Gravitational Instabilities in Circumstellar Disks

Abstract

Star and planet formation are the complex outcomes of gravitational collapse and angular momentum transport mediated by protostellar and protoplanetary disks. In this review we focus on the role of gravitational instability in this process. We begin with a brief overview of the observational evidence for massive disks that might be subject to gravitational instability, and then highlight the diverse ways in which the instability manifests itself in protostellar and protoplanetary disks: the generation of spiral arms, small scale turbulence-like density fluctuations, and fragmentation of the disk itself. We present the analytic theory that describes the linear growth phase of the instability, supplemented with a survey of numerical simulations that aim to capture the non-linear evolution. We emphasize the role of thermodynamics and large scale infall in controlling the outcome of the instability. Despite apparent controversies in the literature, we show a remarkable level of agreement between analytic predictions and numerical results. In the next part of our review, we focus on the astrophysical consequences of the instability. We show that the disks most likely to be gravitationally unstable are young and relatively massive compared to their host star, M d /M * ≥ 0.1. They will develop quasi-stable spiral arms that process infall from the background cloud. While instability is less likely at later times, once infall becomes less important, the manifestations of the instability are more varied. In this regime, the disk thermodynamics, often regulated by stellar irradiation, dictates the development and evolution of the instability. In some cases the instability may lead to fragmentation into bound companions. These companions are more likely to be brown dwarfs or stars than planetary mass objects. Finally, we highlight open questions related to (1) the development of a turbulent cascade in thin disks, and (2) the role of mode-mode coupling in setting the maximum angular momentum transport rate in thick disks. We dedicate this article to the memory of Francesco Palla, who has been a source of inspiration for star formation and disk studies throughout the years. Through his support and encouragement of young scientists, his contributions live on.

Spiral Arms in Disks: Planets or Gravitational Instability?

“…These studies have revealed spiral arms in a growing number of disks (Figure 1), both prominent near-symmetric twoarm spirals (e.g., Grady et al 2013;Benisty et al 2015) and more flocculent multiarm spirals on smaller scales and at lower contrast (e.g., Fukagawa et al 2004;Hashimoto et al 2011). Spiral arms can be produced by either gravitational instability (e.g., Rice et al 2003;Lodato & Rice 2004;Stamatellos & Whitworth 2008;Kratter et al 2010;Kratter & Lodato 2016) or the presence of massive companions (gas giant to stellar masses; e.g., Kley & Nelson 2012;Zhu et al 2015;Muñoz & Lai 2016).…”

The Complex Morphology of the Young Disk MWC 758: Spirals and Dust Clumps around a Large Cavity

“…According to our models, the disk, with a mass of about 1.3×10 −3 M , is not massive enough to be gravitationally unstable (Kratter & Lodato 2016). One explanation for such a complex structure is the presence of planet(s) which can interact with the protoplanetary disk and create features (annuli, spirals or vortices) which can be more easily detected than the planets themselves (Kley & Nelson 2012;Baruteau et al 2014).…”

“…Importantly, in the case of a cavity + a horseshoe, the horseshoe might not be a vortex but might be induced naturally if the arXiv:1712.08845v3 [astro-ph.EP] 12 Feb 2018 disc surrounds a binary system (Ragusa et al 2017). Finally, spirals might also be produced by the development of gravitational instabilities (Kratter & Lodato 2016), by an external high-mass perturber undergoing a flyby (Quillen et al 2005) or induced dynamically as a consequence of a different irradiation from the star due to a warp in the inner disc (Montesinos et al 2016).…”

Slowly-growing gap-opening planets trigger weaker vortices

“…Discs with Q < 2 are subject to gravitational instabilities that generate effective α > 0.01 or ν > 10 −4 r 2 p p (Kratter & Lodato 2016). Even for a factor of ∼5-10 decrease in F crit (increase in Q), disc self-gravity may suppress large-scale vortex formation via the RWI (Lin & Papaloizou 2011).…”