Dark energy and the structure of the Coma cluster of galaxies
  {We consider the Coma cluster of galaxies as a gravitationally bound physical
system embedded in the perfectly uniform static dark energy background as
implied by the $\Lambda$CDM cosmology.} {We ask if the density of dark energy
is high enough to affect the structure of a large rich cluster of galaxies?}
{We use recent observational data on the cluster together with our theory of
local dynamical effects of dark energy, including the zero-gravity radius
$R_{\rm ZG}$ of the local force field as the key parameter.} {1) Three masses
are defined which characterize the structure of a regular cluster: the matter
mass $M_{\rm M}$, the dark-energy effective mass $M_{\rm DE}$ ($<0$) and the
gravitating mass $M_{\rm G}$ ($= M_{\rm M} + M_{\rm DE}$). 2) A new matter
density profile is suggested which reproduces well the observational data for
the Coma cluster in the radius range from 1.4 Mpc to 14 Mpc and takes into
account the dark energy background. 3) Using this profile, we calculate upper
limits for the total size of the Coma cluster, $R \le R_{\rm ZG} \approx 20$
Mpc, and its total matter mass, $M_{\rm M} \la M_{\rm M}(R_{\rm ZG}) = 6.2
\times 10^{15} M_{\odot}$.} {The dark energy antigravity affects strongly the
structure of the Coma cluster at large radii $R \ga 14$ Mpc and should be taken
into account when its total mass is derived.}
