  Unveiling the evolution of toroidal field instability, known as Tayler
instability, is essential to understand the strength and topology of the
magnetic fields observed in early-type stars, in the core of the red giants, or
in any stellar radiative zone. We want to study the non-linear evolution of the
instability of a toroidal field stored in a stably stratified layer, in
spherical symmetry and in the absence of rotation. In particular, we intend to
quantify the suppression of the instability as a function of the
Brunt-V\"ais\"ala ($\omega_{\rm BV}$) and the Alfv\'en ($\omega_{\rm A}$)
frequencies. We use the MHD equations as implemented in the anelastic
approximation in the EULAG-MHD code and perform a large series of numerical
simulations of the instability exploring the parameter space for the
$\omega_{\rm BV}$ and $\omega_{\rm A}$. We show that beyond a critical value
gravity strongly suppress the instability, in agreement with the linear
analysis. The intensity of the initial field also plays an important role:
weaker fields show much slower growth rates. Moreover, in the case of very low
gravity, the fastest growing modes have a large characteristic radial scale, at
variance with the case of strong gravity, where the instability is
characterized by horizontal displacements.
  Our results illustrate that the anelastic approximation can efficiently
describe the evolution of toroidal field instability in stellar interiors. The
suppression of the instability as a consequence of increasing values of
$\omega_{\rm BV}$ might play a role to explain the magnetic desert in Ap/Bp
stars since weak fields are only marginally unstable in the case of strong
gravity.
