  Dark energy is the constituent with an enormous abundance of the present
universe, responsible for the universe's accelerated expansion. Therefore, it
is plausible that dark energy may interact within any compact astrophysical
objects. The author in Ref. [Phys. Rev. D 83, 127501 (2011)], constructs an
exact star solution consisting of an ordinary matter and phantom field from a
constant density star (CDS) known as Schwarzschild interior solution. The star
denotes a dark energy star (DES). The author claims that the phantom field
represents dark energy within the star. So far, the role of the phantom field
as dark energy in DES is not systematically studied yet. Related to this issue,
we analyze the energy condition of DES. We expect that DES shall violate the
strong energy condition (SEC) for a particular condition. We discover that SEC
is fully violated only when the compactness reaches the Buchdahl limit.
Furthermore, we also investigate the causal conditions and stabilities due to
the convective motion and gravitational cracking. We also find that those
conditions are violated. These results indicate that DES is not physically
stable. However, we may consider DES as an ultra-compact object of which we can
calculate the gravitational wave echo time and echo frequency and compare them
to those of CDS. We find that the contribution of the phantom field delays the
gravitational wave echoes. The effective potential of the perturbed DES is also
studied. The potential also enjoys a potential well like CDS but with a deeper
well. We also investigate the possibility that DES could form a gravastar when
$ C=1 $. It is found that gravastar produced from DES possesses no singularity
with a dS-like phase as the interior. These results could open more
opportunities for the observational study of dark energy in the near future,
mostly from the compact astrophysical objects.
