Planet formation, resonant drag instabilities, and vortices

Abstract

The first part of this thesis is a brief overview of modern planet formation theory. I first present the four critical observations that any model should reproduce: planets form from the aggregation of countless dust grains early in the life of almost every protoplanetary disc . I then describe the main stages of the leading ‘core acccretion’ scenario: Brownian coagulation, turbulent coagulation, the metre-scale barrier, planetesimal accretion, pebble accretion, cooling-limited gas accretion, and runaway gas accretion. Finally, I present six possible bridges over the metre gap: sturdy grains, pressure bumps, the gravitational instability, the Safronov-Goldreich-Ward mechanism, the streaming instability (SI), and turbulent concentration. I argue that the most convincing option is the SI. In the second part of the thesis, I explain how the SI works. In fact, the mechanism I uncover drives a whole class of instabilities called ‘resonant drag instabilities’ (RDIs). These appear in mixtures of gas and dust, when the two species drift relative to each other. I use linear perturbation theory and asymptotic methods in the limit of dilute dust to show that the dust’s drift allows the dust to resonate with one of the gas waves. I then show that RDIs are due to a positive feedback loop between two mechanisms. In the first leg of the loop, the resonant gas wave concentrates the dust. In the second leg, the resulting dust density perturbation exerts a force on the gas, accelerating it in such a way as to amplify the original wave. I then apply my general framework to two particular cases: the acoustic RDI – which may affect the winds of cool stars, the torii of active galactic nuclei and interstellar clouds – and the SI. We were already able to make quantitative predictions about those two phenomenas, so my real contribution is to explain how they work. The picture I offer will help evaluate how those instabilities respond to non-ideal effects such as turbulence, magnetic fields, etc. and may help understand how they saturate. In the last part of the thesis, I show that the SI remains active in vortices. This is a major result, because the SI requires a high dust-to-gas ratio, a narrow distribution in particle size, and a low level of turbulence. One of the few places where all those conditions are met is in large-scale vortices, but fluid instabilities are notoriously fragile to modifications of the background flow, and vortex flows differ substantially from disc flows. I use a multiple-timescale analysis in the regime of well-coupled grains to derive the first analytical model for dust-laden vortices in protoplanetary discs. I find that if the vortex is weak and anticyclonic, dust drifts towards its centre. Since the dust concentrates, its specific angular momentum changes. It can increase or decrease, depending on the vortex’s strength relative to disc’s Keplerian rotation. Either way, the gas must respond. It changes its vorticity to keep the total angular momentum constant. I find that this effect morphs strong vortices into epicycles, and shears out weak vortices. Dust concentration eventually stops, and the final dust-to-gas ratio is almost always between 1 and 100. I then analyse the linear stability of my vortices. To do so, I build an analog of the shearing box that follows a vortex streamline instead of a circular orbit, and I write a Floquet differential algebraic equation solver. I find that the dust’s drift powers an instability, and I extend the mathematical framework of chapter 2 to show that this instability is the SI. Interestingly, the ‘vortex SI’ extends to 2D, so it may explain the unknown instability seen in simulations. My results also imply that RDIs are robust to complexity in the background flow and in the wave structure.