Coronal seismology through wavelet analysis

This paper expands on the suggestion of De Moortel & Hood (2000) that it will be possible to infer coronal plasma properties by making a detailed study of the wavelet transform of observed oscillations. TRACE observations, taken on 14 July 1998, of a are-excited, decaying coronal loop oscillation are used to illustrate the possible applications of wavelet analysis. It is found that a decay exponent n approximate to 2 gives the best fit to the double logarithm of the wavelet power, thus suggesting an e(-epsilon tn) damping profile for the observed oscillation. Additional examples of transversal loop oscillations, observed by TRACE on 25 October 1999 and 21 March 2001, are analysed and a damping profile of the form e(-epsilon tn), with n approximate to 0.5 and n approximate to 3 respectively, is suggested. It is demonstrated that an e(-epsilon tn) damping profile of a decaying oscillation survives the wavelet transform, and that the value of both the decay coefficient epsilon and the exponent n can be extracted by taking a double logarithm of the normalised wavelet power at a given scale. By calculating the wavelet power analytically, it is shown that a sufficient number of oscillations have to be present in the analysed time series to be able to extract the period of the time series and to determine correct values for both the damping coefficient and the decay exponent from the wavelet transform.