Surface motion in the pulsating DA white dwarf G29-38

We present time-resolved spectrophotometry of the pulsating DA white dwarf G29-38. As in previous broad-band photometry, the light curve shows the pre sence of a large number of periodicities. Many of these are combination fre quencies, i.e. periodicities occurring at frequencies that are sums or diff erences of frequencies of stronger, real modes. We identify at least six re al modes, and at least five combination frequencies. We measure line-of-sig ht velocities for our spectra and detect periodic variations at the frequen cies of five of the six real modes, with amplitudes of up to 5 km s(-1). We argue that these variations reflect the horizontal surface motion associat ed with the g-mode pulsations. No velocity signals are detected at any of t he combination frequencies, confirming that the flux variations at these fr equencies do not reflect physical pulsation, but rather reflect mixing of f requencies owing to a non-linear transformation in the outer layers of the star. We discuss the amplitude ratios and phase differences found for the v elocity and light variations, as well as those found for the real modes and their combination frequencies, both in a model-independent way and in the context of models based on the convective-driving mechanism. In a companion paper, we use the wavelength dependence of the amplitudes of the modes to infer their spherical degree.