Distinguishing between light curves of ellipsoidal variables with massive dark companions, contact binaries, and semidetached binaries using principal component analysis

Photometric methods for identifying dark companion binaries - binary systems hosting quiescent black holes and neutron stars - operate by detecting ellipsoidal variations caused by tidal interactions. The limitation of this approach is that contact and semidetached binaries can produce similarly looking light curves. In this work, we address the degeneracy of ellipsoidal light curves by studying the differences between synthetically generated light curves of dark companion, semidetached, and contact binary systems. We inject the light curves with various levels of uncorrelated and correlated Gaussian noise to simulate the effects of instrumental noise and stellar spots. Using principal component analysis (PCA) and Fourier decomposition, we construct low-dimensional representations of the light curves. We find that the first two to five PCA components are sufficient to explain $99\%$ of variance in the data. The PCA representations are generally more informative than the Fourier representation for the same number of coefficients as measured by both the silhouette scores of the representations and the macro recalls of random forest classifiers trained on the representations. The random forest classifiers reach macro recalls from $0.97$ to $0.70$, indicating that the classes remain largely separable even under adverse conditions. We find that instrumental noise significantly impacts the class separation only when its standard deviation exceeds $10^{-3}$ mag, whereas the presence of spots can markedly reduce the class separation even when they contribute as little as $1\%$ of the light curve amplitude. We discuss the application of our method to real ellipsoidal samples, and we show that we can increase the purity of a sample of dark companion candidates by a factor of up to $27$ if we assume a prior purity of $1\%$, significantly improving the cost-efficiency of follow-up observations.