A CLOUDINESS INDEX FOR TRANSITING EXOPLANETS BASED ON THE SODIUM AND POTASSIUM LINES: TENTATIVE EVIDENCE FOR HOTTER ATMOSPHERES BEING LESS CLOUDY AT VISIBLE WAVELENGTHS

We present a dimensionless index that quantifies the degree of cloudiness of the atmosphere of a transiting exoplanet. Our cloudiness index is based on measuring the transit radii associated with the line center and wing of the sodium or potassium line. In deriving this index, we revisited the algebraic formulae for inferring the isothermal pressure scale height from transit measurements. We demonstrate that the formulae of Lecavelier et al. and Benneke & Seager are identical: the former is inferring the temperature while assuming a value for the mean molecular mass and the latter is inferring the mean molecular mass while assuming a value for the temperature. More importantly, these formulae cannot be used to distinguish between cloudy and cloud-free atmospheres. We derive values of our cloudiness index for a small sample of seven hot Saturns/Jupiters taken from Sing et al. We show that WASP-17b, WASP-31b, and HAT-P-1b are nearly cloud-free at visible wavelengths. We find the tentative trend that more irradiated atmospheres tend to have fewer clouds consisting of sub-micron-sized particles. We also derive absolute sodium and/or potassium abundances similar to 10(2) cm(-3) for WASP-17b, WASP-31b, and HAT-P-1b (and upper limits for the other objects). Higher-resolution measurements of both the sodium and potassium lines, for a larger sample of exoplanetary atmospheres, are needed to confirm or refute this trend.