  There is introduced a class of barotropic equations of state (EOS) which
become polytropic of index $n = 5$ at low pressure. One then studies
asymptotically flat solutions of the static Einstein equations coupled to
perfect fluids having such an EOS. It is shown that such solutions, in the same
manner as the vacuum ones, are conformally smooth or analytic at infinity, when
the EOS is smooth or analytic, respectively.
