On the validity of Akasofu’s ε parameter and of the Vasyliunas et al. general formula for the rate of solar wind-magnetosphere energy input

The ε parameter of Akasofu and the general formula of Vasyliunas et al. (1982) have been widely used as functions representing the rate of the solar wind energy input into the Earth’s magnetosphere. These two functions have a feature that dependence on the interplanetary magnetic field (IMF) is assumed to be expressed by the combination of B, the magnitude of the IMF, and sin (θ/2), where θ is the clock angle, or by the combination of BT = (By2 + Bz2)1/2, the magnetic field perpendicular to the Sun-Earth line, and sin(θ/2), not by the Bz component. We check the validity of this assumption by presuming that the AL index has good correlation with the solar wind energy input rate and by applying the regression analysis in a power law form to hourly values of the AL index and of solar wind parameters during the period 1966–1987. We show that Bz generally gives high correlation coefficients and shows higher consistency in exponents than the combination of B (or BT) and sin (θ/2). Thus we conclude that the IMF dependence of the rate of the solar wind energy input is described better by Bz than by the combination of B (or BT) and sin(θ/2).