Gravitational instabilities

For a shock wave in a solid, the analogous picture is shown schematically in Fig. 2.6(a). Consider a compression wave on which there are two small compressional disturbances, one ahead of the other. The first wavelet moves with respect to its surroundings at the local sound speed of Aj, which depends on the pressure at that point. Since the medium through which it is propagating is moving with respect to stationary coordinates at a particle velocity Uj, the actual speed of the disturbance in the laboratory reference frame is Aj - -Ui- Similarly, the second disturbance advances at fl2 + 2- Thus the second wavelet overtakes the first, since both sound speed and particle velocity increase with pressure. Just as a shallow water wave steepens, so does the shock. Unlike the surf, a shock wave is not subject to gravitational instabilities, so there is no way for it to overturn. 

Hysteresis Feature in ( >E,E) Plane Following Lin and Pringle (1987), we now consider this hybrid prescription. Firstly, according to Toomre (1964), The basic principles of the self-gravitational instability in a thin rotating disk... 

We consider the criterion for the validity of giving occasion to the recurrence outburst of FU Orionis in our model. As shown in Figure, there are three condition which must be satisfied for our model. (A) the viscosity due to the prescription of self-gravitational instabilities is higher than that of standard ot-disk prescription, v [Pg.241]

The sun, the planets and satellites like the moon were formed 4.5 Gyr ago as a consequence of gravitational instability in a part of a dense interstellar cloud. This particular dense insterstellar cloud no longer exists for obvious reasons, but other dense interstellar clouds can still be observed in our galaxy. Some of these dense... 

Gravitational instability can occur in a cloud characterised by high density and low temperature (Jean s criterion). More precisely-, the mass of the cloud must be of the order of 20 M0 (where M0 is the solar mass) if the density (expressed as the number of dihydrogen molecules per cubic centimeter) is around 103 and the temperature around 10 K. Such a density is precisely what is observed in so-called dense clouds. These dense clouds are also regions of space where a lot of complex molecules are detected by spectroscopy, and where dust particles are observed. Readers interested in interstellar chemistry will find an excellent review of the subject in the recent book by Duley and Williams 13). 

It is possible for instance to test the mode couplings as the gravitational instabilities develop. The amount of non-Gaussianities embedded in cosmic shear surveys then betrays the details of the gravitational instability scenario, allowing for instance the possibility of measuring the mass density of the universe in a totally independent way. That would contribute in the consolidation of the current concordance model of cosmology. 

Planet formation unfolds differently beyond the snowline, where water condensation enhances the surface density. Here massive cores (> 5-10 MEarth) may form rapid enough to accrete directly and retain nebular gas. These massive cores, if formed prior to the dispersal of the gas disk, rapidly reach Jupiter masses, forming giant planets. An alternative mechanism that may be responsible for the formation of some giant planets is gravitational instability in a massive, marginally unstable disk (e.g. Boss 2007 Mayer etal. 2007). 

Figure 3.1 Hubble Space Telescope image of AB Aurigae. The central star is approximately 2.8 M and the disk is approximately 400 AU in diameter (Corder et al. 2005). Spiral structure (density contrasts) can be seen in the outer regions of the disk where the disk is expected to be most susceptible to gravitational instabilities.

While the viscous model for the evolution of protoplanetary disks has had some success in matching some of the general properties of protoplanetary disks, such as the observed mass accretion rates and effective temperatures, the exact source of the viscosity remains the subject of ongoing studies. Currently, the most popular candidates for driving the mass transport in protoplanetary disks are the magneto-rotational instability (MRI) and gravitational instability. A third candidate, shear instability, has also been proposed based on laboratory experiments of rotating fluids (Richard Zahn 1999), but questions remain as to whether these results can be extended to the scale of protoplanetary disks. 

Intrinsic turbulence in the disk poses severe problems for planetesimal formation by either pairwise sticking or gravitational instability. This has led to the development of a third class of model that embraces turbulence as a necessary ingredient for planetesimal formation. 

Since the value of Mn is significantly lower than required for gravitational instability to set in (Toomre, 1964 Goldreich and Lynden-Bell, 1965 Goldreich and Ward, 1973), the nebula is found to be gravitationally stable. 

Boss A. P. (1997) Giant planet formation by gravitational instability. Science 216, 1836-1839. 

Ward (2001) has suggested that the onset of gravitational instability depends sensitively on disk parameters that are poorly constrained at present. There appears to be a critical solid-to-gas surface density ratio necessary for the onset of gravitational instability, which requires enhancement of sohds by a factor of 2-10 times above that expected for material of solar composition (Youdin and Shu, 2002). In a nonturbulent disk, particles would have migrated at different rates in different regions, leading to a pUeup of solid material at certain points (Youdin and Shu, 2002). In addition, particles are likely... 

Cameron (1985) estimated that temperatures in the solar nebula could have reached 2,500-3,500 K at Mercury s distance from the Sun. Recent models of the solar nebula do not predict such high temperatures at 0.4 AU, but it is an interesting idea worth considering. If Mercury had formed very early, perhaps by gravitational instabilities in the gas phase, then its composition... 

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