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Register a new userGoing back to basics: accelerating exoplanet transit modelling using Taylor-series expansion of the orbital motion
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A significant fraction of an exoplanet transit model evaluation time is spent calculating projected distances between the planet and its host star. This is a relatively fast operation for a circular orbit, but slower for an eccentric one. However, because the planets position and its time derivatives are constant for any specific point in orbital phase, the projected distance can be calculated rapidly and accurately in the vicinity of the transit by expanding the planets $x$ and $y$ positions in the sky plane into a Taylor series at mid-transit. Calculating the projected distance for an elliptical orbit using the four first time derivatives of the position vector (velocity, acceleration, jerk, and snap) is $sim100$ times faster than calculating it using the Newtons method, and also significantly faster than calculating $z$ for a circular orbit because the approach does not use numerically expensive trigonometric functions. The speed gain in the projected distance calculation leads to 2-25 times faster transit model evaluation speed, depending on the transit model complexity and orbital eccentricity. Calculation of the four position derivatives using numerical differentiation takes $sim1,mu$s with a modern laptop and needs to be done only once for a given orbit, and the maximum error the approximation introduces to a transit light curve is below 1~ppm for the major part of the physically plausible orbital parameter space.
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The transit of Venus in 2004 offered the rare possibility to remotely sense a well-known planetary atmosphere using ground-based observations for absorption spectroscopy. Transmission spectra of Venus atmosphere were obtained in the near infrared using the Vacuum Tower Telescope (VTT) in Tenerife. Since the instrument was designed to measure the very bright photosphere of the Sun, extracting Venus atmosphere was challenging. CO_2 absorption lines could be identified in the upper Venus atmosphere. Moreover, the relative abundance of the three most abundant CO_2 isotopologues could be determined. The observations resolved Venus limb, showing Doppler-shifted absorption lines that are probably caused by high-altitude winds. This paper illustrates the ability of ground-based measurements to examine atmospheric constituents of a terrestrial planet atmosphere which might be applied in future to terrestrial extrasolar planets.
Vetting of exoplanet candidates in transit surveys is a manual process, which suffers from a large number of false positives and a lack of consistency. Previous work has shown that Convolutional Neural Networks (CNN) provide an efficient solution to these problems. Here, we apply a CNN to classify planet candidates from the Next Generation Transit Survey (NGTS). For training datasets we compare both real data with injected planetary transits and fully-simulated data, as well as how their different compositions affect network performance. We show that fewer hand labelled lightcurves can be utilised, while still achieving competitive results. With our best model, we achieve an AUC (area under the curve) score of $(95.6pm{0.2})%$ and an accuracy of $(88.5pm{0.3})%$ on our unseen test data, as well as $(76.5pm{0.4})%$ and $(74.6pm{1.1})%$ in comparison to our existing manual classifications. The neural network recovers 13 out of 14 confirmed planets observed by NGTS, with high probability. We use simulated data to show that the overall network performance is resilient to mislabelling of the training dataset, a problem that might arise due to unidentified, low signal-to-noise transits. Using a CNN, the time required for vetting can be reduced by half, while still recovering the vast majority of manually flagged candidates. In addition, we identify many new candidates with high probabilities which were not flagged by human vetters.
I present RoadRunner, a fast exoplanet transit model that can use any radially symmetric function to model stellar limb darkening while still being faster to evaluate than the analytical transit model for quadratic limb darkening by Mandel & Agol (2002). CPU and GPU implementations of the model are available in the PyTransit transit modelling package, and come with platform-independent parallelisation, supersampling, and support for modelling complex heterogeneous time series. The code is written in numba-accelerated Python (and the GPU model in OpenCL) without C or Fortran dependencies, which allows for the limb darkening model to be given as any Python-callable function. Finally, as an example of the flexibility of the approach, the latest version of PyTransit comes with a numerical limb darkening model that uses LDTk-generated limb darkening profiles directly without approximating them by analytical models.
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.
Aims: ARCiS, a novel code for the analysis of exoplanet transmission and emission spectra is presented. The aim of the modelling framework is to provide a tool able to link observations to physical models of exoplanet atmospheres. Methods: The modelling philosophy chosen in this paper is to use physical and chemical models to constrain certain parameters while keeping free the parts where our physical understanding is still more limited. This approach, in between full physical modelling and full parameterisation, allows us to use the processes we understand well and parameterise those less understood. A Bayesian retrieval framework is implemented and applied to the transit spectra of a set of 10 hot Jupiters. The code contains chemistry and cloud formation and has the option for self consistent temperature structure computations. Results: The code presented is fast and flexible enough to be used for retrieval and for target list simulations for e.g. JWST or the ESA Ariel missions. We present results for the retrieval of elemental abundance ratios using the physical retrieval framework and compare this to results obtained using a parameterised retrieval setup. Conclusions: We conclude that for most of the targets considered the current dataset is not constraining enough to reliably pin down the elemental abundance ratios. We find no significant correlations between different physical parameters. We confirm that planets in our sample with a strong slope in the optical transmission spectrum are the planets where we find cloud formation to be most active. Finally, we conclude that with ARCiS we have a computationally efficient tool to analyse exoplanet observations in the context of physical and chemical models.
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