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Register a new userThe power of wavelets in analysis of transit and phase curves in presence of stellar variability and instrumental noise I. Method and validation
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Szil\\'ard Csizmadia
Publication date
2021
fields
Physics
and research's language is
English
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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. (...)
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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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We conducted a global analysis of the TRAPPIST Ultra-Cool Dwarf Transit Survey - a prototype of the SPECULOOS transit search conducted with the TRAPPIST-South robotic telescope in Chile from 2011 to 2017 - to estimate the occurrence rate of close-in planets such as TRAPPIST-1b orbiting ultra-cool dwarfs. For this purpose, the photometric data of 40 nearby ultra-cool dwarfs were reanalysed in a self-consistent and fully automated manner starting from the raw images. The pipeline developed specifically for this task generates differential light curves, removes non-planetary photometric features and stellar variability, and searches for transits. It identifies the transits of TRAPPIST-1b and TRAPPIST-1c without any human intervention. To test the pipeline and the potential output of similar surveys, we injected planetary transits into the light curves on a star-by-star basis and tested whether the pipeline is able to detect them. The achieved photometric precision enables us to identify Earth-sized planets orbiting ultra-cool dwarfs as validated by the injection tests. Our planet-injection simulation further suggests a lower limit of 10 per cent on the occurrence rate of planets similar to TRAPPIST-1b with a radius between 1 and 1.3 $R_oplus$ and the orbital period between 1.4 and 1.8 days.
When fitting N-body models to astronomical data - including transit times, radial velocity, and astrometric positions at observed times - the derivatives of the model outputs with respect to the initial conditions can help with model optimization and posterior sampling. Here we describe a general-purpose symplectic integrator for arbitrary orbital architectures, including those with close encounters, which we have recast to maintain numerical stability and precision for small step sizes. We compute the derivatives of the N-body coordinates and velocities as a function of time with respect to the initial conditions and masses by propagating the Jacobian along with the N-body integration. For the first time we obtain the derivatives of the transit times with respect to the initial conditions and masses using the chain rule, which is quicker and more accurate than using finite differences or automatic differentiation. We implement this algorithm in an open source package, NbodyGradient.jl, written in the Julia language, which has been used in the optimization and error analysis of transit-timing variations in the TRAPPIST-1 system. We present tests of the accuracy and precision of the code, and show that it compares favorably in speed to other integrators which are written in C.
We developed a dedicated statistical test for a massive detection of spot- and facula-crossing anomalies in multiple exoplanetary transit lightcurves, based on the frequentist $p$-value thresholding. This test was used to augment our algorithmic pipeline for transit lightcurves analysis. It was applied to $1598$ amateur and professional transit observations of $26$ targets being monitored in the EXPANSION project. We detected $109$ statistically significant candidate events revealing a roughly $2:1$ asymmetry in favor of spots-crossings over faculae-crossings. Although some candidate anomalies likely appear non-physical and originate from systematic errors, such asymmetry between negative and positive events should indicate a physical difference between the frequency of star spots and faculae. Detected spot-crossing events also reveal positive correlation between their amplitude and width, possibly owed to spot size correlation. However, the frequency of all detectable crossing events appears just about a few per cent, so they cannot explain excessive transit timing noise observed for several targets.
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