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

TL;DR

This paper introduces a semi-analytic model to interpret gas kinks caused by planet-disc interactions, enabling planet detection and mass estimation from observed velocity perturbations in protoplanetary disks.

Contribution

It provides a novel semi-analytic framework for modeling velocity perturbations and quantifying planet mass from gas kinks in protoplanetary disks.

Findings

Kinks are consistent with planet-induced wakes.

Kink amplitude scales with the square root of planet mass.

The model includes effects of damping on kink localization.

Abstract

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; iii) show how to extend the theory to include the effect of damping, which may be needed in order to have localized kinks.