The pulsating DAV white dwarf BPM 31594 (VY Hor): evidence for non-linear mode coupling by direct resonance

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Abstract
300 hr of high-speed photometry of the pulsating DAV white dwarf BPM 31594 obtained during 1975–89 is presented. The light curve shows non-sinusoidal pulses with a peak-to-peak range of 30 per cent but with obvious modulation in amplitude and pulse shape. The mean amplitude spectrum shows that the dominant contributor to these oscillations is the principal frequency ƒ = 1.62 mHz. Most of the remaining significant power occurs, with variable amplitude, either at frequencies nƒ or at (1.54±n)ƒ where n is an integer. Other frequencies nearƒ and at 1.48ƒ, 2.48ƒ and 3.48ƒ are occasionally seen, as well as evidence for low-amplitude peaks (∼0.1 per cent) unrelated to nƒ or (1.54±n)ƒ. Detailed frequency analysis shows that in most, but not all of the data, the frequency spectrum near ƒ contains a rotationally split triplet along with another component very close by. Although the central component is present in all the data, the sidebands of the triplet are not always seen. The separation amongst the components of the triplet is 12.7 μHz, implying a rotation period of ∼0.9 d. The frequency of the central component is found to be stable on time-scales of a few months or less; on longer time-scales, significant variation is found which is not monotonic. Analysis of all other significant frequencies results in a total of 25 components, of which 20 are reasonably secure. Most of these are either harmonics of ƒ, or separated from other components by ƒ. The frequency structure of the star appears to be explicable by a small number of independently excited g-modes which drive other modes through non-linear coupling by direct resonance.

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