Planet-driven spirals in protoplanetary discs: limitations of the semi-analytical theory for observations

Abstract: Detecting protoplanets during their formation stage is an important but elusive goal of modern astronomy. Kinematic detections via the spiral wakes in the gaseous disc are a promising avenue to achieve this goal. We aim to test the applicability to observations in the low and intermediate planet mass regimes of a commonly used semi-analytical model for planet induced spiral waves. In contrast with previous works which proposed to use the semi-analytical model to interpret observations, in this study we analyse for the first time both the structure of the velocity and density perturbations. We run a set of FARGO3D hydrodynamic simulations and compare them with the output of the semi-analytic model in the code wakeflow, which is obtained by solving Burgers' equation using the simulations as an initial condition. We find that the velocity field derived from the analytic theory is discontinuous at the interface between the linear and nonlinear regions. After 0.2 r$_p$ from the planet, the behaviour of the velocity field closely follows that of the density perturbations. In the low mass limit, the analytical model is in qualitative agreement with the simulations, although it underestimates the azimuthal width and the amplitude of the perturbations, predicting a stronger decay but a slower azimuthal advance of the shock fronts. In the intermediate regime, the discrepancy increases, resulting in a different pitch angle between the spirals of the simulations and the analytic model. The implementation of a fitting procedure based on the minimisation of intensity residuals is bound to fail due to the deviation in pitch angle between the analytic model and the simulations. In order to apply this model to observations, it needs to be revisited accounting also for higher planet masses.