De-Trending

[ Figure 1. Left: raw light curve, middle: non-uniform cloud passage, and right: resulting light curve ]

NEW: We released the new PDT package. For details, see the PDT page.

Trends in light curves could be caused by various systematic and random noise sources such as cloud passages, changes of airmass, telescope vibration, CCD noise or defects of photometry (e.g. Figure 1). Those trends undermine the intrinsic signals of stars and should be removed.

[ Figure 2. Example of a hierarchical clustering ]

We determine the trends from subsets of stars that are highly correlated among themselves. These subsets are selected based on a hierarchical tree clustering algorithm (Figure 2). A bottom-up merging algorithm based on the departure from normal distribution in the correlation is developed to identify subsets, which we call clusters. After identification of clusters, we determine a trend per cluster (i.e. a master trend) by weighted sum of normalized light curves. We then use quadratic programming to de-trend all individual light curves based on these determined master trends.

We performed experiments using synthetic light curves containing artificial trends and events. We also de-trended the TAOS I and Megacam dataset. The de-trended results of the Megacam is shown in Figure 3. The developed algorithm can be applied to time series for trend removal in both narrow and wide field astronomy. The work is published in MNRAS (Kim+ 2009).

[ Figure 3. An example of Megacam dataset. Top left : Position of stars in identified three clusters. x(y)-axis is the x(y)-coordinate of stars on the CCD plane. Different shapes indicate different clusters. Top right : Determined three master trends. Bottom left, and bottom right : Two example light curves before and after de-trending. Upper panels are before de-trending and lower panels are after de-trending. ]