A new method for the spectroscopic identification of stellar non-radial   pulsation modes. I. The method and numerical tests
  We present the Fourier parameter fit method, a new method for spectroscopically identifying stellar radial and non-radial pulsation modes based on the high-resolution time-series spectroscopy of absorption-line profiles. In contrast to previous methods this one permits a quantification of the statistical significance of the computed solutions. The application of genetic algorithms in seeking solutions makes it possible to search through a large parameter space. The mode identification is carried out by minimizing chi-square, using the observed amplitude and phase across the line profile and their modeled counterparts. Computations of the theoretical line profiles are based on a stellar displacement field, which is described as superposition of spherical harmonics and that includes the first order effects of the Coriolis force. We made numerical tests of the method on a grid of different mono- and multi-mode models for 0 <= l <= 4 in order to explore its capabilities and limitations. Our results show that whereas the azimuthal order m can be unambiguously identified for low-order modes, the error of l is in the range of pm 1. The value of m can be determined with higher precision than with other spectroscopic mode identification methods. Improved values for the inclination can be obtained from the analysis of non-axisymmetric pulsation modes. The new method is ideally suited to intermediatley rotating Delta Scuti and Beta Cephei stars. 
W. Zima