Conclusions

6.1. The big questions revisited Returning to the big questions presented at the beginning of this review, we can see that some of them are addressed head on by recent simulations, and the answers to others can be inferred.

6.1.1. Do gravitational instabilities produce gas giant planets?

Given the formation of dense gas structures by GIs and the tendency of solid particles to concentrate into these features, it seems likely that GIs play a significant role in planet building.

Do they form planets directly on a dynamic time scale? Probably not. The answer to this question is controversial at several levels. While all current researchers agree that, with rapid enough cooling, growing GI spiral waves in disks will fragment into dense clumps, there are disagreements about whether or not such clumps become bound pro-toplanets (§2.3). More seriously, there are sharp disagreements about whether radiative or convective cooling in real disks is ever rapid enough for fragmentation to occur in the first place (§4.2). Recent results (§4.3) by my own hydro group suggest that environmental factors, especially irradiation, can have a damping effect on GIs and that GI behavior may depend more on metallicity and grain size than indicated by work published to date. Although it is premature to rule out direct gas giant formation by GIs on a dynamic time scale, I think the weight of evidence right now tilts away from that conclusion. Realize, however, that we are far from probing the full complexity of this problem. There are regimes yet unexplored, such as behaviors at major opacity boundaries (Johnson & Gammie 2003), equation of state effects, and fully coupled evolution of solids and gas.

Do they accelerate core accretion, instead? Probably. The formation of long-lived rings in some GI simulations, especially at the boundaries between GI active and inactive regions (§3.1 and §5.4), and the rapidity with which meter-sized solids can migrate to the centers of these and other GI structures (§5.2) opens the possibility that, instead of being an alternative gas giant formation mechanism to core accretion plus gas capture, GIs provide the environment in which core accretion can be accelerated to very short times without rapid loss of growing cores into the star due to type I migration. The calculations by Boss (2005), while presented as support for direct formation by disk instability, also show that massive bodies can maintain relatively stable orbits against the background of a GI-active disk. Rings, however, probably provide the most uniform and nurturing milieu for accelerated core accretion. It is important for other researchers to confirm or refute their occurrence, understand the mechanisms that form and sustain them, and determine their ultimate fate.

6.1.2. How fast can GIs transport mass in a disk?

Simulations of GIs in Solar System-sized disks generally have inner regions that are not directly computed, and so accretion induced by GIs cannot be followed all the way down to the star. However, global 3D calculations show that gravitational torques produce mass transport, with inflow predominating over the inner and middle disk regions. Angular momentum removed from the inner disk is transported to the outer disk, which expands. The mass accretion rates in the inflow regions are typically reported to be in the range

10-7 to 10-5 M0 yr-1 (Nelson et al. 2000; Pickett et al. 2003; Boss 2002b; Lodato & Rice 2004; Mejia et al. 2005a,b), which would be healthy mass inflow rates for a young circumstellar gas disk. With a disk mass of 0.1 Mq, these rates lead to disk lifetimes between 104 to 106 years. In the longest simulations to date, GIs appear to settle into an asymptotic behavior where mass accretion is sustained at rates in the lower end of the range for at least many thousands of years and probably much longer (§3.1). The inflow process is variable on a dynamic time scale, with large fluctuations about the average.

Inflow values near 10-5 Mq yr-1 are attained over shorter time scales as GIs initiate in simulations with a global tcooi (§3.1 and §4.3) or during the eruptions of a dead zone (§5.3). Lodato & Rice (2005) find peaks as high as 10-4 Mq yr-1 in the outer disk for Md = Ms. Boss (2002b) even reports a mass inflow rate of 10-3 Mq yr-1. Further modeling of inner disk regions and of dead zone behaviors are needed to determine whether peak accretion rates onto the star are high enough to fuel an FU Orionis outburst.

Is this process local or global? If GIs behave in a local manner, where mass and energy transport can be described accurately using only local disk properties, then they are probably susceptible to an a-type prescription, which is desirable for evolving disks with GIs over long time intervals (§3.2). Simulations suggest that "locality" depends on several factors. First of all, if disks are extremely massive (Md/Ms ^ 0.25) and thick (scale height > 0.1r), then GIs will behave globally in some respects regardless of other constraints. For less massive disks with moderate to small scale heights, the "locality" of GIs depends on whether the cooling time tcool behaves locally (i.e., tcoolQ « constant) or globally (i.e., tcool « constant; §3.3). For local tcools, equation (3.1) appears to be accurate; for global cases, the mass inflow greatly exceeds what is expected from (3.1). Simulations of disks with radiative cooling (§4.3) show that real disks are probably better described as having global tcools. Gravitational stresses dominate in all 3D global simulations, but are matched by Reynolds stresses in thin-disk local simulations. When GIs are global, transport is mediated by a few low-order, usually two-armed, modes. A key point that remains to be resolved is whether nonlocal energy transport by waves occurs in global tcool calculations.

Does it produce persistent structures, like dense arms and rings? Yes. Simulations integrated for tens of orbits indicate relaxation of disks into an asymptotic behavior with persistent turbulent spiral wave structure. In simulations where GIs behave globally, long-lived dense rings may also grow near boundaries between GI-active and inactive parts of the disk.

6.1.3. When do GIs occur in disks?

GIs may occur during the protostellar core collapse phase as a massive disk first forms (e.g., Laughlin & Bodenheimer 1994) and at later phases of disk evolution due to mass accumulation in a dead zone at a few AU from the star (e.g., Gammie 1996; Armitage et al. 2001) or in outer disk regions due to a fall off in the value of Q with increasing r (e.g., D'Alessio et al. 1999).

Do they occur in the early embedded phase? It depends. Although it is commonly assumed that this is the prime time to have vigorous GIs in protoplanetary disks, the results discussed in Section 4.3.1 sound a cautionary note. Irradiation, if sufficiently strong, may suppress GIs by preventing the disk from reaching unstable values of Q. The same heating also tends to thicken the disk and result in greater stability than given by the usual Q-criterion (see Mayer et al. 2004). The message is that one has to consider the detailed structure of a disk and the intensity of its radiation environment in order to properly assess its stability and the strength of any resultant GIs.

Do they occur in dead zones ? Probably. A thorough discussion of ionization conditions in protoplanetary disks goes beyond the scope of this review, but dead zones (§5.3) of low ionization, where MRIs cannot operate, are likely to exist and may lead to episodic bursting GI behavior (e.g., Armitage et al. 2001). Further modeling of this situation in full 3D with radiative hydrodynamics could reveal connections with FU Ori outbursts, thermal processing of solids, and planet formation (Boss & Durisen 2005a). To understand this fully, magnetic fields (Fromang et al. 2004) have to be included.

6.1.4. How do GIs affect solids and contaminants?

This could be the most exciting area of current development in the study of GIs in disks.

Do they mix solids and contaminants? Yes. Studies by Boss (2004b) and Boley et al. (2005; SS5.1 and 5.2) show that motions associated with the turbulent spiral structure of a GI-active disk can mix contaminants and entrained dust grains both vertically and horizontally over tenths of AU scales on a dynamic time scale. This mixing tends to correlate with the dense spiral wave structure of the disk.

Do they concentrate solids into coherent structures? Yes. Haghighipour and Boss (2003a,b) and Rice et al. (2004) demonstrate extremely short timescales for meter-sized solids to be swept into both relatively static ring-like structures and dynamic GI spiral waves. It is very likely then that planetesimal formation and perhaps core growth can be accelerated by GIs.

Do they cause thermal processing of solids? Yes. Boss & Durisen (2005a) and Boley et al. (2005) show that the dense clumps and spirals in GI-active disks can produce strong enough shocks to process solid materials.

6.2. Parting thoughts

The study of gravitational instabilities in disks and of their relationships to planet formation and disk evolution is on the verge of becoming a mature research area, where a full array of relevant processes are treated by a variety of sophisticated methods and where consensus builds on a broad foundation of key results and principles. Neither criterion for maturity currently applies, but pathways are emerging along which we can make progress toward this goal. Fundamental disagreements remain about cooling times for disks and longevity of fragments. These will hopefully be resolved through the participation of more research groups and through collaborations by existing groups for a common purpose, such as the one now being led by Lucio Mayer on fragmentation (2005, private communication). At the same time, there are a few consensus results in the bag, such as the Gammie fragmentation criterion and the central importance of thermal physics to GI behavior.

At the moment, I find it most exciting to have some tantalizing initial tastes of the de-liciously complex interplay that must occur between solids and gas through both opacity effects and dynamics. This could eventually engender a significant paradigm shift in our view of planet formation towards scenarios involving both GIs and core accretion plus gas capture. Similar appetizers are offered by efforts to blend the two most important disk transport mechanisms, GIs and magnetorotational instabilities, into a coherent global picture. I invite more researchers to break out their formal wear (or software) and join the coming banquet.

I would like to thank P. J. Armitage, A. C. Boley, A. P. Boss, K. Cai, D. N. C. Lin, J. J. Lissauer, G. Lodato, L. Mayer, A. C. Mejia, S. Michael, M. K. Pickett, J. E. Pringle, and W. K. Rice for useful recent discussions or email and, in some cases, for specific help with this manuscript. Extra special thanks are due to A. C. Boley for dealing with troublesome graphics format conversions. I was supported during this work by NASA Origins of Solar Systems grant NAG5-11964.

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