In the following figures, I am plotting two things
the distribution of substorms as a function of the total energy transferred to the magnetosphere by the solar wind
2 hours before the onset
2 hours after the onset.
I define two types of substorms
Isolated ⇒ No substorm onset 3 hours before the current onset
Single ⇒ No substorms within 3 hours after the current onset
Isolated ⇒ No substorm onset 3 hours before the current onset
Multi ⇒ There is at least one onset within 3 hours after the current onset
Total energy transfer is defined using the following energy coupling function
$\epsilon(t) = V_{sw}B^2 \sin^4(\Theta/2)l_0^2$ The energy coupling function between the solar wind and magnetosphere Kan and Lee., 1979 Newell et al., 2011. $l_o$ is a constant $\approx 7 R_E$. This is approximately the power delivered by the solar wind dynamo to the open magnetosphere.
Energy transfer
Pre-onset: $\int_{t_0 -2 \mathrm{Hrs}}^{t_0} \epsilon(t) \mathrm{dt}$
Post-onset: $\int_{t_0}^{t_0+2\mathrm{Hrs}} \epsilon(t) \mathrm{dt}$
The distribution is plotted with the above energy transfer parameter in the horizontal axis, and in the vertical axis we have the number of substorms per bin.
The substorm definition is based on the SuperMag substorm catalog, which uses SML - magnetic index bays.
Distribution of single- and multi-onset substorms with total solar wind power transferred before and after the onset
Distribution of a superposed epoch average of 15 randomly selected single- and multi-onset substorms with total solar wind power transferred before and after the onset
Distribution of a superposed epoch average of 1000 randomly selected single- and multi-onset substorms with total solar wind power transferred before and after the onset
