A model to estimate energy deposition within the geomagnetosphere using Dst as a proxy for the Akasofu ϵ parameter

Abstract

This study compares the energy deposited into the geomagnetosphere by 14 co-rotating interaction regions (CIRs) and 14 interplanetary coronal mass ejections (ICMEs), selected from solar cycle 23, and covering a broad range of activity. The energy ($E$) is estimated using the Akasofu empirical coupling function and it was found that, on average, the ICMEs deposit about 15 times the energy contributed by the CIRs. The energy correlates very significantly with the peak (most negative) of the hourly $D_{st}$ geomagnetic index observed during each event (first order fit, $\rho$ = -0.94; second order fit, $\rho$ = -0.97). Two modifications to the Akasofu relation proposed by de Lucas et al. are then incorporated into the energy calculations: the first replaces the radius of the effective area for the dayside magnetopause with a value which is a function of the solar wind ram pressure, and the second takes into account the dynamic pressure of the solar wind itself. As a result, $\rho$ strengthens for the first order fit to -0.96, but weakens slightly for the second to -0.96, though all these correlations are highly significant. An empirical model is proposed of the form $E=f\left(D_{st}\right)$, for which regression equations, correlation coefficients, standard errors and 1$\sigma$ uncertainties are provided for both first and second order fits. The model provides an estimate of the energy deposited into the magnetosphere by solar particle events, using ground-based measurements, without recourse to in-situ measurements of the solar wind which are prone to data gaps during very energetic events.