Four-parameter fits to the initial mass function using stable distributions Four-parameter fits to the IMF
Four-parameter fits to the initial mass function using stable distributions Four-parameter fits to the IMF
复制标题
使用稳定分布对初始质量函数进行四参数拟合 对 IMF 进行四参数拟合
DOI：
10.1111/j.1365-2966.2012.20795.x
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发表时间：
2012
影响因子：
4.8
通讯作者：
Cartwright A
中科院分区：
文献类型：
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作者：
Cartwright A
我们建议使用统计上建立良好的稳定分布的帕累托-利维族来表征恒星和前恒星群的质量分布。这个分布族，包括高斯分布，利维分布和柯西分布，可以证明服从中心极限定理。这使它们成为由许多独立变量组合而成的人口的统计上合理的模型。将公开可用的软件应用于原始数据集，我们发现与数据匹配的概率分布达到95%的置信度。这种自动过程比一般的决定箱大小和阈值的过程更简单、更快和更客观，并且只需要四个参数就可以定义最佳拟合的稳定分布。由于只有一个函数来描述整个质量范围，所以没有必要推测不同子范围之间的“阈值”的物理意义。通过稳定分布拟合，我们发现蛇夫座、天鹰座和猎户座的核心质量函数的峰型峰和峰宽存在显著差异，峰宽随峰质量的增大而增大。大质量幂律的斜率是难以区分的。
We propose the use of the statistically well-founded Pareto–Levy family of stable distributions for the characterization of the mass distributions of stellar and pre-stellar populations. This family of distributions, which includes the Gaussian, Levy and Cauchy distributions, can be shown to obey the central limit theorem. This makes them statistically justifiable models for populations resulting from the combination of many independent variables. Applying publicly available software to raw data sets we find probability distributions which fit the data to 95 per cent confidence levels. This automatic process is much simpler, faster and more objective than the normal procedure of deciding upon bin sizes and thresholds, and only four parameters are required to define the best-fitting stable distribution. As there is only one function to describe the whole mass range, there is no need to speculate upon the physical significance of ‘thresholds’ between different subranges. Using stable distribution fits we demonstrate that the modal peaks and widths of the peaks for core mass functions from Ophiuchus, Aquila and Orion are measurably different, width increasing with peak mass. The slopes of the high-mass power laws are indistinguishable.