A comparison of spectroscopic methods for detecting the starlight scattered by transiting hot Jupiters, with an application to Subaru data for HD 209458b and HD 189733b

The measurement of the light scattered from extrasolar planets informs atmospheric and formation models. With the discovery of many hot Jupiter planets orbiting nearby stars, this motivates the development of robust methods of characterization from follow-up observations. In this paper, we discuss two methods for determining the planetary albedo in transiting systems. First, the most widely used method for measuring the light scattered by hot Jupiters is investigated for application for typical echelle spectra of a transiting planet system, showing that a detection requires high-signal-to-noise-ratio data of bright planets. Secondly, a new Fourier analysis method is also presented, which is model-independent and utilizes the benefits of the reduced number of unknown parameters in transiting systems. This approach involves solving for the planet and stellar spectra in Fourier space by least squares. The sensitivities of the methods are determined via Monte Carlo simulations for a range of planet-to-star flux ratios. We find the Fourier analysis method to be better suited to the ideal case of typical observations of a well-constrained transiting system than the Collier Cameron et al. method. To guide future observations of transiting planets with ground-based capabilities, the expected sensitivity to the planet-to-star flux ratio is quantified as a function of the signal-to-noise ratio and wavelength range. We apply the Fourier analysis method for extracting the light scattered by transiting hot Jupiters from high-resolution spectra to echelle spectra of HD 209458 and HD 189733. Unfortunately, we are unable to improve on the previous upper limit of the planet-to-star flux ratio for HD 209458b set by space-based observations. A 1σ upper limit on the planet-to-star flux ratio of HD 189733b is measured in the wavelength range of 558.83-599.56 nm yielding ε < 4.5 × 10^-4. This limit is not sufficiently strong to constrain models. Improvement in the measurement of the upper limit of the planet-to-star flux ratio of this system, with ground-based capabilities, requires data with a higher signal-to-noise ratio and increased stability of the telescope.