Scaling and correlation analysis of galactic images
Scaling and correlation analysis of galactic images
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星系图像的缩放和相关分析
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
H Germany
中科院分区：
文献类型：
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作者：
P. Frick;R. Beck;E. M. Berkhuijsen;I. O. F. Mechanics;Perm;Russia.;M. F. Radioastronomie;Bonn;H Germany
讨论了不同尺度和自相关特性及其在天文图象中的应用：结构函数、自相关函数、傅里叶谱和小波谱。数学工具的选择对图像的尺度分析至关重要。例如，结构函数不能解析与主导大尺度结构接近的尺度，并可能导致错误的解释，即存在具有幂律的连续尺度范围。传统的傅立叶技术，适用于真实的数据，给出非常尖峰的光谱，其中的分离的真实的最大值和高次谐波可能是困难的。我们建议作为最佳工具的小波频谱与适当的选择分析小波。我们引入小波互相关函数，这使我们能够研究图像之间的相关性作为尺度的函数。互相关系数强烈地依赖于尺度。如果银河系图像中存在明亮的、扩展的中心区域或扩展的圆盘，经典的互相关系数可能会产生误导。本文分析了邻近旋涡星系NGC 6946的九幅光学和射电图的标度和互相关特性。小波光谱使我们能够分离不同尺度上的结构，如螺旋臂和扩散扩展发射。只有热射电辐射和Ha辐射的图像在最小分辨率尺度O 160 - 800 pcU上给出了三维Kolmogorov型湍流的指示。NGC 6946图像之间的互相关表明，所有尺度上的总射电发射，红光和中红外尘埃发射图像之间具有很强的相似性。最好的相关性被发现之间的总无线电发射和尘埃排放。热射电连续谱和Ha发射在大约1弧分的尺度上是最好的相关。1：6 kpc，螺旋臂的典型宽度。在类似的尺度上，偏振射电和Ha发射的图像是相互关联的，这一事实仍然没有被经典的互相关分析检测到。
ABSTRA C T Different scaling and autocorrelation characteristics and their application to astronomical images are discussed: the structure function, the autocorrelation function, Fourier spectra and wavelet spectra. The choice of the mathematical tool is of great importance for the scaling analysis of images. The structure function, for example, cannot resolve scales that are close to the dominating large-scale structures, and can lead to the wrong interpretation that a continuous range of scales with a power law exists. The traditional Fourier technique, applied to real data, gives very spiky spectra, in which the separation of real maxima and high harmonics can be difficult. We recommend as the optimal tool the wavelet spectrum with a suitable choice of the analysing wavelet. We introduce the wavelet cross-correlation function, which enables us to study the correlation between images as a function of scale. The crosscorrelation coefficient strongly depends on the scale. The classical cross-correlation coefficient can be misleading if a bright, extended central region or an extended disc exists in the galactic images. An analysis of the scaling and cross-correlation characteristics of nine optical and radio maps of the nearby spiral galaxy NGC 6946 is presented. The wavelet spectra allow us to separate structures on different scales like spiral arms and diffuse extended emission. Only the images of thermal radio emission and Ha emission give indications of three-dimensional Kolmogorov-type turbulence on the smallest resolved scales O160‐800 pcU. The crosscorrelations between the images of NGC 6946 show strong similarities between the images of total radio emission, red light and mid-infrared dust emission on all scales. The best correlation is found between total radio emission and dust emission. Thermal radio continuum and Ha emission are best correlated on a scale of about 1 arcmin . 1:6 kpc, the typical width of a spiral arm. On a similar scale, the images of polarized radio and Ha emission are anticorrelated, a fact that remains undetected with classical cross-correlation analysis.