Combination frequencies in the Fourier spectra of white dwarfs

Combination frequencies are observed in the Fourier spectra of pulsating DA and DB white dwarfs, along with frequencies that are associated with stellar gravity modes. They appear at the sum and difference frequencies of the stellar modes. Brickhill proposed that the combination frequencies result from mixing of the eigenmode signals by a depth-varying surface convection zone when undergoing pulsation. The depth changes cause time-dependent thermal impedance.
Following Brickhill's proposal, we developed analytical expressions for 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 the 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 credible values for these parameters, we apply our expressions to DA and DB variable white dwarfs. We find reasonable agreement between theory and observation, although some discrepancies remain unexplained. It is possible to identify the spherical degrees of the pulsation modes using the combination frequencies.