The least‐squares (or Lomb–Scargle) periodogram is a powerful tool that is routinely used in many branches of astronomy to search for periodicities in observational data. The problem of assessing the statistical significance of candidate periodicities for a number of periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are given. These include an upper limit to the false alarm probability (or a lower limit to the significance). The estimations are tested numerically in order to establish regions of their practical applicability.
The Second Workshop on Extreme Precision Radial Velocities defined circa 2015 the state of the art Doppler precision and identified the critical path challenges for reaching 10 cm s −1 measurement precision. The presentations and discussion of key issues for instrumentation and data analysis and the workshop recommendations for achieving this bold precision are summarized here.Beginning with the HARPS spectrograph, technological advances for precision radial velocity measurements have focused on building extremely stable instruments. To reach still higher precision, future spectrometers will need to improve upon the state of the art, producing even higher fidelity spectra. This should be possible with improved environmental control, greater stability in the illumination of the spectrometer optics, better detectors, more precise wavelength calibration, and broader bandwidth spectra. Key data analysis challenges for the precision radial velocity community include distinguishing center of mass Keplerian motion from photospheric velocities (time correlated noise) and the proper treatment of telluric contamination. Success here is coupled to the instrument design, but also requires the implementation of robust statistical and modeling techniques. Center of mass velocities produce Doppler shifts that affect every line identically, while photospheric velocities produce line profile asymmetries with wavelength and temporal dependencies that are different from Keplerian signals.Exoplanets are an important subfield of astronomy and there has been an impressive rate of discovery over the past two decades. However, higher precision radial velocity measurements are required to serve as a discovery technique for potentially habitable worlds, to confirm and characterize detections from transit missions, and to provide mass measurements for other space-based missions. The future of exoplanet science has very different trajectories depending on the precision that can ultimately be achieved with Doppler measurements.
The role of radial velocity (RV) jitter in extrasolar planet search surveys is discussed. Based on the maximum likelihood principle, improved statistical algorithms for RV fitting and period search are developed. These algorithms incorporate a built-in jitter determination, so that resulting estimations of planetary parameters account for this jitter automatically. This approach is applied to RV data for several extrasolar planetary systems. It is shown that many RV planet search surveys suffer from periodic systematic errors which increase effective RV jitter and can lead to erroneous conclusions. For instance, the planet candidate HD74156 d may be a false detection made due to annual systematic errors.Comment: 10 pages, 1 figure, 1 table; accepted to MNRAS; 4th version due to a few extra minor corrections in Sect.11 and Tab.
We perform a detailed analysis of the latest HARPS and Keck radial velocity data for the planet-hosting red dwarf GJ581, which attracted a lot of attention in recent time. We show that these data contain important correlated noise component ("red noise") with the correlation timescale of the order of 10 days. This red noise imposes a lot of misleading effects while we work in the traditional white-noise model. To eliminate these misleading effects, we propose a maximum-likelihood algorithm equipped by an extended model of the noise structure. We treat the red noise as a Gaussian random process with exponentially decaying correlation function.Using this method we prove that: (i) planets b and c do exist in this system, since they can be independently detected in the HARPS and Keck data, and regardless of the assumed noise models; (ii) planet e can also be confirmed independently by the both datasets, although to reveal it in the Keck data it is mandatory to take the red noise into account; (iii) the recently announced putative planets f and g are likely just illusions of the red noise; (iv) the reality of the planet candidate GJ581 d is questionable, because it cannot be detected from the Keck data, and its statistical significance in the HARPS data (as well as in the combined dataset) drops to a marginal level of ∼ 2σ, when the red noise is taken into account.Therefore, the current data for GJ581 really support existence of no more than four (or maybe even only three) orbiting exoplanets. The planet candidate GJ581 d requests serious observational verification.
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