  We study self-gravitating multi-pion systems (pion stars) in a state of the
Bose condensate. To ensure stability of such stars, it is assumed that they are
immersed in the lepton background. Two different phenomenological equations of
state (EoS) for the pion matter are used, some of them having the first order
phase transition. The model parameters are chosen to reproduce the recent
lattice QCD data at zero temperature and large isospin chemical potential. It
is shown that the mass-radius diagrams of pion stars obtained with
phenomenological EoS are close to ones calculated in the ideal gas model. We
analyze properties of neutrino clouds which are necessary for stabilizing the
pion stars.

High Energy Physics - Phenomenology;General Relativity and Quantum Cosmology