Combination Frequencies in the Fourier Spectra of White Dwarfs

Abstract

Combination frequencies are observed in the Fourier spectra of pulsating DA and DB white dwarfs. They appear at sums and differences of frequencies associated with the stellar gravity-modes. Brickhill (1992) proposed that the combination frequencies result from mixing of the eigenmode signals as the surface convection zone varying in depth when undergoing pulsation. This depth changes cause time-dependent thermal impedance, which mix different harmonic frequencies in the light curve. Following Brickhill's proposal, we developed analytical expressions to describe the amplitudes and phases of these combination frequencies. The parameters that appear in these expressions are: the depth of the stellar convection zone when at rest, the sensitivity of this depth towards changes in stellar effective temperature, the inclination angle of the stellar pulsation axis with respect to the line of sight, and lastly, the spherical degrees of the eigenmodes involved in the mixing. Adopting reasonable values for these parameters, we apply our expressions to a DA and a DB variable white dwarf. We find reasonable agreement between theory and observation, though some discrepancies remain unexplained. We show that it is possible to identify the spherical degrees of the pulsation modes using the combination frequencies.