# Modulation of Solar Wind Impact on the Earth's Magnetosphere during the Solar Cycle
## 3 Results and Discussion  
An empirical indication of how the geomagnetic activity is affected by the energy content of the SW can be obtained by constructing the two-dimensional bivariate histogram on the \(E\)-\(Dst\) plane. In Figure 3, we show the distributions of the \(Dst\) index as a function of the total (top panels), kinetic (middle panels), and magnetic (bottom panels) energy, during the intervals of maximum activity (left panels) and of minimum activity (right panels). The black line tracks the maximum of the distributions in each energy bin, giving the most probable values of the \(Dst\) index within the 68% confidence bounds, indicated as the gray shaded area. A clear link between the enhancement of \(Dst\) and the total energy carried by the SW is observed for both periods. Indeed, most of the events causing a sensible disturbance (\(Dst\leq-10\) nT) correspond to SW energy in the range \(E\in[1,10]\). Nearly zero \(Dst\), indicating an unperturbed current system, is observed for \(E_{t}\leq 0.2\) for the maximum activity period, and for \(E_{t}\leq 0.4\) for the minimum activity period. A similar behavior is observed for the distributions \(Dst-E_{v}\) (kinetic energy), and \(Dst-E_{b}\) (magnetic energy), shown respectively in the central and bottom rows of Figure 3. A roughly logarithmic decay is observed for all distributions. In general, faster decay is seen for the maximum activity period. During this period, the decay rate is not constant, but, instead, shows a break and a faster decay when the energy exceeds \(E_{b}\), \(E_{t}>2\), or \(E_{v}>4\). This is the signature of the stronger perturbations in the \(Dst\) index being associated with larger SW energies. On the other hand, in the period of the solar minimum, a saturation to a nearly constant value, \(Dst\approx-20\) nT, is observed at the same \(E_{t},E_{v},E_{b}\geq 1.8\) for the total, kinetic and magnetic SW energies. It is evident that, during maximum solar activity periods, severe disturbances, characterized by an index up to \(Dst\geq-50\) nT, are observed. Conversely, during the minimum period, the strongest disturbances reach values of the order of \(Dst\approx-50\) nT for comparable values of the SW energy. This difference could be related to the different rate of occurrence of events generating GSs. Indeed, during maximum activity the solar wind typically carries more frequent disturbances that impact on the magnetosphere than at the minima of activity. Therefore, the typical recovery time before successive events affecting the \(Dst\) index is short and does not allow the relaxation of the magnetospheric configuration, so that energy (and therefore perturbations) keep on accumulating in the system. As a result, stronger disturbances may be observed. In other words, extreme perturbations can be linked to the superposition of several events occurring during a short time interval, whose energy accumulates, \"charging\" the magnetosphere. On the other hand, during the minimum activity period, extreme events are generated at a lower rate, so that geo-effective events are more sparse. After an event, the system has more time for relaxing and reorganizing the local magnetospheric structure, so that the total response does not reach the severity of the maximum activity case. Finally, to evaluate the role of the SW speed, Figure 4 shows the distributions of the median values of the SW bulk speed \(V\) in the \(E\)-\(Dst\) plane. During the solar maximum period (left panels), a large cluster of events located in the core region of the distribution has SW speed \(300\leq V\leq 550\) km s\({}^{-1}\), carrying a total energy \(E_{t}\in[0.3,1]\), with the \(Dst\) index indicating weak geomagnetic storm activity \(Dst\in[-10,-50]\). Such a cluster represents the peak of the distributions seen in Figure 3 within the 68% confidence bounds. On the other hand, the peripheral left and right regions of the distribution are relative to either low- or extreme-energy wind, respectively.