线极化梯度的多尺度分析
Multiscale Analysis of the Gradient of Linear Polarisation
摘要：
我们提出了一种新的多尺度方法来计算的线性极化矢量的梯度的幅度，使用基于小波的形式主义。我们证明了这种方法使用的加拿大银河平面调查（CGPS）的领域，并表明，通常看到的线性偏振图的梯度的concretary结构强烈依赖于仪器的分辨率。我们的分析表明，不同的网络的细丝存在于不同的角度尺度。小波形式主义使我们能够计算线性偏振图的梯度中看到的波动的功率谱，并确定这个量的标度行为。发现功率谱遵循伽马~ 2.1的幂律。我们发现在80 < l < 300弧分的尺度之间功率有一个小的下降，这很好地对应于Effelsberg 100-m望远镜和DRAO 26-m望远镜数据之间的u-v平面的重叠。我们认为，这种下降是由于采样不足，目前在26米望远镜的数据。此外，小波系数分布在小尺度上比在大尺度上表现出更高的偏度。这些分布尾部的异常值的空间分布创建了跨多个尺度相关的细丝的相干子集，其跟踪场内偏振矢量P的最急剧变化。我们认为，这些结构可能与介质中的高压缩冲击有关。不包括这些异常值的场的功率谱显示出gamma ~ 2.5的更陡的幂律。
英文摘要：
We propose a new multiscale method to calculate the amplitude of the gradient of the linear polarisation vector using a wavelet-based formalism. We demonstrate this method using a field of the Canadian Galactic Plane Survey (CGPS) and show that the filamentary structure typically seen in gradients of linear polarisation maps depends strongly on the instrumental resolution. Our analysis reveals that different networks of filaments are present on different angular scales. The wavelet formalism allows us to calculate the power spectrum of the fluctuations seen in gradients of linear polarisation maps and to determine the scaling behaviour of this quantity. The power spectrum is found to follow a power law with gamma ~ 2.1. We identify a small drop in power between scales of 80 < l < 300 arcmin, which corresponds well to the overlap in the u-v plane between the Effelsberg 100-m telescope and the DRAO 26-m telescope data. We suggest that this drop is due to undersampling present in the 26-m telescope data. In addition, the wavelet coefficient distributions show higher skewness on smaller scales than at larger scales. The spatial distribution of the outliers in the tails of these distributions creates a coherent subset of filaments correlated across multiple scales, which trace the sharpest changes in the polarisation vector P within the field. We suggest that these structures may be associated with highly compressive shocks in the medium. The power spectrum of the field excluding these outliers shows a steeper power law with gamma ~ 2.5.
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