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Register a new userStacked Bayesian general Lomb-Scargle periodogram: Identifying stellar activity signals
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Context. Distinguishing between a signal induced by either stellar activity or a planet is currently the main challenge in radial velocity searches for low-mass exoplanets. Even when the presence of a transiting planet and hence its period are known, stellar activity can be the main barrier to measuring the correct amplitude of the radial velocity signal. Several tools are being used to help understand which signals come from stellar activity in the data. Aims. We aim to present a new tool that can be used for the purpose of identifying periodicities caused by stellar activity, and show how it can be used to track the signal-to-noise ratio (SNR) of the detection over time. The tool is based on the principle that stellar activity signals are variable and incoherent. Methods. We calculate the Bayesian general Lomb-Scargle periodogram for subsets of data and by adding one extra data point we track what happens to the presence and significance of periodicities in the data. Publicly available datasets from HARPS and HARPS-N were used for this purpose. Additionally, we analysed a synthetic dataset that we created with SOAP2.0 to simulate pure stellar activity and a mixture of stellar activity and a planet. Results. We find that this tool can easily be used to identify unstable and incoherent signals, such as those introduced by stellar activity. The SNR of the detection grows approximately as the square root of the number of data points, in the case of a stable signal. This can then be used to make decisions on whether it is useful to keep observing a specific object. The tool is relatively fast and easy to use, and thus lends itself perfectly to a quick analysis of the data.
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The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an offset and weights ($chi^{2}$ fitting). Compared to the Lomb-Scargle periodogram, the generalisation is superior as it provides more accurate frequencies, is less susceptible to aliasing, and gives a much better determination of the spectral intensity. Only a few modifications are required for the computation and the computational effort is similar. Our approach brings together several related methods that can be found in the literature, viz. the date-compensated discrete Fourier transform, the floating-mean periodogram, and the spectral significance estimator used in the SigSpec program, for which we point out some equivalences. Furthermore, we present an algorithm that implements this generalisation for the evaluation of the Keplerian periodogram that searches for the period of the best-fitting Keplerian orbit to radial velocity data. The systematic and non-random algorithm is capable of detecting eccentric orbits, which is demonstrated by two examples and can be a useful tool in searches for the orbital periods of exoplanets.
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.
To date, only 18 exoplanets with radial velocity (RV) semi-amplitudes $<2$ m/s have had their masses directly constrained. The biggest obstacle to RV detection of such exoplanets is variability intrinsic to stars themselves, e.g. nuisance signals arising from surface magnetic activity such as rotating spots and plages, which can drown out or even mimic planetary RV signals. We use Kepler-37 - known to host three transiting planets, one of which, Kepler-37d, should be on the cusp of RV detectability with modern spectrographs - as a case study in disentangling planetary and stellar activity signals. We show how two different statistical techniques - one seeking to identify activity signals in stellar spectra, and another to model activity signals in extracted RVs and activity indicators - can enable detection of the hitherto elusive Kepler-37d. Moreover, we show that these two approaches can be complementary, and in combination, facilitate a definitive detection and precise characterisation of Kepler-37d. Its RV semi-amplitude of $1.22pm0.31$ m/s (mass $5.4pm1.4$ $M_oplus$) is formally consistent with TOI-178bs $1.05^{+0.25}_{-0.30}$ m/s, the latter being the smallest detected RV signal of any transiting planet to date, though dynamical simulations suggest Kepler-37ds mass may be on the lower end of our $1sigma$ credible interval. Its consequent density is consistent with either a water-world or that of a gaseous envelope ($sim0.4%$ by mass) surrounding a rocky core. Based on RV modelling and a re-analysis of Kepler-37 TTVs, we also argue that the putative (non-transiting) planet Kepler-37e should probably be stripped of its confirmed status.
The properties of inhomogeneities on the surface of active stars (i.e. dark spots and bright faculae) significantly influence the determination of the parameters of an exoplanet. The chromatic effect they have on transmission spectroscopy could affect the analysis of data from future space missions such as JWST and Ariel. To quantify and mitigate the effects of those surface phenomena, we developed a modelling approach to derive the surface distribution and properties of active regions by modelling simultaneous multi-wavelength time-series observables. By using the StarSim code, now featuring the capability to solve the inverse problem, we analysed $sim$ 600 days of BVRI multiband photometry from TJO and STELLA telescopes exoplanet host star WASP-52. From the results, we simulated the chromatic contribution of surface phenomena on the observables of its transits. We are able to determine the relevant activity parameters of WASP-52 and reconstruct the time-evolving longitudinal map of active regions. The star shows a heterogeneous surface composed of dark spots with a mean temperature contrast of $575pm150$ K with filling factors ranging from 3 to 14 %. We studied the chromatic effects on the depths of transits obtained at different epochs with different stellar spot distributions. For WASP-52, with peak-to-peak photometric variations of $sim$7 % in the visible, the residual effects of dark spots on the measured transit depth, after applying the calculated corrections, are about $10^{-4}$ at 550 nm and $3times10^{-5}$ at 6$mu$m. We demonstrate that by using contemporaneous ground-based multiband photometry of an active star, it is possible to reconstruct the parameters and distribution of active regions over time, and thus, quantify the chromatic effects on the planetary radii measured with transit spectroscopy and mitigate them by about an order of magnitude.
Robertson et al.(Reports, July 25 2014, p440-444)(1) claimed that activity-induced variability is responsible for the Doppler signal of the proposed planet candidate GJ 581d. We point out that their analysis using periodograms of residual data is incorrect, further promoting inadequate tools. Since the claim challenges the viability of the method to detect exo-Earths, we urge for more appropriate analyses (see appendix).
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