Non-linear behaviour of the pulsating white dwarf G29-38 – III. Relative amplitudes of the cross-frequencies

In each season when the DA pulsating white dwarf G29-38 has been observed, its period spectrum appears very different, but it always contains a forest of harmonics and cross-frequencies. The ratio of the amplitude of these non-linear frequencies A _c to the product of the amplitudes of the corresponding parent modes A ₁ A ₂ has been measured. The results are compared with the predictions given by three existing theoretical models. Our analysis shows that the non-linear frequencies present in the period spectrum of G29-38 owe their presence mostly to the inelastic response of the stellar medium to the perturbation travelling through it, rather than to the non-linear response of the emergent luminous flux to the surface temperature variation. This analysis also confirms that most identified modes are ℓ=1, as previously asserted by Kleinman et al.