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Register a new userOn fragmentation of turbulent self-gravitating discs in the long cooling time regime
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Ken Rice
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It has recently been suggested that in the presence of driven turbulence discs may be much less stable against gravitational collapse than their non turbulent analogs, due to stochastic density fluctuations in turbulent flows. This mode of fragmentation would be especially important for gas giant planet formation. Here we argue, however, that stochastic density fluctuations due to turbulence do not enhance gravitational instability and disc fragmentation in the long cooling time limit appropriate for planet forming discs. These fluctuations evolve adiabatically and dissipate away by decompression faster than they could collapse. We investigate these issues numerically in 2D via shearing box simulations with driven turbulence and also in 3D with a model of instantaneously applied turbulent velocity kicks. In the former setting turbulent driving leads to additional disc heating that tends to make discs more, rather than less, stable to gravitational instability. In the latter setting, the formation of high density regions due to convergent velocity kicks is found to be quickly followed by decompression, as expected. We therefore conclude that driven turbulence does not promote disc fragmentation in protoplanetary discs and instead tends to make the discs more stable. We also argue that sustaining supersonic turbulence is very difficult in discs that cool slowly.
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We investigate how a protoplanetary discs susceptibility to gravitational instabilities and fragmentation depends on the mass of its host star. We use 1D disc models in conjunction with 3D SPH simulations to determine the critical disc-to-star mass ratios at which discs become unstable against fragmentation, finding that discs become increasingly prone to the effects of self-gravity as we increase the host star mass. The actual limit for stability is sensitive to the disc temperature, so if the disc is optically thin stellar irradiation can dramatically stabilise discs against gravitational instability. However, even when this is the case we find that discs around $2$M$_{odot}$ stars are prone to fragmentation, which will act to produce wide-orbit giant planets and brown dwarfs. The consequences of this work are two-fold: that low mass stars could in principle support high disc-to-star mass ratios, and that higher mass stars have discs that are more prone to fragmentation, which is qualitatively consistent with observations that favour high-mass wide-orbit planets around higher mass stars. We also find that the initial masses of these planets depends on the temperature in the disc at large radii, which itself depends on the level of stellar irradiation.
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