Multivariate characterization of hydrogen Balmer emission in cataclysmic variables

Abstract

The ratios of hydrogen Balmer emission line intensities in cataclysmic variables are signatures of the physical processes that produce them. To quantify those signatures relative to classifications of cataclysmic variable types, we applied the multivariate statistical analysis methods of principal components analysis and discriminant function analysis to the spectroscopic emission data set of Williams (1983). The two analysis methods reveal two different sources of variation in the ratios of the emission lines. The source of variation seen in the principal components analysis was shown to be correlated with the binary orbital period. The source of variation seen in the discriminant function analysis was shown to be correlated with the equivalent width of the H$β$ line. Comparison of the data scatterplot with scatterplots of theoretical models shows that Balmer line emission from T CrB systems is consistent with the photoionization of a surrounding nebula. Otherwise, models that we considered do not reproduce the wide range of Balmer decrements, including "inverted" decrements, seen in the data.