Line-profile tomography of exoplanet transits I: The Doppler shadow of HD 189733b
We present a direct method for isolating the component of the starlight blocked by a planet as it transits its host star, and apply it to spectra of the bright transiting planet HD 189733b. We model the global shape of the stellar cross-correlation function as the convolution of a limb-darkened rotation profile and a gaussian representing the Doppler core of the average photospheric line profile. The light blocked by the planet during the transit is a gaussian of the same intrinsic width, whose trajectory across the line profile yields a precise measure of the misalignment angle and an independent measure of v sin I. We show that even when v sin I is less than the width of the intrinsic line profile, the travelling Doppler "shadow" cast by the planet creates an identifiable distortion in the line profiles which is amenable to direct modelling. Direct measurement of the trajectory of the missing starlight yields self-consistent measures of the projected stellar rotation rate, the intrinsic width of the mean local photospheric line profile, the projected spin-orbit misalignment angle, and the system's centre-of-mass velocity. Combined with the photometric rotation period, the results give a geometrical measure of the stellar radius which agrees closely with values obtained from high-precision transit photometry if a small amount of differential rotation is present in the stellar photosphere.