Model description

It is an empirical model of the bow shock and magnetic pile-up boundary. Required parameters are solar wind dynamic pressure, total solar ionizing flux, and magnitude of crustal magnetic field (P_sw, F, B_surf). The MSO coordinate system with corrected abberation is used. Furthermore, cylindrical symetry is assumed. The coordinate variables are x and ρ. The boundary shapes are given by the parabola equation:

ρ² = α(x₀ - x),

where x₀ is the subsolar standoff distance and α represents boundary flaring. Furthermore, the subsolar standoff distance dependence is as follows:

x₀ = CP^β_swF^γB^δ_surf.

The parameters α, C, β, γ, and δ are summarized in the following table:

	Bow shock	Magnetic pile-up boundary
α	4.219 ± 0.027	1.567 ± 0.007
C	1.464 ± 0.006	1.187 ± 0.003
β	-0.063 ± 0.003	-0.065 ± 0.002
γ	0.205 ± 0.006	0.094 ± 0.005
δ	0.018 ± 0.005	0.038 ± 0.001