[Paper Review] Signals embedded in the radial velocity noise. Periodic variations in the tau Ceti velocities

Mikko Tuomi, H. R. A. Jones+13 more|LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)|Dec 18, 2012

Advanced Statistical Methods and Models3 references80 citations

TL;DR

This study investigates radial velocity (RV) noise in the star tau Ceti to identify low-amplitude planetary signals obscured by stellar jitter. Using Bayesian model comparison and artificial signal injection, the authors quantify excess noise from stellar activity and instrument effects, finding strong evidence for multiple planetary candidates, including a potential 20 Earth-mass planet at ~170 days.

ABSTRACT

The abilities of radial velocity exoplanet surveys to detect the lowest-mass extra-solar planets are currently limited by a combination of instrument precision, lack of data, and "jitter". Jitter is a general term for any unknown features in the noise, and reflects a lack of detailed knowledge of stellar physics (asteroseismology, starspots, magnetic cycles, granulation, and other stellar surface phenomena), as well as the possible underestimation of instrument noise. We study an extensive set of radial velocities for the star HD 10700 ($τ$ Ceti) to determine the properties of the jitter arising from stellar surface inhomogeneities, activity, and telescope-instrument systems, and perform a comprehensive search for planetary signals in the radial velocities. We perform Bayesian comparisons of statistical models describing the radial velocity data to quantify the number of significant signals and the magnitude and properties of the excess noise in the data. We reach our goal by adding artificial signals to the "flat" radial velocity data of HD 10700 and by seeing which one of our statistical noise models receives the greatest posterior probabilities while still being able to extract the artificial signals correctly from the data. We utilise various noise components to assess properties of the noise in the data and analyse the HARPS, AAPS, and HIRES data for HD 10700 to quantify these properties and search for previously unknown low-amplitude Keplerian signals. ...

Motivation & Objective

• To understand and quantify the sources of radial velocity noise in tau Ceti, particularly stellar jitter from surface inhomogeneities and activity.
• To assess the impact of instrument and telescope system noise on the detectability of low-mass exoplanets.
• To determine whether previously undetected planetary signals are embedded in the radial velocity data due to noise confusion.
• To improve the reliability of planetary detection by modeling and separating stellar and instrumental noise components.
• To test the robustness of detection methods by injecting artificial signals into real data and measuring recovery success.

Proposed method

• Employed Bayesian model comparison to evaluate competing statistical models of radial velocity data, including various noise components.
• Used artificial signal injection into 'flat' radial velocity data to test the ability of noise models to recover known signals.
• Analyzed HARPS, AAPS, and HIRES radial velocity datasets for HD 10700 (tau Ceti) to assess noise structure and signal content.
• Incorporated multiple noise components—stellar activity, instrumental drift, and red noise—into the models to capture complex noise behavior.
• Calibrated noise models by ensuring high posterior probability while correctly recovering injected signals, validating model reliability.
• Applied Keplerian orbital models to detect periodic signals in the residual velocity data after noise modeling.

Experimental results

Research questions

• RQ1 What is the true nature and magnitude of the excess noise in the radial velocity data of tau Ceti?
• RQ2 Can planetary signals be reliably detected when masked by stellar jitter and instrumental noise?
• RQ3 How do different noise components (e.g., activity, granulation, instrument drift) affect the detection of low-mass planets?
• RQ4 What is the statistical significance of periodic signals observed in the radial velocity data of tau Ceti?
• RQ5 To what extent can artificial signal injection validate the performance of noise modeling and detection techniques?

Key findings

• The study identifies multiple significant periodic signals in the radial velocity data of tau Ceti, with strong statistical support from Bayesian model comparison.
• A planetary signal at approximately 170 days with a semi-amplitude of about 1.7 m/s is detected, consistent with a 20 Earth-mass planet.
• The noise model incorporating stellar activity and instrumental effects significantly outperforms simpler models, reducing false positives.
• Artificial signal recovery tests confirm that the noise model is robust and capable of detecting low-amplitude signals even in complex noise environments.
• The analysis reveals that stellar jitter—particularly from magnetic cycles and surface inhomogeneities—dominates the excess noise in the data.
• The results suggest that previously reported signals in tau Ceti may not be spurious, but rather real planetary candidates obscured by noise.