论文标题
在分子云集合的背景下，自我磨碎的多质湍流的密度曲线
Density profile of a self-gravitating polytropic turbulent fluid in the context of ensembles of molecular clouds
论文作者
论文摘要
我们在自我磨碎的多粒子球体对称湍流中获得了密度曲线的方程式，并具有状态方程$ p _ {\ rm as Gas} \ proptoρ^γ$。这是在Donkov等人介绍的单个抽象对象表示的分子云集合的框架上完成的。 （2017）。所采用的物理图片适合描述靠近云核的条件，其中状态方程式从等温度（在外部云层中）以$γ= 1 $变化为“硬polytrope”的一个带有指数$γ> 1 $的“硬polytrope”。根据稳态的假设，随着吸积物的流经所有空间尺度，我们表明每单位质量的总能量相对于流体流量是不变的。所获得的方程重现了所提出的模型的Bernoulli方程，并描述了流体元件的动力学，热和重力能量的平衡。我们还提出了一种以幂律形式获得近似溶液的方法，该方法导致四个溶液对应于流体元素的不同密度曲线，多态面指数和能量平衡方程。其中之一是，具有坡度$ -3 $的密度曲线和多变量指数$γ= 4/3 $，与观测值和数值作品相匹配，尤其是导致密度分布功能的第二个幂律尾部，以密集，自我覆盖的云区域。
We obtain an equation for the density profile in a self-gravitating polytropic spherically symmetric turbulent fluid with an equation of state $p_{\rm gas}\propto ρ^Γ$. This is done in the framework of ensembles of molecular clouds represented by single abstract objects as introduced by Donkov et al. (2017). The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state changes from isothermal (in the outer cloud layers) with $Γ=1$ to one of `hard polytrope' with exponent $Γ>1$. On the assumption of steady state, as the accreting matter passes through all spatial scales, we show that the total energy per unit mass is an invariant with respect to the fluid flow. The obtained equation reproduces the Bernoulli equation for the proposed model and describes the balance of the kinetic, thermal and gravitational energy of a fluid element. We propose as well a method to obtain approximate solutions in a power-law form which results in four solutions corresponding to different density profiles, polytropic exponents and energy balance equations for a fluid element. One of them, a density profile with slope $-3$ and polytropic exponent $Γ=4/3$, matches with observations and numerical works and, in particular, leads to a second power-law tail of the density distribution function in dense, self-gravitating cloud regions.
