  We study the self-gravitating stars with a linear equation of state, $P=a
\rho$, in AdS space, where $a$ is a constant parameter. There exists a critical
dimension, beyond which the stars are always stable with any central energy
density; below which there exists a maximal mass configuration for a certain
central energy density and when the central energy density continues to
increase, the configuration becomes unstable. We find that the critical
dimension depends on the parameter $a$, it runs from $d=11.1429$ to 10.1291 as
$a$ varies from $a=0$ to 1. The lowest integer dimension for a dynamically
stable self-gravitating configuration should be $d=12$ for any $a \in [0,1]$
rather than $d=11$, the latter is the case of self-gravitating radiation
configurations in AdS space.
