  The distribution of dark energy density in the vicinity of compact static
objects is analyzed. Dark energy is assumed to be in the form of a scalar field
with three parameters: the background density, the equation of state parameter
and the effective sound speed. Compact object is assumed to be a homogeneous
spherical object of constant radius. We use the solutions of the hydrodynamical
equations for dark energy in the gravitational fields of such objects for cases
of static distribution of dark energy in the vicinity of star and stationary
accretion onto black hole in order to analyze the possibility of constraining
of the parameters of dark energy from astrophysical data. We show that
dependence of density of dark energy in the vicinity of such object on the
effective sound speed, background density and equation of state parameter of
dark energy makes it possible to try such tests. Here we exploit the accuracy
of determination of masses of Sun and black hole in the center of Milky Way to
obtain the lower limit on the effective sound speed of dark energy.
