Transit Least Squares: An optimized transit detection algorithm to search for periodic transits of small planets. (arXiv:1901.02015v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Hippke_M/0/1/0/all/0/1">Michael Hippke</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Heller_R/0/1/0/all/0/1">René Heller</a>
We present a new method to detect planetary transits from time-series
photometry, the Transit Least Squares (TLS) algorithm. TLS searches for
transit-like features while taking the stellar limb darkening and planetary
ingress and egress into account. We have optimized TLS for both signal
detection efficiency (SDE) of small planets and computational speed. TLS
analyses the entire, unbinned phase-folded light curve. We compensate for the
higher computational load by (i.) using algorithms like “Mergesort” (for the
trial orbital phases) and by (ii.) restricting the trial transit durations to a
smaller range that encompasses all known planets, and using stellar density
priors where available. A typical K2 light curve, including 80d of observations
at a cadence of 30min, can be searched with TLS in ~10s real time on a standard
laptop computer, as fast as the widely used Box Least Squares (BLS) algorithm.
We perform a transit injection-retrieval experiment of Earth-sized planets
around sun-like stars using synthetic light curves with 110ppm white noise per
30min cadence, corresponding to a photometrically quiet KP=12 star observed
with Kepler. We determine the SDE thresholds for both BLS and TLS to reach a
false positive rate of 1% to be SDE~7 in both cases. The resulting true
positive (or recovery) rates are ~93% for TLS and ~76% for BLS, implying more
reliable detections with TLS. We also test TLS with the K2 light curve of the
TRAPPIST-1 system and find six of seven Earth-sized planets using an iterative
search for increasingly lower signal detection efficiency, the phase-folded
transit of the seventh planet being affected by a stellar flare. TLS is more
reliable than BLS in finding any kind of transiting planet but it is
particularly suited for the detection of small planets in long time series from
Kepler, TESS, and PLATO. We make our Python implementation of TLS publicly
available.
We present a new method to detect planetary transits from time-series
photometry, the Transit Least Squares (TLS) algorithm. TLS searches for
transit-like features while taking the stellar limb darkening and planetary
ingress and egress into account. We have optimized TLS for both signal
detection efficiency (SDE) of small planets and computational speed. TLS
analyses the entire, unbinned phase-folded light curve. We compensate for the
higher computational load by (i.) using algorithms like “Mergesort” (for the
trial orbital phases) and by (ii.) restricting the trial transit durations to a
smaller range that encompasses all known planets, and using stellar density
priors where available. A typical K2 light curve, including 80d of observations
at a cadence of 30min, can be searched with TLS in ~10s real time on a standard
laptop computer, as fast as the widely used Box Least Squares (BLS) algorithm.
We perform a transit injection-retrieval experiment of Earth-sized planets
around sun-like stars using synthetic light curves with 110ppm white noise per
30min cadence, corresponding to a photometrically quiet KP=12 star observed
with Kepler. We determine the SDE thresholds for both BLS and TLS to reach a
false positive rate of 1% to be SDE~7 in both cases. The resulting true
positive (or recovery) rates are ~93% for TLS and ~76% for BLS, implying more
reliable detections with TLS. We also test TLS with the K2 light curve of the
TRAPPIST-1 system and find six of seven Earth-sized planets using an iterative
search for increasingly lower signal detection efficiency, the phase-folded
transit of the seventh planet being affected by a stellar flare. TLS is more
reliable than BLS in finding any kind of transiting planet but it is
particularly suited for the detection of small planets in long time series from
Kepler, TESS, and PLATO. We make our Python implementation of TLS publicly
available.
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