Improved signal detection algorithms for unevenly sampled data. Six signals in the radial velocity data for GJ876

Abstract

The hunt for Earth analogue planets orbiting Sun-like stars has forced the introduction of novel methods to detect signals at, or below, the level of the intrinsic noise of the observations. We present a new global periodogram method that returns more information than the classic Lomb-Scargle periodogram method for radial velocity signal detection. Our method uses the Minimum Mean Squared Error as a framework to determine the optimal number of genuine signals present in a radial velocity timeseries using a global search algorithm, meaning we can discard noise spikes from the data before follow-up analysis. This method also allows us to determine the phase and amplitude of the signals we detect, meaning we can track these quantities as a function of time to test if the signals are stationary or non-stationary. We apply our method to the radial velocity data for GJ876 as a test system to highlight how the phase information can be used to select against non-stationary sources of detected signals in radial velocity data, such as rotational modulation of star spots. Analysis of this system yields two new statistically significant signals in the combined Keck and HARPS velocities with periods of 10 and 15 days.Although a planet with a period of 15 days would relate to a Laplace resonant chain configuration with three of the other planets (8:4:2:1), we stress that follow-up dynamical analyses are needed to test the reliability of such a six planet system.

Radial velocity data analysis with compressed sensing techniques

“…They find the following periods: 61.03±3.81, 30.23±0.19, 15.04±0.04, 1.94±0.001, 10.01±0.02 and 124.69±90.04 days. To compare our results with Jenkins et al (2014), the significance of the signals is tested with FAPs as previously. We use different weight matrix models according to equation (14) figure 4.c, we see that the six tallest signals correspond to the periods we expect.…”

“…However, with parallel progamming on GPUs one can handle up to ≈25 frequencies depending on the number of measurements (Baluev 2013a). Jenkins et al (2014) explicitly mentions the above problem and suggests a tree-like algorithm to explore the frequency space. They analyse GJ 876 with their procedure and find six significant harmonics, which we confirm section 4.5.2.…”

“…Furthermore, Baluev (2011) shows that the maximum of a posterior likelihood including a noise model as the one used here (equation ( 14)) occurs at σ W = 1.31 m.s -1 , σ R = 1.8 m.s -1 and τ = 3 days. Jenkins et al (2014) takes a different approach and searches for sine functions in the signal. They claim six significant sinusoidal signals are in the data.…”

The SOPHIE search for northern extrasolar planets

“…Data were obtained from the exoplanets.eu(Schneider et al 2011) website whenever available. The parameters of the planets are reported inAnglada-Escudé et al (2014,Ribas et al (2018),Hatzes et al (2000),Benedict et al (2006),Bonfils et al (2018),Howard et al (2014), Feng et al (2017, 2018,Astudillo-Defru et al (2017b,c),Burt et al (2014),Correia et al (2010),Rivera et al (2010), Jenkins et al (2014), Wittenmyer et al (2014. The limits of the habitable zone for a star like Gl 411 are indicated by green dotted lines.…”

Proxima Centauri b is not a transiting exoplanet

“…Their occurrence rate for planets with masses below 10 M⊕ (Earth masses) is at least one per star, with a habitable zone (HZ) occurrence rate in the mass range 3-10 M⊕ of 0.21 +0.03 −0.05 planets per star (Tuomi et al 2014). Within this population are dense multi-planet systems like the seven planet candidates orbiting GJ 667C (Anglada-Escudé et al 2013) and the four planets around GJ 876 (Rivera et al 2010;Jenkins et al 2014). Furthermore, Ribas et al (2018) detected a small planetary candidate orbiting Barnard's star.…”