Wavelet analysis and the determination of coronal plasma properties

The usefulness of wavelet analysis is demonstrated by considering analytical expressions for phase mixed Alfvén waves in different physical circumstances. The wavelet analysis is briefly introduced, using the complex-valued Morlet wavelet, consisting of a plane wave modulated by a Gaussian, as the basic wavelet. The time and scale resolution of the wavelet transform are then discussed in more detail, by working out the transform of simple harmonic functions analytically. As an illustration of the power of wavelet analysis, phase mixed Alfvén waves are investigated. A comparison is made between a truly finite harmonic wave and an Alfvén wave, dissipated by phase mixing and, using the wavelet transform, it is demonstrated that it is possible to distinguish between these two ‘finite’ signals. It is also possible to extract the value of the dissipation coefficient from the wavelet transform. When considering phase mixing of Alfvén waves in a gravitationally stratified atmosphere, the lengthening of the wavelengths is clearly evident in the transform, which provides an independent estimate of the value of the pressure scale height. In a radially diverging atmosphere, the shortening of the wavelengths is also apparent in the wavelet transform, showing how the Alfvén speed varies along the loop and thus providing information on the coronal density and magnetic field. When applying wavelet analysis to observed wavelike oscillations, it should be possible to infer properties of the coronal plasma by making a detailed study of the wavelet transform.