A new functional form to study the solar wind control of the magnetopause size and shape

In this study a new functional form, r = r 0 [2/(1 + cos θ)] α , is used to fit. the size and shape of the magnetopause using crossings from ISEE 1 and 2, Active Magnetospheric Particle Tracer Explorers/Ion Release Module (AMPTE/IRM), and IMP 8 satellites. This functional form has two parameters, τ 0 and α, representing the standoff distance and the level of tail flaring. The value r is the radial distance at an angle (θ) between the Sun-Earth line and the direction of τ. It is found that r 0 varies with the interplanetary magnetic field (IMF) B z component and has a break in the slope at B z = 0 nT. The best-fit value of τ 0 decreases with increasing southward IMF B z . For northward IMF B z , the best-fit value of τ 0 increases slightly with increasing B z . The best-fit value of α increases monotonically with decreasing IMF B z . The dynamic pressure (D p ) also changes τ 0 and α. The parameters D p and τ 0 are related by a power law of -1/(6.6±0.8). The best-fit value of α is slightly larger for larger dynamic pressure, which implies that D p also has a role in flux transfer from the dayside to the nightside, but the size of this effect is small. An explicit function for the size and shape of the magnetopause, in terms of D p and B z , is obtained by using multiple parameter fitting in a form that is useful for operational space applications such as predicting when satellites at geosynchronous orbit will be found in the magnetosheath.