  This paper proves the nonlinear asymptotic stability of the Lane-Emden
solutions for spherically symmetric motions of viscous gaseous stars if the
adiabatic constant $\gamma$ lies in the stability range $(4/3, 2)$. It is shown
that for small perturbations of a Lane-Emden solution with same mass, there
exists a unique global (in time) strong solution to the vacuum free boundary
problem of the compressible Navier-Stokes-Poisson system with spherical
symmetry for viscous stars, and the solution captures the precise physical
behavior that the sound speed is $C^{{1}/{2}}$-H$\ddot{\rm o}$lder continuous
across the vacuum boundary provided that $\gamma$ lies in $(4/3, 2)$. The key
is to establish the global-in-time regularity uniformly up to the vacuum
boundary, which ensures the large time asymptotic uniform convergence of the
evolving vacuum boundary, density and velocity to those of the Lane-Emden
solution with detailed convergence rates, and detailed large time behaviors of
solutions near the vacuum boundary.
