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Register a new userRoadRunner: a fast and flexible exoplanet transit model
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Hannu Parviainen
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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.
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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.
Since the start of the Wide Angle Search for Planets (WASP) program, more than 160 transiting exoplanets have been discovered in the WASP data. In the past, possible transit-like events identified by the WASP pipeline have been vetted by human inspection to eliminate false alarms and obvious false positives. The goal of the present paper is to assess the effectiveness of machine learning as a fast, automated, and reliable means of performing the same functions on ground-based wide-field transit-survey data without human intervention. To this end, we have created training and test datasets made up of stellar light curves showing a variety of signal types including planetary transits, eclipsing binaries, variable stars, and non-periodic signals. We use a combination of machine learning methods including Random Forest Classifiers (RFCs) and Convolutional Neural Networks (CNNs) to distinguish between the different types of signals. The final algorithms correctly identify planets in the test data ~90% of the time, although each method on its own has a significant fraction of false positives. We find that in practice, a combination of different methods offers the best approach to identifying the most promising exoplanet transit candidates in data from WASP, and by extension similar transit surveys.
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.
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.
Near-IR observations are important for the detection and characterization of exoplanets using the transit technique, either in surveys of large numbers of stars or for follow-up spectroscopic observations of individual planets. In a controlled laboratory experiment, we imaged $sim 10^4$ critically sampled spots onto an Teledyne Hawaii-2RG (H2RG) detector to emulate an idealized star-field. We obtained time-series photometry of up to $simeq 24$ hr duration for ensembles of $sim 10^3$ pseudo-stars. After rejecting correlated temporal noise caused by various disturbances, we measured a photometric performance of $<$50 ppm-hr$^{-1/2}$ limited only by the incident photon rate. After several hours we achieve a photon-noise limited precision level of $10sim20$ ppm after averaging many independent measurements. We conclude that IR detectors such as the H2RG can make the precision measurements needed to detect the transits of terrestrial planets or detect faint atomic or molecular spectral features in the atmospheres of transiting extrasolar planets.
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