[Paper Review] Counting the number of planets around GJ 581. False positive rate of Bayesian signal detection methods

Mikko Tuomi, J. S. Jenkins|arXiv (Cornell University)|Nov 6, 2012

Scientific Research and Discoveries4 references4 citations

TL;DR

This study re-evaluates the number of planets around GJ 581 using Bayesian signal detection on HARPS and HIRES radial velocity data, demonstrating that noise correlations (red noise) significantly affect signal significance. The authors conclude there are four robust Keplerian signals, and the previously reported 433-day planet is likely a false positive due to inadequate noise modeling, not planetary origin.

ABSTRACT

The four-planet system around GJ 581 has received attention because it has been claimed that there are possibly two additional low-mass companions as well - one of them being a planet in the middle of the stellar habitable zone. We re-analyse the available HARPS and HIRES Doppler data in an attempt to determine the false positive rate of our Bayesian data analysis techniques and to count the number of Keplerian signals in the GJ 581 data. We apply the common Lomb-Scargle periodograms and posterior sampling techniques in the Bayesian framework to estimate the number of signals in the radial velocities. We also analyse the HARPS velocities sequentially after each full observing period to compare the sensitivities and false positive rates of the two signal detection techniques. By relaxing the assumption that the radial velocity noise is white, we also demonstrate the consequences that noise correlations have on the obtained results and the significances of the signals. According to our analyses, the number of Keplerian signals favoured by the publicly available HARPS and HIRES radial velocity data of GJ 581 is four. This result relies on the sensitivity of the Bayesian statistical analysis techniques but also depends on the assumed noise model. We also show that the radial velocity noise is actually not white and that this feature has to be accounted for when analysing radial velocities in a search for low-amplitude signals corresponding to low-mass planets. ...

Motivation & Objective

• To determine the false positive rate of Bayesian signal detection methods in radial velocity data for the GJ 581 system.
• To assess whether the claimed 433-day planet and other low-mass companions are genuine or artifacts of noise modeling.
• To evaluate the impact of correlated (red) noise on signal significance and detection reliability in exoplanet searches.
• To compare the sensitivity and reliability of Bayesian techniques using sequential HARPS data subsets.
• To establish whether the four-planet model is statistically favored over five-planet models when accounting for realistic noise.

Proposed method

• Applies Bayesian posterior sampling and model comparison techniques to HARPS and HIRES radial velocity data.
• Uses Lomb-Scargle periodograms as a baseline for signal detection and compares results with Bayesian methods.
• Implements a first-order moving average (AR(1)) noise model to account for red noise, improving model fit over white noise assumptions.
• Analyzes HARPS data sequentially after each observing cycle to assess detection consistency and false positive rate.
• Employs the Bayesian model inadequacy criterion (Tuomi et al. 2011) to test consistency between HARPS and HIRES datasets.
• Compares model evidence (Bayes factors) across models with 4, 5, and 6 Keplerian signals to determine the preferred number of planets.

Experimental results

Research questions

• RQ1 How many Keplerian signals are statistically supported by the HARPS and HIRES radial velocity data of GJ 581?
• RQ2 To what extent do correlated (red) noise components in radial velocity data lead to false positive detections of planetary signals?
• RQ3 How does the false positive rate of Bayesian signal detection methods vary when applied to sequential subsets of HARPS data?
• RQ4 Is the 433-day signal reported by Vogt et al. (2010) a genuine planetary signal or an artifact of inadequate noise modeling?
• RQ5 Can the combined HARPS and HIRES data sets support the existence of a fifth planet in the habitable zone, or is it a spurious detection?

Key findings

• The Bayesian analysis of the HARPS and HIRES data supports four Keplerian signals as the most probable model, with no evidence for false positives in sequential HARPS subsets.
• The 433-day signal reported by Vogt et al. (2010) is likely a false positive caused by unmodeled red noise, as it vanishes when an AR(1) noise model is applied.
• The radial velocity noise in the GJ 581 data is not white but exhibits significant correlations (red noise), which, if ignored, can mimic planetary signals.
• The combined HARPS and HIRES data set, when modeled with white noise, shows a spurious 43.7-day signal that disappears under a more accurate AR(1) noise model.
• The Bayesian detection criteria are robust against false positives from noise when the noise model is accurate, but can still be misled by poor noise modeling or data inconsistencies.
• The study concludes that only four planets—GJ 581 b, c, d, and e—are robustly supported by the data, and the existence of a habitable-zone planet (GJ 581 g) remains unsupported by current evidence.