A Study of Two Periodogram Algorithms for Improving the Detection of Small Transiting Planets

Abstract

The sensitivities of two periodograms are compared for weak signal planet detection in transit surveys: the widely used Box Least Squares (BLS) algorithm following light curve detrending and the Transit Comb Filter (TCF) algorithm following autoregressive ARIMA modeling. Small depth transits are injected into light curves with different simulated noise characteristics. Two measures of spectral peak significance are examined: the periodogram signal-to-noise ratio (S/N) and a false alarm probability (FAP) based on the generalized extreme value distribution. The relative performance of the BLS and TCF algorithms for small planet detection is examined for a range of light curve characteristics, including orbital period, transit duration, depth, number of transits, and type of noise. We find that the TCF periodogram applied to ARIMA fit residuals with the S/N detection metric is preferred when short-memory autocorrelation is present in the detrended light curve and even when the light curve noise had white Gaussian noise. BLS is more sensitive to small planets only under limited circumstances with the FAP metric. BLS periodogram characteristics are inferior when autocorrelated noise is present due to heteroscedastic noise and false period detection. Application of these methods to TESS light curves with known small exoplanets confirms our simulation results. The study ends with a decision tree that advises transit survey scientists on procedures to detect small planets most efficiently. The use of ARIMA detrending and TCF periodograms can significantly improve the sensitivity of any transit survey with regularly spaced cadence.

DIAmante TESS AutoRegressive Planet Search (DTARPS). I. Analysis of 0.9 Million Light Curves

“…This replaces the traditional BLS method applied to detrended light curves that do not involve differencing. A simulation study by Gondhalekar et al (2023) shows in detail that the ARIMA-TCF sequence 10 https://tess.mit.edu/toi-releases outperforms a standard detrender followed by BLS in most TESS-like light curves. The TCF periodogram exhibits fewer spurious speaks, reduced heteroscedasticity (noise varying with period), and reduced trend compared to the BLS periodogram.…”

“…The code involves the same triple loop as the traditional Box Least Squares algorithm (Kovács et al 2002). Gondhalekar et al (2023) show that the TCF periodogram of ARIMA residuals is typically more sensitive to small planetary transits than the BLS periodogram of residuals from a standard smoother.…”

“…The right panels of Figure 4 illustrate that short-memory autocorrelation is often still present in the preprocessed light curves, even though the noise level is often reduced below 0.1%. This autocorrelated behavior can increase noise in periodograms such as Box Least Squares (BLS) and thus reduce sensitivity to weaker planetary transits (Gondhalekar et al 2023). Some of autocorrelation variations may be due to planetary transits, but typically it is intrinsic to the star.…”

“…We can compare this situation to the earlier application of ARPS methodology to the Kepler 4 yr mission where Caceres et al (2019a) identified 97 new mostly Earth-and Mars-size candidates. Gondhalekar et al (2023) finds that application of ARIMA detrending of light curves and TCF periodograms is usually more sensitive to small planets than traditional detrending methods and BLS periodograms. However, the DTARPS-S completeness is low for small planets with shallow transits (Figure 17 and the histogram in Figure 18).…”

“…The TCF periodogram is then calculated to identify and characterize periodic transit-like behavior in the light curves (Section 3.2). Statistical virtues of TCF have been eludicated by Gondhalekar et al (2023). The most likely transit signal period was chosen as the TCF periodogram peak with the greatest robust signal-to-noise ratio after detrending the periodogram.…”