The theory of kinks - I. A semi-analytic model of velocity perturbations due to planet-disc interaction

A new technique to detect protoplanets is by observing the kinematics of the surrounding gas. Gravitational perturbations from a planet produce peculiar 'kinks' in channel maps of different gas species. In this paper, we show that such kinks can be reproduced using semi-analytic models for the velocity perturbation induced by a planet. In doing so we (i) confirm that the observed kinks are consistent with the planet-induced wake; (ii) show how to quantify the planet mass from the kink amplitude; in particular, we show that the kink amplitude scales with the square root of the planet mass for channels far from the planet velocity, steepening to linear as the channels approach the planet; and (iii) show how to extend the theory to include the effect of damping, which may be needed in order to have localized kinks.