966).
2. J. Katz, MNRAS, 183, 765 (1978).
3. W.E. Harris, AJ, 112, 1487 (1996).
