Disc-planet interactions in inviscid discs

Abstract

Planets are born in protoplanetary discs (PPDs), made of gas and dust, which surround newly formed stars. Gravitational coupling provides planets with means to interact with their birth environment, leading to the excitation of global spiral density waves, which drive evolution of the disc (such as the opening of gaps) and the planets’ orbital properties (known as migration). Modern observations of PPDs, provided for example by the high resolution interferometer ALMA, have shown intriguing features in continuum dust emission, such as lobes and arcs neighbouring darker ring-like gaps. These have been interpreted as dust-loaded vortices, which might be efficiently formed via the instability of the edges of planet-driven gaps. The main motivation of this thesis is to improve our understanding of their formation in order to put constraints on yet unseen planets. Consequently, in this thesis, we investigate this interaction of young planets with the disc gas they are embedded in, focussing on the non-linear shock-driven damping of global waves, subsequent disc evolution and the stability of the resulting flow. We perform a detailed numerical study of this process at the highest spatial resolution to date, investigating the formation, propagation and shock-driven damping of global density waves. The high fidelity of our numerical models allows us to thoroughly test previous theories of weakly nonlinear wave propagation due to Goodman and Rafikov (2001) and Rafikov (2002b), finding agreement with simulations on a qualitative but not quantitative level. As we show, this shortcoming is mainly due to the fact that this theory does not include the dispersion of shearing waves in differentially rotating discs. We provide fitting formulae for characteristics of the shocking wave and use it to explain observed vortensity production the closely related opening of a gap. This detailed study allowed us to understand how planet masses and disc surface density slope control this process from first principles. One of the main results of this work is a simple one-dimensional framework, which uses these fits in order to efficiently construct time-dependent gap models for various disc and planet parameters. Our model is verified against long-term numerical simulations and we use it further to perform a linear stability analysis of the gap edges against the Rossby wave instability (RWI). We find a power-law like behaviour of time-scales of instability and subsequent vortex formation, which are both strong functions of planet mass. Again, we provide useful fitting parameters. Further, we present a new method of constraining the age and masses of putative planets in observed gaps, depending on the presence or absence of vortex signatures. Being very sensitive to the disc temperature, such constraints will become more stringent as measurements of this parameter improve. Lastly, a detailed study of the more global structure of density waves and their gravitational coupling to the planet is presented. We investigate a repetitive pattern in the excitation torque density, which has been previously observed in simulations. We show that this phenomenon is indeed physical, giving a detailed explanation of its origin and reason why it only occurs in the outer disc. By varying the disc model, we show that the phenomenon occurs using barotropic and adiabatic equations of state, as well as in discs that allow for thermal relaxation. It is also robust against some wave nonlinearity such that our results may be applied also to other systems, such as circumbinary discs, as we show.