  Using Galois descent tools, we extend the Altmann-Hausen presentation of
normal affine algebraic varieties endowed with an effective torus action over
an algebraically closed field of characteristic zero to the case where the
ground field is an arbitrary field of characteristic zero. In this context, the
acting torus may have non-trivial torsors and we need additional data to encode
such varieties. Finally, we focus on affine varieties endowed with a
two-dimensional torus action and we provide a method for determining when a
torsor is trivial, in which case the Altmann-Hausen presentation simplifies.
