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Register a new userImproving transit characterisation with Gaussian process modelling of stellar variability
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Susana Cristina Cabral de Barros
Publication date
2020
fields
Physics
and research's language is
English
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New photometric space missions to detect and characterise transiting exoplanets are focusing on bright stars to obtain high cadence, high signal-to-noise light curves. Since these missions will be sensitive to stellar oscillations and granulation even for dwarf stars, they will be limited by stellar variability. We tested the performance of Gaussian process (GP) regression on the characterisation of transiting planets, and in particular to determine how many components of variability are necessary to describe high cadence, high signal-to-noise light curves expected from CHEOPS and PLATO. We found that the best GP stellar variability model contains four to five variability components: one stellar oscillation component, two to four granulation components, and/or one rotational modulation component. This high number of components is in contrast with the one-component GP model (1GP) commonly used in the literature for transit characterisation. Therefore, we compared the performance of the best multi-component GP model with the 1GP model in the derivation of transit parameters of simulated transits. We found that for Jupiter- and Neptune-size planets the best multi-component GP model is slightly better than the 1GP model, and much better than the non-GP model that gives biased results. For Earth-size planets, the 1GP model fails to retrieve the transit because it is a poor description of stellar activity. The non-GP model gives some biased results and the best multi-component GP is capable of retrieving the correct transit model parameters. We conclude that when characterising transiting exoplanets with high signal-to-noise ratios and high cadence light curves, we need models that couple the description of stellar variability with the transits analysis, like GPs. Moreover, for Earth-like exoplanets a better description of stellar variability improves the planetary characterisation.
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Stellar photometric variability and instrumental effects, like cosmic ray hits, data discontinuities, data leaks, instrument aging etc. cause difficulties in the characterization of exoplanets and have an impact on the accuracy and precision of the modelling and detectability of transits, occultations and phase curves. This paper aims to make an attempt to improve the transit, occultation and phase-curve modelling in the presence of strong stellar variability and instrumental noise. We invoke the wavelet-formulation to reach this goal. We explore the capabilities of the software package Transit and Light Curve Modeller (TLCM). It is able to perform a joint radial velocity and light curve fit or light curve fit only. It models the transit, occultation, beaming, ellipsoidal and reflection effects in the light curves (including the gravity darkening effect, too). The red-noise, the stellar variability and instrumental effects are modelled via wavelets. The wavelet-fit is constrained by prescribing that the final white noise level must be equal to the average of the uncertainties of the photometric data points. This helps to avoid the overfit and regularizes the noise model. The approach was tested by injecting synthetic light curves into Keplers short cadence data and then modelling them. The method performs well over a certain signal-to-noise (S/N) ratio. In general a S/N ratio of 10 is needed to get good results but some parameters requires larger S/N, some others can be retrieved at lower S/Ns. We give limits in terms of signal-to-noise ratio for every studied system parameter which is needed to accurate parameter retrieval. The wavelet-approach is able to manage and to remove the impacts of data discontinuities, cosmic ray events, long-term stellar variability and instrument ageing, short term stellar variability and pulsation and flares among others. (...)
Radial-velocity (RV) planet searches are often polluted by signals caused by gas motion at the stars surface. Stellar activity can mimic or mask changes in the RVs caused by orbiting planets, resulting in false positives or missed detections. Here we use Gaussian process (GP) regression to disentangle the contradictory reports of planets vs. rotation artifacts in Kapteyns star (Anglada-Escude et al. 2014, Robertson et al. 2015, Anglada-Escude et al. 2016). To model rotation, we use joint quasi-periodic kernels for the RV and H-alpha signals, requiring that their periods and correlation timescales be the same. We find that the rotation period of Kapteyns star is 125 days, while the characteristic active-region lifetime is 694 days. Adding a planet to the RV model produces a best-fit orbital period of 100~years, or 10 times the observing time baseline, indicating that the observed RVs are best explained by star rotation only. We also find no significant periodic signals in residual RV data sets constructed by subtracting off realizations of the best-fit rotation model and conclude that both previously reported planets are artifacts of the stars rotation and activity. Our results highlight the pitfalls of using sinusoids to model quasi-periodic rotation signals.
The study of exoplanetary atmospheres epitomises a continuous quest for higher accuracy measurements. Systematic effects and noise associated with both the stellar activity and the instrument can bias the results and thus limit the precision of the analysis. To reach a high photometric and spectroscopic precision, it is therefore essential to correct for these effects. We present here a novel non-parametric approach, named Gaussian Process method for Star Characterization (GPSC), to remove effects of stellar activity and instrumental systematics on planetary signals, with a view to preserve the atmospheric contribution which can be as small as 10$^{-4}$ or even 10$^{-5}$ the flux of the star. We applied our method to data recorded with Kepler, focussing on a sample of lightcurves with different effective temperatures and flux modulations. We found that GPSC can very effectively correct for the short and long term stellar activity and instrumental systematics. Additionally we run the GPSC on both real and simulated transit data, finding transit depths consistent with the original ones. Consequently we considered 10 hours of continuous observations: daily, every other day and weekly, and we used the GPSC to reconstruct the lightcurves. When data are recorded more frequently than once every five days we found that our approach is able to extrapolate the stellar flux at the 10$^{-4}$ level compared to the full stellar flux. These results show a great potential of GPSC to isolate the relevant astrophysical signal and achieve the precision needed for the correction of short and long term stellar activity.
Stellar magnetic activity produces time-varying distortions in the photospheric line profiles of solar-type stars. These lead to systematic errors in high-precision radial-velocity measurements, which limit efforts to discover and measure the masses of low-mass exoplanets with orbital periods of more than a few tens of days. We present a new data-driven method for separating Doppler shifts of dynamical origin from apparent velocity variations arising from variability-induced changes in the stellar spectrum. We show that the autocorrelation function (ACF) of the cross-correlation function used to measure radial velocities is effectively invariant to translation. By projecting the radial velocities on to a subspace labelled by the observation identifiers and spanned by the amplitude coefficients of the ACFs principal components, we can isolate and subtract velocity perturbations caused by stellar magnetic activity. We test the method on a 5-year time sequence of 853 daily 15-minute observations of the solar spectrum from the HARPS-N instrument and solar-telescope feed on the 3.58-m Telescopio Nazionale Galileo. After removal of the activity signals, the heliocentric solar velocity residuals are found to be Gaussian and nearly uncorrelated. We inject synthetic low-mass planet signals with amplitude $K=40$ cm s$^{-1}$ into the solar observations at a wide range of orbital periods. Projection into the orthogonal complement of the ACF subspace isolates these signals effectively from solar activity signals. Their semi-amplitudes are recovered with a precision of $sim~6.6$ cm s$^{-1}$, opening the door to Doppler detection and characterization of terrestrial-mass planets around well-observed, bright main-sequence stars across a wide range of orbital periods.
Nearly 15 years of radial velocity (RV) monitoring and direct imaging enabled the detection of two giant planets orbiting the young, nearby star $beta$ Pictoris. The $delta$ Scuti pulsations of the star, overwhelming planetary signals, need to be carefully suppressed. In this work, we independently revisit the analysis of the RV data following a different approach than in the literature to model the activity of the star. We show that a Gaussian Process (GP) with a stochastically driven damped harmonic oscillator kernel can model the $delta$ Scuti pulsations. It provides similar results as parametric models but with a simpler framework, using only 3 hyperparameters. It also enables to model poorly sampled RV data, that were excluded from previous analysis, hence extending the RV baseline by nearly five years. Altogether, the orbit and the mass of both planets can be constrained from RV only, which was not possible with the parametric modelling. To characterize the system more accurately, we also perform a joint fit of all available relative astrometry and RV data. Our orbital solutions for $beta$ Pic b favour a low eccentricity of $0.029^{+0.061}_{-0.024}$ and a relatively short period of $21.1^{+2.0}_{-0.8}$ yr. The orbit of $beta$ Pic c is eccentric with $0.206^{+0.074}_{-0.063}$ with a period of $3.36pm0.03$ yr. We find model-independent masses of $11.7pm1.4$ and $8.5pm0.5$ M$_{Jup}$ for $beta$ Pic b and c, respectively, assuming coplanarity. The mass of $beta$ Pic b is consistent with the hottest start evolutionary models, at an age of $25pm3$ Myr. A direct direction of $beta$ Pic c would provide a second calibration measurement in a coeval system.
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