A Hyperbolic Decay of the Dst Index during the Recovery Phase of Intense   Geomagnetic Storms
  What one commonly considers for reproducing the recovery phase of magnetosphere, as seen by the Dst index, is exponential function. However, the magnetosphere recovers faster in the first hours than in the late recovery phase. The early steepness followed by the late smoothness in the magnetospheric response is a feature that leads to the proposal of a hyperbolic decay function to reproduce the recovery phase, instead of the exponential function. A superposed epoch analysis of recovery phases of intense storms from 1963-2006 was performed, categorizing the storms by their intensity into five subsets. The hyperbolic decay function reproduces experimental data better than what the exponential function does for any subset of storms, which indicates a non-linear coupling between dDst/dt and Dst. Moreover, this kind of mathematical function, where the degree of reduction of the Dst index depends on time, allows for explaining different lifetimes of the physical mechanisms involved in the recovery phase and provides new insights for the modeling of the Dst index. 
J. Aguado, C. Cid, E. Saiz, and Y. Cerrato
astro-ph.EP physics.geo-ph physics.space-ph