Application of the trend filtering algorithm to the MACHO database

Abstract

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.

Study of globular cluster M53: new variables, distance, metallicity

“…Therefore, the improvement introduced by TFA filters out some transient signals. We found transient systematics also in other variables, similarly to the ones reported by Szulágyi et al (2009). The unbiased standard deviation of the residuals around the best-fitting Fourier-sum dropped by 14%, which is a good improvement over the original data.…”

“…The method is described in detail by Kovács et al (2005) and also summarized recently by Bakos et al (2009) and Szulágyi et al (2009). Here we only briefly note that the method is based on the idea of correcting elements of the systematic variation in the target time series by using the light curves of many other objects, available in the CCD frame.…”

“…Unfortunately, we do not have a good method to select a "representative" small set of templates, therefore we use a large set that includes both "useful" and "useless" (e.g., pure noise) template time-series. Attempts have been made to determine an optimum number of templates but it seems that it is hard to settle at a value lower than a few hundred (Szulágyi et al 2009). Since in the present case we have only 340 data points per time-series, we have to limit the number of templates considerably (i.e., about half of the number of the data points) to avoid overfitting and a sudden increase of the false alarm probability (FAP).…”

“…Then, in a post-processing phase, we filter out temporal trends by using the trend filtering algorithm (TFA) of Kovács et al (2005). This latter method has been extensively used during the past several years by the HATNet Project 1 in the search for transiting extrasolar planets and also employed successfully in general variable searches (Kovács & Bakos 2008;Szulágyi et al 2009). The main purpose of this paper is to search for variables in the full dataset and not limit the investigation to the well-known regions of variability (i.e., the RR Lyrae strip, the blue straggler and the upper red giant branch regions of the Hertzspring-Russell diagram).…”

Periodic transit and variability search with simultaneous systematics filtering: Is it worth it?

“…Whether or not these signals preferred by the full model are real, can be decided only by careful case-by-case studies, e.g., by running the analysis on varying TFA template numbers (Kovács & Bakos 2007), inspecting the LCs and checking other stars with similar periods. Our variable star works on various datasets show that the loss rate of long-period variables is small, and can be handled in the way mentioned (e.g., Dékány & Kovács 2009;Szulágyi et al 2009;Kovács et al 2014).…”