  Recently, we have shown that dynamically stable ergostar solutions
(equilibrium neutron stars that contain an ergoregion) with a compressible and
causal equation of state exist [A. Tsokaros, M. Ruiz, L. Sun, S. L. Shapiro,
and K. Ury\=u, Phys. Rev. Lett. 123, 231103 (2019)]. These stars are
hypermassive, differentially rotating, and highly compact. In this work, we
make a systematic study of equilibrium models in order to locate the position
of ergostars in parameter space. We adopt four equations of state that differ
in the matching density of a maximally stiff core. By constructing a large
number of models both with uniform and differential rotation of different
degrees, we identify the parameters for which ergostars appear. We find that
the most favorable conditions for the appearance of dynamically stable
ergostars are a significant finite density close to the surface of the star
(i.e., similar to self-bound quark stars) and a small degree of differential
rotation.
