Structure analysis of interstellar clouds - I. Improving the Delta-variance method
Structure analysis of interstellar clouds - I. Improving the Delta-variance method
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星际云的结构分析——一、改进Delta-variance方法
DOI：
10.1051/0004-6361:20079106
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发表时间：
2008
影响因子：
6.5
通讯作者：
J. Stutzki
中科院分区：
文献类型：
--
作者：
V. Ossenkopf;M. Krips;M. Krips;J. Stutzki
上下文。Δ-Variance分析是一种基于小波的天文地图结构统计尺度测量方法，已被证明是刻画星际湍流功率谱的一种有效而准确的方法。它已被应用于观测的分子云图和由湍流云模式生成的相应的模拟图。然而，目前使用的实现有几个缺点。它没有考虑地图中不同点的地图值的不同不确定性程度，其通过空间坐标卷积的计算非常耗时，并且小波的选择具有一定的随意性，并且没有为跟踪的比例尺提供精确值。目标。针对二维数据提出了一种改进的Δ-Variance算法并对其进行了测试，该算法适用于具有可变误差条的地图，并且可以在傅立叶空间中快速计算。我们对Δ-方差谱的空间分辨率进行了标定。方法：研究方法。新的Δ-Variance算法是基于在傅立叶空间对数据进行适当的滤波。它使用一个补充重要性函数，每个数据点都通过该函数进行加权。这使得我们能够将变量噪声的影响与地图中实际的小尺度结构区分开来，这有助于处理非周期和/或不规则有界地图的边界问题。将该方法应用于含有可变噪声的人工地形图，结果表明，该方法可以大大扩展动态范围，从而可靠地确定光谱指数。我们尝试了几个小波，并使用已知结构尺寸的人工地图测试了它们的空间敏感度。在傅立叶空间中执行卷积可以大大加快分析速度。结果。结果表明，不同的小波在检测特征结构和谱指数方面表现出不同的优势，即地图结构的不同方面。作为对最优Δ-Variance滤波器的一种合理的普遍折衷，我们提出了核心直径与环空直径之比为1.5时的墨西哥帽滤波。当主要用于测量光谱折射率时，直径比约为2.3的法式帽子滤光片也是合适的。在论文II中，我们通过将新方法应用于不同的天文数据来发挥新方法的优势。
Context. The Δ-variance analysis, introduced as a wavelet-based measure for the statistical scaling of structures in astronomical maps, has proven to be an efficient and accurate method of characterising the power spectrum of interstellar turbulence. It has been applied to observed molecular cloud maps and corresponding simulated maps generated from turbulent cloud models. The implementation presently in use, however, has several shortcomings. It does not take into account the different degree of uncertainty of map values for different points in the map, its computation by convolution in spatial coordinates is very time-consuming, and the selection of the wavelet is somewhat arbitrary and does not provide an exact value for the scales traced. Aims. We propose and test an improved Δ-variance algorithm for two-dimensional data sets, which is applicable to maps with variable error bars and which can be quickly computed in Fourier space. We calibrate the spatial resolution of the Δ-variance spectra. Methods. The new Δ-variance algorithm is based on an appropriate filtering of the data in Fourier space. It uses a supplementary significance function by which each data point is weighted. This allows us to distinguish the influence of variable noise from the actual small-scale structure in the maps and it helps for dealing with the boundary problem in non-periodic and/or irregularly bounded maps. Applying the method to artificial maps with variable noise shows that we can extend the dynamic range for a reliable determination of the spectral index considerably. We try several wavelets and test their spatial sensitivity using artificial maps with well known structure sizes. Performing the convolution in Fourier space provides a major speed-up of the analysis. Results. It turns out that different wavelets show different strengths with respect to detecting characteristic structures and spectral indices, i.e. different aspects of map structures. As a reasonable universal compromise for the optimum Δ-variance filter, we propose the Mexican-hat filter with a ratio between the diameters of the core and the annulus of 1.5. When the main focus lies on measuring the spectral index, the French-hat filter with a diameter ratio of about 2.3 is also suitable. In Paper II we exploit the strength of the new method by applying it to different astronomical data.