Lorentzian line shape and modal parameters

An individual resonance appears in the power spectrum as a line with a Lorentzian (Lorentz) shape — a symmetric peak whose profile corresponds to a damped oscillator excited by broadband noise (lightning). The Lorentzian shape is therefore a natural model of the SR spectral line.

From the measured spectrum the modal parameters — the central frequency f_n, the amplitude and the Q-factor (or the width \Delta f) — are obtained by a Lorentzian fit: by fitting a sum of Lorentzian profiles (one for each mode) to the measured spectrum. This procedure is the standard way of extracting physically meaningful numbers from the data, which can then be compared with cavity models (see #18, #19, #22).

Recall that the position and number of lines are determined by the angular structure of the solution of the wave equation on the sphere — the spherical harmonics Y_n^m and Legendre functions P_n(\cos\theta) (see #15, #16) — while their width and mutual overlaps are dictated by the losses (low Q). The Lorentzian fit thus connects the observed spectrum with all the preceding physics of the cluster: from the eigenmodes through the losses to the line splitting of modes (#24).

*Cluster C file — part of the Schumann resonance knowledge base.*