**EOS
of
star matter and its impact on astrophysics**

Francesca
Gulminelli

*LPC/University
of
Caen, Caen, France*

Dense
matter
as it can be found in core-collapse supernovae and neutron stars
is
expected to exhibit different phase transitions which impact the
matter
composition and equation of state, with important consequences
on the dynamics
of core-collapse supernova explosion and on the structure of
neutron stars.

In
this
talk we will address the specific phenomenology of two of such
transitions, namely the crust-core solid-liquid transition at
sub-saturation
density, and the possible strange transition at super-saturation
density in the
presence of hyperons degrees of freedom.

Concerning
the
neutron star crust-core phase transition at zero and finite
temperature, it
will be shown that, as a consequence of the presence of long
range Coulomb
interactions, the equivalence of statistical ensembles is
violated and a
clusterized phase is expected which is not accessible in the
grand-canonical
ensemble. A
specific analytical Nuclear
Statistical Equilibrium model will be presented and some
quantitative results
relevant for the supernova dynamics will be shown.

The
opening
of hyperons degrees of freedom at the higher densities
corresponding to
the neutron stars core modifies the equation of state with
important
consequences on the total mass and radius of the star. The general
characteristics and order of
phase transitions in this regime will be analyzed in the
framework of a
self-consistent mean-field approach.