Application of the trend filtering algorithm to the MACHO database*

Aims. Because of the strong effect of systematics (or trends) in variable star observations, we apply the Trend Filtering Algorithm (TFA) to a subset of the MACHO database and search for variable stars. Methods. TFA has been applied successfully in planetary transit searches, where weak, short-duration periodic dimmings are sought in the presence of noise and various systematics (due to, e.g., imperfect flat-fielding, crowding, etc.). These latter effects introduce colored noise in the photometric time-series that can completely overwhelm the signal. By using a large number of available photometric time-series of a given field, TFA utilizes the fact that the same types of systematics appear in several or many time-series of the same field. As a result, we attempt to reproduce each target time-series by a linear combination of templates, optimized by least-squares. After a signal has been identified in the residuals between the original time-series and the systematics computed by TFA, we reconstruct the signal by employing the full model, including the signal, systematics, and noise. Results. We apply TFA to the brightest ~5300 objects from subsets of each of the MACHO Large Magellanic Cloud fields #1 and #79. We find that the Fourier frequency analysis performed on the original data detect some 60% of the objects as trend-dominated. This figure decreases to almost zero after using TFA. In total, we detect 387 variables in the two fields, 183 of which would have remained undetected without using TFA. Where possible, we provide preliminary classification of the variables found.