Transits of transparent planets-atmospheric lensing effects

Light refracted by the planet's atmosphere is usually ignored in analysis of planetary transits. Here, we show that refraction can add shoulders to the transit light curve, i.e., an increase in the observed flux, mostly just before and after the transit. During transit, light may be refracted away from the observer. Therefore, even completely transparent planets will display a very similar signal to that of a standard transit, i.e., of an opaque planet. We provide analytical expression for the amount of additional light deflected toward the observer before the transit, and show that the effect may be as large as 10^-4 of the stellar light and therefore measurable by current instruments. By observing this effect, we can directly measure the scale height of the planet's atmosphere. We also consider the attenuation of starlight in the planetary atmosphere due to Rayleigh scattering and discuss the conditions under which the atmospheric lensing effect is most prominent. We show that, for planets on orbital periods larger than about 70 days, the size of the transit is determined by refraction effects, and not by absorption within the planet.