It has recently been shown that turbulence in the interstellar medium (ISM) can significantly accelerate the growth of dust grains by accretion of molecules, but the turbulent gas-density distribution also plays a crucial role in shaping the grain-size distribution. The growth velocity, i.e., the rate of change of the mean grain radius, is proportional to the local gas density if the growth species (molecules) are well-mixed in the gas. As a consequence, grain growth happens at vastly different rates in different locations, since the gas-density distribution of the ISM shows a considerable variance. Here, it is shown that grain-size distribution (GSD) rapidly becomes a reflection of the gas-density distribution, irrespective of the shape of the initial GSD. This result is obtained by modelling ISM turbulence as a Markov process, which in the special case of an Ornstein-Uhlenbeck process leads to a lognormal gas-density distribution, consistent with numerical simulations of isothermal compressible turbulence. This yields an approximately lognormal GSD; the sizes of dust grains in cold ISM clouds may thus not follow the commonly adopted power-law GSD with index -3.5, but corroborates the use of a log-nomral GSD for large grains, suggested by several studies. It is also concluded that the very wide range of gas densities obtained in the high Mach-number turbulence of molecular clouds must allow formation of a tail of very large grains reaching radii of several microns.

中文翻译：

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湍流粉尘生长的粒度分布

最近的研究表明，星际介质 (ISM) 中的湍流可以通过分子的吸积显着加速尘埃颗粒的生长，但湍流气体密度分布在塑造颗粒尺寸分布方面也起着至关重要的作用。如果生长物质（分子）在气体中充分混合，则生长速度，即平均颗粒半径的变化率，与局部气体密度成正比。因此，由于 ISM 的气体密度分布显示出相当大的差异，因此不同位置的晶粒生长速度大不相同。这里表明，无论初始 GSD 的形状如何，晶粒尺寸分布 (GSD) 都会迅速成为气体密度分布的反映。该结果是通过将 ISM 湍流建模为马尔可夫过程而获得的，这在 Ornstein-Uhlenbeck 过程的特殊情况下导致对数正态气体密度分布，与等温可压缩湍流的数值模拟一致。这产生了近似对数正态 GSD；因此，冷 ISM 云中尘埃颗粒的大小可能不遵循指数为 -3.5 的普遍采用的幂律 GSD，但证实了对大颗粒使用对数规范 GSD，这是几项研究的建议。还得出结论，在分子云的高马赫数湍流中获得的非常广泛的气体密度必须允许形成半径达到几微米的非常大的颗粒尾部。因此，冷 ISM 云中尘埃颗粒的大小可能不遵循指数为 -3.5 的普遍采用的幂律 GSD，但证实了对大颗粒使用对数规范 GSD，这是几项研究的建议。还得出结论，在分子云的高马赫数湍流中获得的非常广泛的气体密度必须允许形成半径达到几微米的非常大的颗粒尾部。因此，冷 ISM 云中尘埃颗粒的大小可能不遵循指数为 -3.5 的普遍采用的幂律 GSD，但证实了对大颗粒使用对数规范 GSD，这是几项研究的建议。还得出结论，在分子云的高马赫数湍流中获得的非常广泛的气体密度必须允许形成半径达到几微米的非常大的颗粒尾部。