湍流行星从来都不是稳定的：碎裂和Turbulence促进的行星形成
Turbulent Disks are Never Stable: Fragmentation and Turbulence-Promoted Planet Formation
摘要：
在我们对盘的理解中，一个基本的假设是，当托姆雷Q>>1时，盘是稳定的，不会分裂成自引力物体（因此不能通过直接坍缩形成行星）。但是如果圆盘是湍流的，这就忽略了随机密度波动的频谱，这种波动可以产生罕见的高密度质量集中。在这里，我们使用最近开发的分析框架来预测这些波动的统计数据，即在湍流开普勒盘中形成的碎片的碎片和质谱的速率。湍流磁盘从来没有完全稳定的：我们计算（总是有限的）概率形成自引力结构通过随机湍流密度波动在这样的磁盘。马赫数~0.1以上的适度亚音速湍流，即使Q>>1且冷却缓慢（t_cool>>t_orbit），也能在~Myr的时间尺度上产生一些随机碎裂或“直接坍缩”事件。在跨音速湍流中，这一数值可扩展到Q~100。我们推导出抑制这种事件所需的真实Q准则，它与马赫数成指数关系。我们指定由MRI，对流，或螺旋波驱动的湍流，并推导出等效标准的Q和冷却时间。可能需要>~50*t_dyn的冷却时间以完全抑制碎裂。这些重力湍流事件产生的质量谱峰值接近~M_disk*（Q*M_disk/M_star）^[2]（岩石到巨行星质量，随着与恒星的距离增加）。我们将其应用于原行星盘模型，并表明，即使是最小质量的太阳星云可以经历随机崩溃事件，提供了一个动荡的来源。
英文摘要：
A fundamental assumption in our understanding of disks is that when the Toomre Q>>1, the disk is stable against fragmentation into self-gravitating objects (and so cannot form planets via direct collapse). But if disks are turbulent, this neglects a spectrum of stochastic density fluctuations that can produce rare, high-density mass concentrations. Here, we use a recently-developed analytic framework to predict the statistics of these fluctuations, i.e. the rate of fragmentation and mass spectrum of fragments formed in a turbulent Keplerian disk. Turbulent disks are never completely stable: we calculate the (always finite) probability of forming self-gravitating structures via stochastic turbulent density fluctuations in such disks. Modest sub-sonic turbulence above Mach number ~0.1 can produce a few stochastic fragmentation or 'direct collapse' events over ~Myr timescales, even if Q>>1 and cooling is slow (t_cool>>t_orbit). In trans-sonic turbulence this extends to Q~100. We derive the true Q-criterion needed to suppress such events, which scales exponentially with Mach number. We specify to turbulence driven by MRI, convection, or spiral waves, and derive equivalent criteria in terms of Q and the cooling time. Cooling times >~50*t_dyn may be required to completely suppress fragmentation. These gravoturbulent events produce mass spectra peaked near ~M_disk*(Q*M_disk/M_star)^2 (rocky-to-giant planet masses, increasing with distance from the star). We apply this to protoplanetary disk models and show that even minimum mass solar nebulae could experience stochastic collapse events, provided a source of turbulence.
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