Multiscale Analysis of the Gradient of Linear Polarisation

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.