A Goldilocks principle for modelling radial velocity noise

The doppler measurements of stars are diluted and distorted by stellar activity noise. Different choices of noise models and statistical methods have led to much controversy in the confirmation of exoplanet candidates obtained through analysing radial velocity data. To quantify the limitation of various models and methods, we compare different noise models and signal detection criteria for various simulated and real data sets in the Bayesian framework. According to our analyses, the white noise model tend to interpret noise as signal, leading to false positives. On the other hand, the red noise models are likely to interprete signal as noise, resulting in false negatives. We find that the Bayesian information criterion combined with a Bayes factor threshold of 150 can efficiently rule out false positives and confirm true detections. We further propose a Goldilocks principle aimed at modeling radial velocity noise to avoid too many false positives and too many false negatives. We propose that the noise model with RHK-dependent jitter is used in combination with the moving average model to detect planetary signals for M dwarfs. Our work may also shed light on the noise modeling for hotter stars, and provide a valid approach for finding similar principles in other disciplines.