  Two approximations, namely the subseismic approximation and the anelastic
approximation, are presently used to filter out the acoustic modes when
computing low frequency modes of a star (gravity modes or inertial modes). In a
precedent paper (Dintrans & Rieutord 2001), we observed that the anelastic
approximation gave eigenfrequencies much closer to the exact ones than the
subseismic approximation. Here, we try to clarify this behaviour and show that
it is due to the different physical approach taken by each approximation: On
the one hand, the subseismic approximation considers the low frequency part of
the spectrum of (say) gravity modes and turns out to be valid only in the
central region of a star; on the other hand, the anelastic approximation
considers the Brunt-Vaisala frequency as asymptotically small and makes no
assumption on the order of the modes. Both approximations fail to describe the
modes in the surface layers but eigenmodes issued from the anelastic
approximation are closer to those including acoustic effects than their
subseismic equivalent.
  We conclude that, as far as stellar eigenvalue problems are concerned, the
anelastic approximation is better suited for simplifying the eigenvalue problem
when low-frequency modes of a star are considered, while the subseismic
approximation is a useful concept when analytic solutions of high order
low-frequency modes are needed in the central region of a star.
