The disk instability model (Boss 1997; Cameron 1978; Kuiper 1951) entails the formation of planets from the breakup of a protoplanetary disk due to gravitational instability forming self gravitating clumps of gas, which eventually evolve into planets. The thermodynamic state of the disk is a critical part of the model. For a disk to form, self-gravity has to dominate the thermal pressure and sheer inside the disk. The threshold for axisymmetric density perturbations to occur in a thin gaseous disk is given by the Toomre criterion (Safronov 1960; Toomre 1964),

$Q = \frac{c_s \kappa}{\pi G \sigma_g}$

where $c_s$ is the speed of sound, $\kappa$ the epicyclic frequency and $\sigma_g$ the gas surface density. Disk fragmentation will only occur if $Q\lesssim 1$. As such, disks with a large mass (high gravity) at low temperatures ($c_s = \sqrt{kT/m} \sim \sqrt{P/\rho}$) and high densities ($\sigma_g$) are more likely to form gravitational instabilities. Disk instability is however not enough for planets to form as a result of the fragmentation. The disk must also be able to cool efficiently on a timescale comparable to the local disk orbital period. ($\tau_{\mathrm{cool}}/\tau_{\mathrm{rot}}$ less than $f_{\mathrm{frag}}$ where $\tau_{\mathrm{cool}}$ and $\tau_{\mathrm{rot}}$ are the cooling and rotation time scales of the disc and $f_{\mathrm{frag}}$ the ratio between them). Disk fragmentation is expected to more readily occur further out in the protoplanetary disk (several tens of AU) where the radiative cooling rates are higher and $Q$ lower (Cai et al. 2006; Rafikov 2007). As such, one would expect a large number of planets on wide orbits if disk instability is the dominant formation mechanism. Janson et al 2012 found that <10% of FGKM-type stars form and retain companions through disk instability at 99% confidence, independent of outer disk radii (within the regime 5-500AU) taking disk migration into account. Only companions with masses [latex size=2]<100~M_{\mathrm{Jup}}[/latex] were considered. Despite this result, some observations are best explained by formation via disk instability. Examples are the four giant planets (or BDs using the formation based definition of BDs) around HR~9799 with semi-major axis of 14.5, 24, 38, 64 AU (Marois et al. 2008, 2010) and Fomalhaut b (Kalas et al. 2008) at 119~AU. Although core accretion is the dominant planet formation model, the disk instability model is still a viable formation theory for gas giants with a large mass on wide orbits (Dodson-Robinson et al. 2009; Boley 2009).

on Formation via disk instability.
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[…] According to exoplanetary astronomer Paul Wilson, if disk instability dominates the formation of planets, it should produce a wide number of worlds […]

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[…] to exoplanetary astronomer Paul Wilson, if disk instability dominates the formation of planets, it should produce a wide number of worlds […]

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[…] to exoplanetary astronomer Paul Wilson , if disk instability dominates the formation of planets, it should produce a wide number of worlds […]

4. […] to exoplanetary astronomer Paul Wilson , if disk instability dominates the formation of planets, it should produce a wide number of worlds […]

5. […] to exoplanetary astronomer Paul Wilson, if disk instability dominates the formation of planets, it should produce a wide number of worlds […]

6. |

[…] According to exoplanetary astronomer Paul Wilson, if disk instability dominates the formation of planets, it should produce a wide number of worlds […]

7. |

[…] to exoplanetary astronomer Paul Wilson , if disk instability dominates the formation of planets, it should produce a wide number of worlds […]