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Register a new userPlanet-driven density waves in protoplanetary discs: numerical verification of nonlinear evolution theory
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Nicolas Patrick Cimerman
Publication date
2021
fields
Physics
and research's language is
English
Authors
Nicolas P. Cimerman DAMTP
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Gravitational coupling between protoplanetary discs and planets embedded in them leads to the emergence of spiral density waves, which evolve into shocks as they propagate through the disc. We explore the performance of a semi-analytical framework for describing the nonlinear evolution of the global planet-driven density waves, focusing on the low planet mass regime (below the so-called thermal mass). We show that this framework accurately captures the (quasi-)self-similar evolution of the wave properties expressed in terms of properly rescaled variables, provided that certain theoretical inputs are calibrated using numerical simulations (an approximate, first principles calculation of the wave evolution based on the inviscid Burgers equation is in qualitative agreement with simulations but overpredicts wave damping at the quantitative level). We provide fitting formulae for such inputs, in particular, the strength and global shape of the planet-driven shock accounting for nonlinear effects. We use this nonlinear framework to theoretically compute vortensity production in the disc by the global spiral shock and numerically verify the accuracy of this calculation. Our results can be used for interpreting observations of spiral features in discs, kinematic signatures of embedded planets in CO line emission (kinks), and for understanding the emergence of planet-driven vortices in protoplanetary discs.
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It is expected that a pressure bump can be formed at the inner edge of a dead-zone, and where vortices can develop through the Rossby Wave Instability (RWI). It has been suggested that self-gravity can significantly affect the evolution of such vortices. We present the results of 2D hydrodynamical simulations of the evolution of vortices forming at a pressure bump in self-gravitating discs with Toomre parameter in the range $4-30$. We consider isothermal plus non-isothermal disc models that employ either the classical $beta$ prescription or a more realistic treatment for cooling. The main aim is to investigate whether the condensating effect of self-gravity can stabilize vortices in sufficiently massive discs. We confirm that in isothermal disc models with ${cal Q} gtrsim 15$, vortex decay occurs due to the vortex self-gravitational torque. For discs with $3lesssim {cal Q} lesssim 7$, the vortex develops gravitational instabilities within its core and undergoes gravitational collapse, whereas more massive discs give rise to the formation of global eccentric modes. In non-isothermal discs with $beta$ cooling, the vortex maintains a turbulent core prior to undergoing gravitational collapse for $beta lesssim 0.1$, whereas it decays if $beta ge 1$. In models that incorpore both self-gravity and a better treatment for cooling, however, a stable vortex is formed with aspect ratio $chi sim 3-4$. Our results indicate that self-gravity significantly impacts the evolution of vortices forming in protoplanetary discs, although the thermodynamical structure of the vortex is equally important for determining its long-term dynamics.
Many stars are in binaries or higher-order multiple stellar systems. Although in recent years a large number of binaries have been proven to host exoplanets, how planet formation proceeds in multiple stellar systems has not been studied much yet from the theoretical standpoint. In this paper we focus on the evolution of the dust grains in planet-forming discs in binaries. We take into account the dynamics of gas and dust in discs around each component of a binary system under the hypothesis that the evolution of the circumprimary and the circumsecondary discs is independent. It is known from previous studies that the secular evolution of the gas in binary discs is hastened due to the tidal interactions with their hosting stars. Here we prove that binarity affects dust dynamics too, possibly in a more dramatic way than the gas. In particular, the presence of a stellar companion significantly reduces the amount of solids retained in binary discs because of a faster, more efficient radial drift, ultimately shortening their lifetime. We prove that how rapidly discs disperse depends both on the binary separation, with discs in wider binaries living longer, and on the disc viscosity. Although the less-viscous discs lose high amounts of solids in the earliest stages of their evolution, they are dissipated slowly, while those with higher viscosities show an opposite behaviour. The faster radial migration of dust in binary discs has a striking impact on planet formation, which seems to be inhibited in this hostile environment, unless other disc substructures halt radial drift further in. We conclude that if planetesimal formation were viable in binary discs, this process would take place on very short time scales.
We study the linear perturbations of collisionless near-Keplerian discs. Such systems are models for debris discs around stars and the stellar discs surrounding supermassive black holes at the centres of galaxies. Using a finite-element method, we solve the linearized collisionless Boltzmann equation and Poissons equation for a wide range of disc masses and rms orbital eccentricities to obtain the eigenfrequencies and shapes of normal modes. We find that these discs can support large-scale `slow modes, in which the frequency is proportional to the disc mass. Slow modes are present for arbitrarily small disc mass so long as the self-gravity of the disc is the dominant source of apsidal precession. We find that slow modes are of two general types: parent modes and hybrid child modes, the latter arising from resonant interactions between parent modes and singular van Kampen modes. The most prominent slow modes have azimuthal wavenumbers $m=1$ and $m=2$. We illustrate how slow modes in debris discs are excited during a fly-by of a neighbouring star. Many of the non-axisymmetric features seen in debris discs (clumps, eccentricity, spiral waves) that are commonly attributed to planets could instead arise from slow modes; the two hypotheses can be distinguished by long-term measurements of the pattern speed of the features.
Low-mass objects embedded in isothermal protoplanetary discs are known to suffer rapid inward Type I migration. In non-isothermal discs, recent work has shown that a decreasing radial profile of the disc entropy can lead to a strong positive corotation torque which can significantly slow down or reverse Type I migration in laminar viscous disc models. It is not clear however how this picture changes in turbulent disc models. The aim of this study is to examine the impact of turbulence on the torque experienced by a low-mass planet embedded in a non-isothermal protoplanetary disc. We particularly focus on the role of turbulence on the corotation torque whose amplitude depends on the efficiency of diffusion processes in the planets horseshoe region. We performed 2D numerical simulations using a grid-based hydrodynamical code in which turbulence is modelled as stochastic forcing. In order to provide estimations for the viscous and thermal diffusion coefficients as a function of the amplitude of turbulence, we first set up non-isothermal disc models for different values of the amplitude of the turbulent forcing. We then include a low-mass planet and determine the evolution of its running time-averaged torque. We show that in non-isothermal discs, the entropy-related corotation torque can indeed remain unsaturated in the presence of turbulence. For turbulence amplitudes that do not strongly affect the disc temperature profile, we find that the running time-averaged torque experienced by an embedded protoplanet is in fairly good agreement with laminar disc models with appropriate values for the thermal and viscous diffusion coefficients. In discs with turbulence driven by stochastic forcing, the corotation torque therefore behaves similarly as in laminar viscous discs and can be responsible for significantly slowing down or reversing Type I migration.
Large-scale vertical magnetic fields are believed to play a key role in the evolution of protoplanetary discs. Associated with non-ideal effects, such as ambipolar diffusion, they are known to launch a wind that could drive accretion in the outer part of the disc ($R> 1$ AU). They also potentially lead to self-organisation of the disc into large-scale axisymmetric structures, similar to the rings recently imaged by sub-millimetre or near-infrared instruments (ALMA and SPHERE). The aim of this paper is to investigate the mechanism behind the formation of these gaseous rings, but also to understand the dust dynamics and its emission in discs threaded by a large-scale magnetic field. To this end, we performed global magneto-hydrodynamics (MHD) axisymmetric simulations with ambipolar diffusion using a modified version of the PLUTO code. We explored different magnetisations with the midplane $beta$ parameter ranging from $10^5$ to $10^3$ and included dust grains -- treated in the fluid approximation -- ranging from $100 mu$m to 1 cm in size. We first show that the gaseous rings (associated with zonal flows) are tightly linked to the existence of MHD winds. Secondly, we find that millimetre-size dust is highly sedimented, with a typical scale height of 1 AU at $R=100$ AU for $beta=10^4$, compatible with recent ALMA observations. We also show that these grains concentrate into pressure maxima associated with zonal flows, leading to the formation of dusty rings. Using the radiative transfer code MCFOST, we computed the dust emission and make predictions on the ring-gap contrast and the spectral index that one might observe with interferometers like ALMA.
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