Sahl Rowther | Suppressing Gravitational Instabilities In Self-Gravitating Protoplanetary Discs

Suppressing Gravitational Instabilities In Protoplanetary Discs

Sahl Rowther, Farzana Meru, Rebecca Nealon, Grant M. Kennedy, Christophe Pinte

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Where are the Gravitationally Unstable Discs?

When discs are young, they are expected to be quite massive. A characteristic feature of massive discs are large scale spiral features due to gravitational instabilities. However, observations of recent protoplanetary discs (Andrews et al. 2018, Long et al. 2018) in the last few years have shown that most discs tend to be axisymmetric, with some also showing ring and gap structures. Even observations of very young Class 1 discs such as GY 91 (Sheehan & Eisner 2018) and IRS 63 (Segura-Cox et al. 2020), both thought to be less than half a million years old, show rings & gaps.

Does the lack of observed large scale spiral structures imply that young discs are not as massive as expected? Or can signatures of gravitational instabilities be hidden? It is reasonable to assume that gravitationally unstable discs do not evolve in isolation. The physical processes that are often used to explain observed substructures such as rings and gaps, along with the mechanisms that can warp a disc will also influence the evolution of young self-gravitating discs. Our aim is to investigate whether physical processes such as warps and planet-disc interactions can hide signatures of gravitational instability.

A Warped Disc

As the disc evolves, the warp propagates radially both inwards and outwards.
Since the warp was introduced numerically, it is not sustained. Thus as the disc continues to evolve, the warp smooths out and the disc becomes coplanar.
The influence of the warp quickly suppresses the spiral structures yielding an axisymmetric gravitationally stable disc.

Rowther et al. 2022

Evolution of a warped self-gravitating protoplanetary disc.

Planet-Disc Interactions

The planet suppresses large scale spiral structures due to gravitational instabilities and carves open a gap.
The spiral arms generated by the planet are responsible for heating up the disc pushing it into the gravitationally stable regime resulting in a largely axisymmetric disc.
The disc appears completely axisymmetric with ring and gap structures in mock observations in certain ALMA configurations. The planet's presence can be inferred from it's spiral arms (in some ALMA configurations) and from the kink it causes in the gas kinematics.

Rowther et al. 2020

Evolution of a self-gravitating protoplanetary disc with a 3 Jupiter mass planet.

Why does the disc heat up?

In both scenarios, the PdV work plays an important role in altering the disc's evolution. The divergence of the velocity is directly linked to the PdV work, so we use it as a proxy for the PdV work.

Impact of the warp

In the warped region of the disc, adjacent annuli of gas are misaligned with varying vertical height \(z\). This results in an (oscillating radial pressure gradient) as the gas traverses an orbit.
This oscillating radial pressure gradient can trigger a strong response in the radial velocity of the disc (Lodato & Pringle 2007), which heats up the disc. This is especially apparent in the early stages as seen by the large magnitudes of the velocity divergence.
As the warp dissipates, there is little variance in the pressure gradient. Thus, the magnitude of velocity divergence has greatly decreased as expected leading to less heating from PdV work.

The warp induces a strong response in the velocity flow of the disc, which heats it up.

Impact of the planet

The spiral wakes generated by the planet as it migrates are regions of relative overdensities with respect to the disc background.
The radially propagating spiral wakes can evolve into shocks.
The exchange of momentum and energy between the density wakes and the disc at the shocks influence the global properties of the disc, heating it up.

The spiral wakes generated by the planet heating up the disc.

Summary

Both a warp and a giant planet can shorten the gravitationally unstable phase of a massive disc by suppressing the spiral structures, yielding axisymmetric ring and gap structures.
In both scenarios, the disc is heated up pushing it into the gravitationally stable regime.
Our results show that young massive discs do not necessarily have to show large scale spiral structures, potentially resolving the descreprancy between theory and observations.