Field line resonance (FLR) has the potential to account for magnetic and electric oscillations observed near the equatorial region of the magnetosphere and on the ground associated with auroral arcs. Previous theoretical works based on dipolar field lines give frequencies too high to match with the observed frequencies when typical mass density is used. Inclusion of magnetic field stretching from empirical magnetic field models brings good agreement, but these models have no assurance of specifying an equilibrium magnetosphere. In this paper we present, for the first time, quantitative results of the resonance frequencies for the shear Alfvén and slow mode branches of FLR threading the auroral zone for field lines stretched to various distances in the nightside based on a self-consistent equilibrium magnetosphere. The calculation is done in two steps. For a given degree of field line stretching we first obtain an MHD equilibrium magnetosphere with a finite temperature through a self-consistent solution of the Grad-Shafranov equation. We then solve for FLR frequencies of stretched magnetic field lines in the equilibrium magnetosphere according to the MHD theory of FLR. The results show that field line stretching can lead to low frequencies of FLR as observed without invoking unrealistically high mass density. Dependent on the wave mode and the amount of field line stretching, the FLR frequencies found in this calculation differ from those for a simple magnetic dipole of the Earth by varying degrees, from agreement within a factor of 2 to a disparity of greater than a factor of 10.
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