"These conjectures on the formation of the stars and the solar system I present with all the distrust which everything which is not a result of observations or of calculations ought to inspire." —Pierre Simon de Laplace, 1796.

1.1. Focus

Although we now have sufficiently conclusive observational evidence that the Kant-Laplace Nebular Hypothesis for the origin of planetary systems is correct in broad outline, and although we have much greater theoretical capacity to analyze the relevant physical processes than was available to Kant and Laplace, we are still far from achieving a consensus about how planets form from protoplanetary disks. Since Boss (1997) revived the Kuiper (1951) and Cameron (1978) idea that gas giant planets might form all at once through disk instability triggered by self-gravity, the planetary science and astrophysics communities have been embroiled in a stimulating debate about the relative merits of the disk instability mechanism and the "standard" core accretion plus gas capture picture of gas giant planet formation (Hubickyj, this volume). Much of the debate has hinged on how fast gas giant planet formation must happen due to finite gas disk lifetimes versus how fast core accretion can proceed. In this review, I will take a different tack. Whether or not gravitational instabilities (GIs) are involved in planet building, they are likely to occur in disks formed around stars by the collapse of rotating interstellar clouds (e.g., Laughlin & Bodenheimer 1994; Yorke & Bodenheimer 1999). This chapter concentrates on GIs as a physical process and attempts to bring the reader up to date on what is known about how disks behave when they become unstable (for earlier reviews, see Durisen 2001; Durisen et al. 2003). Although GIs in particulate disks and subdisks are another topic of contemporary interest (Youdin & Shu 2002), I will discuss only gas dynamical GIs.

1.2. The big questions and an outline There are several important questions and attendant sub-questions that will be addressed in this review:

• Do gravitational instabilities produce gas giant planets?

o Do they form planets directly on a dynamic time scale? o Or do they accelerate core accretion, instead?

• How fast can GIs transport mass in a disk? o Is this process local or global?

o Does it produce persistent structures, like dense arms and rings?

o Do they occur in the early embedded phase?

o Do they occur in dead zones, where turbulent transport by other mechanisms breaks down?

• How do GIs affect solids? o Do they mix solids?

o Do they concentrate solids into coherent structures? o Do they cause thermal processing of solids?

I begin in Section 2 by describing the general characteristics of GIs that most, if not all, researchers currently agree upon. What emerges is unanimity about the central importance of radiative cooling for understanding the strength and outcome of GIs. As a result, the next two sections present in detail recent results from work with simple idealized cooling laws (§3) and realistic radiative cooling (§4). Additional physical processes, such as hydraulic jumps, gas-solid interactions, and the effect on GIs of other transport mechanisms, are discussed in Section 5.

Section 6 returns to the big questions posed above and presents some tentative answers.

Some of us, like myself, are visual thinkers, so I have sprinkled this review liberally with images. Although snapshots are helpful, movies and animations are sometimes even more informative when trying to grasp 3D flows. A number of relevant animations based on simulations by my own hydrodynamics group are available under the "Movie" tab at

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