A Gaussian process framework for modelling instrumental systematics: application to transmission spectroscopy

Transmission spectroscopy, which consists of measuring the wavelength-dependent absorption of starlight by a planet's atmosphere during a transit, is a powerful probe of atmospheric composition. However, the expected signal is typically orders of magnitude smaller than instrumental systematics, and the results are crucially dependent on the treatment of the latter. In this paper, we propose a new method to infer transit parameters in the presence of systematic noise using Gaussian processes, a technique widely used in the machine learning community for Bayesian regression and classification problems. Our method makes use of auxiliary information about the state of the instrument, but does so in a non-parametric manner, without imposing a specific dependence of the systematics on the instrumental parameters, and naturally allows for the correlated nature of the noise. We give an example application of the method to archival NICMOS transmission spectroscopy of the hot Jupiter HD 189733, which goes some way towards reconciling the controversy surrounding this dataset in the literature. Finally, we provide an appendix giving a general introduction to Gaussian processes for regression, in order to encourage their application to a wider range of problems.Comment: 6 figures, 1 table, accepted for publication in MNRA

The prevalence of dust on the exoplanet HD 189733b from Hubble and Spitzer observations

The hot Jupiter HD189733b is the most extensively observed exoplanet. Its atmosphere has been detected and characterised in transmission and eclipse spectroscopy, and its phase curve measured at several wavelengths. This paper brings together results of our campaign to obtain the complete transmission spectrum of the atmosphere of this planet from UV to IR with HST, using STIS, ACS and WFC3. We provide a new tabulation of the transmission spectrum across the entire visible and IR range. The radius ratio in each wavelength band was rederived to ensure a consistent treatment of the bulk transit parameters and stellar limb-darkening. Special care was taken to correct for, and derive realistic estimates of the uncertainties due to, both occulted and unocculted star spots. The combined spectrum is very different from the predictions of cloud-free models: it is dominated by Rayleigh scattering over the whole visible and near infrared range, the only detected features being narrow Na and K lines. We interpret this as the signature of a haze of condensate grains extending over at least 5 scale heights. We show that a dust-dominated atmosphere could also explain several puzzling features of the emission spectrum and phase curves, including the large amplitude of the phase curve at 3.6um, the small hot-spot longitude shift and the hot mid-infrared emission spectrum. We discuss possible compositions and derive some first-order estimates for the properties of the putative condensate haze/clouds. We finish by speculating that the dichotomy between the two observationally defined classes of hot Jupiter atmospheres, of which HD189733b and HD209458b are the prototypes, might not be whether they possess a temperature inversion, but whether they are clear or dusty. We also consider the possibility of a continuum of cloud properties between hot Jupiters, young Jupiters and L-type brown dwarfs.Comment: Accepted for publication in MNRAS. 31 pages, 19 figures, 8 table

A Gemini ground-based transmission spectrum of WASP-29b: a featureless spectrum from 515 to 720nm

We report Gemini-South GMOS observations of the exoplanet system WASP-29 during primary transit as a test case for differential spectrophotometry. We use the multi-object spectrograph to observe the target star and a comparison star simultaneously to produce multiple light curves at varying wavelengths. The 'white' light curve and fifteen 'spectral' light curves are analysed to refine the system parameters and produce a transmission spectrum from 515 to 720nm. All light curves exhibit time-correlated noise, which we model using a variety of techniques. These include a simple noise rescaling, a Gaussian process model, and a wavelet based method. These methods all produce consistent results, although with different uncertainties. The precision of the transmission spectrum is improved by subtracting a common signal from all the spectral light curves, reaching a typical precision of ~1x10^-4 in transit depth. The transmission spectrum is free of spectral features, and given the non-detection of a pressure broadened Na feature, we can rule out the presence of a Na rich atmosphere free of clouds or hazes, although we cannot rule out a narrow Na core. This indicates that Na is not present in the atmosphere, and/or that clouds/hazes play a significant role in the atmosphere and mask the broad wings of the Na feature, although the former is a more likely explanation given WASP-29b's equilibrium temperature of ~970 K, at which Na can form various compounds. We also briefly discuss the use of Gaussian process and wavelet methods to account for time correlated noise in transit light curves.Comment: 15 pages, 9 figures, 3 tables. Published in MNRAS. Figure 2 corrected in version

The optical transmission spectrum of the hot Jupiter HAT-P-32b: clouds explain the absence of broad spectral features?

We report Gemini-North GMOS observations of the inflated hot Jupiter HAT-P-32b during two primary transits. We simultaneously observed two comparison stars and used differential spectro-photometry to produce multi-wavelength light curves. 'White' light curves and 29 'spectral' light curves were extracted for each transit and analysed to refine the system parameters and produce transmission spectra from 520-930nm in ~14nm bins. The light curves contain time-varying white noise as well as time-correlated noise, and we used a Gaussian process model to fit this complex noise model. Common mode corrections derived from the white light curve fits were applied to the spectral light curves which significantly improved our precision, reaching typical uncertainties in the transit depth of ~2x10^-4, corresponding to about half a pressure scale height. The low resolution transmission spectra are consistent with a featureless model, and we can confidently rule out broad features larger than about one scale height. The absence of Na/K wings or prominent TiO/VO features is most easily explained by grey absorption from clouds in the upper atmosphere, masking the spectral features. However, we cannot confidently rule out clear atmosphere models with low abundances (~10^-3 solar) of TiO, VO or even metal hydrides masking the Na and K wings. A smaller scale height or ionisation could also contribute to muted spectral features, but alone are unable to to account for the absence of features reported here.Comment: 17 pages, 11 figures, 2 tables, accepted for publication in MNRA

Thermoelectric Processes and Materials

Contains reports on three research projects.United States Navy, Office of Naval Research (Contract Nonr-1841(51)

Thermoelectric Processes and Materials

Contains reports on two research projects.Office of Naval Research (Contract Nonr-1841(51

Noise properties of the CoRoT data: a planet-finding perspective

In this short paper, we study the photometric precision of stellar light curves obtained by the CoRoT satellite in its planet finding channel, with a particular emphasis on the timescales characteristic of planetary transits. Together with other articles in the same issue of this journal, it forms an attempt to provide the building blocks for a statistical interpretation of the CoRoT planet and eclipsing binary catch to date. After pre-processing the light curves so as to minimise long-term variations and outliers, we measure the scatter of the light curves in the first three CoRoT runs lasting more than 1 month, using an iterative non-linear filter to isolate signal on the timescales of interest. The bevhaiour of the noise on 2h timescales is well-described a power-law with index 0.25 in R-magnitude, ranging from 0.1mmag at R=11.5 to 1mmag at R=16, which is close to the pre-launch specification, though still a factor 2-3 above the photon noise due to residual jitter noise and hot pixel events. There is evidence for a slight degradation of the performance over time. We find clear evidence for enhanced variability on hours timescales (at the level of 0.5 mmag) in stars identified as likely giants from their R-magnitude and B-V colour, which represent approximately 60 and 20% of the observed population in the direction of Aquila and Monoceros respectively. On the other hand, median correlated noise levels over 2h for dwarf stars are extremely low, reaching 0.05mmag at the bright end.Comment: 5 pages, 4 figures, accepted for publication in A&

Modelling solar-like variability for the detection of Earth-like planetary transits. II) Performance of the three-spot modelling, harmonic function fitting, iterative non-linear filtering and sliding boxcar filtering

We present a comparison of four methods of filtering solar-like variability to increase the efficiency of detection of Earth-like planetary transits by means of box-shaped transit finder algorithms. Two of these filtering methods are the harmonic fitting method and the iterative non-linear filter that, coupled respectively with the Box Least-Square (BLS) and Box Maximum-Likelihood algorithms, demonstrated the best performance during the first detection blind test organized inside the CoRoT consortium. The third method, the 3-spot model, is a simplified physical model of Sun-like variability and the fourth is a simple sliding boxcar filter. We apply a Monte Carlo approach by simulating a large number of 150-day light curves (as for CoRoT long runs) for different planetary radii, orbital periods, epochs of the first transit and standard deviations of the photon shot noise. Stellar variability is given by the Total Solar Irradiance variations as observed close to the maximum of solar cycle 23. After filtering solar variability, transits are searched for by means of the BLS algorithm. We find that the iterative non-linear filter is the best method to filter light curves of solar-like stars when a suitable window can be chosen. As the performance of this filter depends critically on the length of its window, we point out that the window must be as long as possible, according to the magnetic activity level of the star. We show an automatic method to choose the extension of the filter window from the power spectrum of the light curves. The iterative non-linear filter, when used with a suitable choice of its window, has a better performance than more complicated and computationally intensive methods of fitting solar-like variability, like the 200-harmonic fitting or the 3-spot model.Comment: accepted by A&

Modelling solar-like variability for the detection of Earth-like planetary transits. II. Performance of the three-spot modelling, harmonic function fitting, iterative nonlinear filtering, and sliding boxcar filtering

Copyright © The European Southern Observatory (ESO)Aims. As an extension of a previous work, we present a comparison of four methods of filtering solar-like variability to increase the efficiency of detection of Earth-like planetary transits by means of box-shaped transit finder algorithms. Two of these filtering methods are the harmonic fitting method and the iterative nonlinear filter that, coupled respectively with the box least-square (BLS) and box maximum likelihood algorithms, demonstrated the best performance during the first detection blind test organised inside the CoRoT consortium. The third method, the 3-spot model, is a simplified physical model of Sun-like variability and the fourth is a simple sliding boxcar filter. Methods. We apply a Monte Carlo approach by simulating a large number of 150-day light curves (as for CoRoT long runs) for different planetary radii, orbital periods, epochs of the first transit, and standard deviations of the photon shot noise. Stellar variability is given by the total solar irradiance variations as observed close to the maximum of solar cycle 23. After filtering solar variability, transits are searched for by means of the BLS algorithm. Results. We find that the iterative nonlinear filter is the best method for filtering light curves of solar-like stars when a suitable window can be chosen. As the performance of this filter depends critically on the length of its window, we point out that the window must be as long as possible, according to the magnetic activity level of the star. We show an automatic method to choose the extension of the filter window from the power spectrum of the light curves. Conclusions. The iterative nonlinear filter, when used with a suitable choice of its window, has a better performance than more complicated and computationally intensive methods of fitting solar-like variability, like the 200-harmonic fitting or the 3-spot model

Thermoelectric Processes and Materials

Contains research objectives and reports on two research projects.U. S. Navy (Office of Naval Research) under Contract Nonr-1841(51