Analysis of power spectra of Doppler shift time series as a diagnostic tool for quiescent coronal loops

Context. Analysing the structure of solar coronal loops is crucial to our understanding of the processes which heat and maintain the coronal plasma at multimillion degree temperatures. The determination of the physical parameters of the loops remains both an observational and theoretical challenge. Aims. The present work is aimed at tackling some of these challenges such as the determination of the average loop temperature and its distribution along a given loop. Methods. A novel diagnostic technique for quiescent coronal loops based on the analysis of power spectra of Doppler shift time series is proposed. It is assumed that the loop is heated randomly both in space and time by small-scale discrete impulsive events of unspecified nature. The loop evolution is characterised by longitudinal motions caused by the random heating events. These random motions can be represented as a superposition of the normal modes of the loop, i.e., its standing acoustic wave harmonics. The idea is borrowed from helioseismology where a similar approach resulted in a deep understanding of the solar interior. Results. It is shown that depending on the heliographic position of the loop and its geometrical orientation, various harmonics can be identified in the power spectra of the line shift time series. The highest power peak corresponds to the fundamental mode. The peaks become smaller as the frequency increases. The frequencies of the harmonics are determined by the loop length and temperature and thus are suggested to be used as a temperature diagnostic tool. It is demonstrated that the analysis of the power spectra allows the distinction between uniformly heated loops from loops heated near their footpoints and to estimate the average energy of a single heating event. The proposed new method could in principle be used to study the multithermal structure of coronal loops. Conclusions. The power spectrum analysis is a potentially powerful technique for coronal loop diagnostics.