  The present paper is dedicated to the large time asymptotic behavior of
global strong solutions near constant equilibrium (away from vacuum) to the
compressible Navier-Stokes-Poisson equations. Precisely, we present that under
the same regularity assumptions as in \cite{SX2}, a \textit{different}
time-decay framework of the $\dot{B}_{p,1}^{s}$ norm of the critical global
solutions is established. The proof mainly depends on the pure energy argument
\textit{without the spectral analysis}, which allows us to remove \textit{the
usual smallness assumption of low frequencies of initial data}.
