Signals In Radial Velocity Data Research Articles

ExoplANNET: A deep learning algorithm to detect and identify planetary signals in radial velocity data

The detection of exoplanets with the radial velocity (RV) method consists in detecting variations of the stellar velocity caused by an unseen substellar companion. Instrumental errors, irregular time sampling, and different noise sources originating in the intrinsic variability of the star can hinder interpretation of the data, and even lead to spurious detections. Machine learning algorithms are being increasingly employed in the field of extrasolar planets, some with results that exceed those obtained with traditional techniques in terms of precision. We seek to explore the scope of neural networks in conjunction with the RV method, in particular for exoplanet detection in the presence of correlated noise of stellar origin. In this work, a neural network is proposed to replace the computation of the significance of the signal detected with the RV method and to classify it as of planetary origin or not. The algorithm is trained using synthetic data for systems with and without planetary companions. We injected realistic correlated noise into the simulations based on previous studies of the behaviour of stellar activity. The performance of the network is compared to the traditional method based on null-hypothesis significance testing. The network achieves 28% fewer false positives. This improvement is observed mainly in the detection of small-amplitude signals associated with low-mass planets. In addition, its execution time is five orders of magnitude faster than the traditional method. The superior performance of our algorithm has only been showcased with simulated RV data so far. Although in principle it should be straightforward to adapt it for use in real time series, its performance remains to be thoroughly tested. Future work should allow us to evaluate its potential for adoption as a valuable tool for exoplanet detection.

Accounting for stellar activity signals in radial-velocity data by using change point detection techniques

Context.Active regions on the photosphere of a star have been the major obstacle for detecting Earth-like exoplanets using the radial velocity (RV) method. A commonly employed solution for addressing stellar activity is to assume a linear relationship between the RV observations and the activity indicators along the entire time series, and then remove the estimated contribution of activity from the variation in RV data (overall correction method). However, since active regions evolve on the photosphere over time, correlations between the RV observations and the activity indicators will correspondingly be anisotropic.Aims.We present an approach that recognizes the RV locations where the correlations between the RV and the activity indicators significantly change in order to better account for variations in RV caused by stellar activity.Methods.The proposed approach uses a general family of statistical breakpoint methods, often referred to as change point detection (CPD) algorithms; several implementations of which are available in R and python. A thorough comparison is made between the breakpoint-based approach and the overall correction method. To ensure wide representativity, we use measurements from real stars that have different levels of stellar activity and whose spectra have different signal-to-noise ratios.Results.When the corrections for stellar activity are applied separately to each temporal segment identified by the breakpoint method, the corresponding residuals in the RV time series are typically much smaller than those obtained by the overall correction method. Consequently, the generalized Lomb–Scargle periodogram contains a smaller number of peaks caused by active regions. The CPD algorithm is particularly effective when focusing on active stars with long time series, such asαCen B. In that case, we demonstrate that the breakpoint method improves the detection limit of exoplanets by 74% on average with respect to the overall correction method.Conclusions.CPD algorithms provide a useful statistical framework for estimating the presence of change points in a time series. Since the process underlying the RV measurements generates anisotropic data by its intrinsic properties, it is natural to use CPD to obtain cleaner signals from RV data. We anticipate that the improved exoplanet detection limit may lead to a widespread adoption of such an approach. Our test on the HD 192310 planetary system is encouraging, as we confirm the presence of the two hosted exoplanets and we determine orbital parameters consistent with the literature, also providing much more precise estimates for HD 192310 c.

Ghost in the time series: no planet for Alpha Cen B

Abstract We re-analyse the publicly available radial velocity (RV) measurements for Alpha Cen B, a star hosting an Earth-mass planet candidate, Alpha Cen Bb, with 3.24 d orbital period. We demonstrate that the 3.24 d signal observed in the Alpha Cen B data almost certainly arises from the window function (time sampling) of the original data. We show that when stellar activity signals are removed from the RV variations, other significant peaks in the power spectrum of the window function are coincidentally suppressed, leaving behind a spurious yet apparently significant ‘ghost’ of a signal that was present in the window function's power spectrum ab initio. Even when fitting synthetic data with time sampling identical to the original data, but devoid of any genuine periodicities close to that of the planet candidate, the original model used to infer the presence of Alpha Cen Bb leads to identical conclusions: viz., the 3σ detection of a half-a-metre-per-second signal with 3.236 d period. Our analysis underscores the difficulty of detecting weak planetary signals in RV data, and the importance of understanding in detail how every component of an RV data set, including its time sampling, influences final statistical inference.

DETERMINING THE MASS OF KEPLER-78b WITH NONPARAMETRIC GAUSSIAN PROCESS ESTIMATION

Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hours. The mass of Kepler-78b has been independently reported by two teams based on radial velocity measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in radial velocity data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the radial velocity datasets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV datasets, giving a Doppler amplitude of 1.86 $\pm$ 0.25 m s$^{-1}$ and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87 $^{+0.27}_{-0.26}$ M$_{\oplus}$ is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0$^{+1.9}_{-1.4}$ g cm$^{-3}$. We estimate that Kepler-78b is 32$\pm$26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.

A Gaussian process framework for modelling stellar activity signals in radial velocity data

To date, the radial velocity (RV) method has been one of the most productive techniques for detecting and confirming extrasolar planetary candidates. Unfortunately, stellar activity can induce RV variations which can drown out or even mimic planetary signals - and it is notoriously difficult to model and thus mitigate the effects of these activity-induced nuisance signals. This is expected to be a major obstacle to using next-generation spectrographs to detect lower mass planets, planets with longer periods, and planets around more active stars. Enter Gaussian processes (GPs) which, we note, have a number of attractive features that make them very well suited to disentangling stellar activity signals from planetary signals. We present here a GP framework we developed to model RV time series jointly with ancillary activity indicators (e.g. bisector velocity spans, line widths, chromospheric activity indices), allowing the activity component of RV time series to be constrained and disentangled from e.g. planetary components. We discuss the mathematical details of our GP framework, and present results illustrating its encouraging performance on both synthetic and real RV datasets, including the publicly-available Alpha Centauri B dataset.

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

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 that we can discard noise spikes from the data before a follow-up analysis. This method also allows us to determine the phase and amplitude of the signals we detect, meaning that 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 the 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 d. Although a planet with a period of 15 d would relate to a Laplace resonant chain configuration with three of the other planets (8:4:2:1), we stress that the follow-up dynamical analyses are needed to test the reliability of such a six-planet system.

Probabilities of exoplanet signals from posterior samplings

Estimating the marginal likelihoods is an essential feature of model selection in the Bayesian context. It is especially crucial to have good estimates when assessing the number of planets orbiting stars when the models explain the noisy data with different numbers of Keplerian signals. We introduce a simple method for approximating the marginal likelihoods in practice when a statistically representative sample from the parameter posterior density is available. We use our truncated posterior mixture estimate to receive accurate model probabilities for models with differing number of Keplerian signals in radial velocity data. We test this estimate in simple scenarios to assess its accuracy and rate of convergence in practice when the corresponding estimates calculated using deviance information criterion can be applied to receive trustworthy results for reliable comparison. As a test case, we determine the posterior probability of a planet orbiting HD 3651 given Lick and Keck radial velocity data. The posterior mixture estimate appears to be a simple and an accurate way of calculating marginal integrals from posterior samples. We show, that it can be used to estimate the marginal integrals reliably in practice, given a suitable selection of parameter \lambda, that controls its accuracy and convergence rate. It is also more accurate than the one block Metropolis-Hastings estimate and can be used in any application because it is not based on assumptions on the nature of the posterior density nor the amount of data or parameters in the statistical model.