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Register a new userSignals embedded in the radial velocity noise
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Authors
Mikko Tuomi
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Bayesian data analysis techniques, together with suitable statistical models, can be used to obtain much more information from noisy data than the traditional frequentist methods. For instance, when searching for periodic signals in noisy data, the Bayesian techniques can be used to define exact detection criteria for low-amplitude signals - the most interesting signals that might correspond to habitable planets. We present an overview of Bayesian techniques and present detailed analyses of the HARPS-TERRA velocities of HD 40307, a nearby star observed to host a candidate habitable planet, to demonstrate in practice the applicability of Bayes rule to astronomical data.
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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 ($tau$ 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. ...
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.
Exoplanet detection with precise radial velocity (RV) observations is currently limited by spurious RV signals introduced by stellar activity. We show that machine learning techniques such as linear regression and neural networks can effectively remove the activity signals (due to starspots/faculae) from RV observations. Previous efforts focused on carefully filtering out activity signals in time using modeling techniques like Gaussian Process regression (e.g. Haywood et al. 2014). Instead, we systematically remove activity signals using only changes to the average shape of spectral lines, and no information about when the observations were collected. We trained our machine learning models on both simulated data (generated with the SOAP 2.0 software; Dumusque et al. 2014) and observations of the Sun from the HARPS-N Solar Telescope (Dumusque et al. 2015; Phillips et al. 2016; Collier Cameron et al. 2019). We find that these techniques can predict and remove stellar activity from both simulated data (improving RV scatter from 82 cm/s to 3 cm/s) and from more than 600 real observations taken nearly daily over three years with the HARPS-N Solar Telescope (improving the RV scatter from 1.47 m/s to 0.78 m/s, a factor of ~ 1.9 improvement). In the future, these or similar techniques could remove activity signals from observations of stars outside our solar system and eventually help detect habitable-zone Earth-mass exoplanets around Sun-like stars.
GJ667C is the least massive component of a triple star system which lies at a distance of about 6.8 pc (22.1 light-years) from Earth. GJ667C has received much attention recently due to the claims that it hosts up to seven planets including three super-Earths inside the habitable zone. We present a Bayesian technique for the analysis of radial velocity (RV) data-sets in the presence of correlated noise component (red noise), with unknown parameters. We also introduce hyper-parameters in our model in order to deal statistically with under or over-estimated error bars on measured RVs as well as inconsistencies between different data-sets. By applying this method to the RV data-set of GJ667C, we show that this data-set contains a significant correlated (red) noise component with correlation timescale for HARPS data of order 9 days. Our analysis shows that the data only provides strong evidence for the presence of two planets: GJ667Cb and c with periods 7.19d and 28.13d respectively, with some hints towards the presence of a third signal with period 91d. The planetary nature of this third signal is not clear and additional RV observations are required for its confirmation. Previous claims of the detection of additional planets in this system are due the erroneous assumption of white noise. Using the standard white noise assumption, our method leads to the detection of up to five signals in this system. We also find that with the red noise model, the measurement uncertainties from HARPS for this system are under-estimated at the level of ~50 per cent.
Planetary rotation rates and obliquities provide information regarding the history of planet formation, but have not yet been measured for evolved extrasolar planets. Here we investigate the theoretical and observational perspective of the Rossiter-McLauglin effect during secondary eclipse (RMse) ingress and egress for transiting exoplanets. Near secondary eclipse, when the planet passes behind the parent star, the star sequentially obscures light from the approaching and receding parts of the rotating planetary surface. The temporal block of light emerging from the approaching (blue-shifted) or receding (red-shifted) parts of the planet causes a temporal distortion in the planets spectral line profiles resulting in an anomaly in the planets radial velocity curve. We demonstrate that the shape and the ratio of the ingress-to-egress radial velocity amplitudes depends on the planetary rotational rate, axial tilt and impact factor (i.e. sky-projected planet spin-orbital alignment). In addition, line asymmetries originating from different layers in the atmosphere of the planet could provide information regarding zonal atmospheric winds and constraints on the hot spot shape for giant irradiated exoplanets. The effect is expected to be most-pronounced at near-infrared wavelengths, where the planet-to-star contrasts are large. We create synthetic near-infrared, high-dispersion spectroscopic data and demonstrate how the sky-projected spin axis orientation and equatorial velocity of the planet can be estimated. We conclude that the RMse effect could be a powerful method to measure exoplanet spins.
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