  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.
