An affine stellar model represents a fluid body by a time-dependent ellipsoid whose internal velocity is linear in position. Its axis lengths become finitely many dynamical degrees of freedom.
The affine breathing mode changes all three principal axes by the same fraction and therefore changes the stellar volume and density.
An affine quadrupole mode has axis perturbations whose fractional sum vanishes. It changes the ellipsoidal shape without changing volume to first order.
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