MAGNETOPAUSE SHAPE AS A BIVARIATE FUNCTION OF INTERPLANETARY MAGNETIC-FIELD B(Z) AND SOLAR-WIND DYNAMIC PRESSURE

We present a new method for determining the shape of the magnetopause as a bivariate function of the hourly averaged solar wind dynamic pres sure (p) and the north-south component of the interplanetary magnetic field (IMF) B(z). We represent the magnetopause (for X(GSE) > -40R(E)) as an ellipsoid of revolution in solar-wind-aberrated coordinates and express the (p, B(z)) dependence of each of the three ellipsoid param eters as a second-order (6-term) bivariate expansion in lnp and B(z). We define 12 overlapping bins in a normalized dimensionless (p, B(z)) ''control space'' and fit an ellipsoid to those magnetopause crossings having (p, B(z)) values within each bin. We also calculate the bivari ate (lnp, B(z)) moments to second order over each bin in control space . We can then calculate the six control-space expansion coefficients f or each of the three ellipsoid parameters in configuration space. From these coefficients we can derive useful diagnostics of the magnetopau se shape as joint functions of p and B(z): the aspect ratio of the ell ipsoid's minor-to-major axes; the flank distance, radius of curvature, and flaring angle (at X(GSE) = 0); and the subsolar distance and radi us of curvature. We confirm and quantify previous results that during periods of southward B(z) the subsolar magnetopause moves inward, whil e at X(GSE) = 0 the flank magnetopause moves outward and the flaring a ngle increases. These changes are most pronounced during periods of lo w pressure, wherein all have a dependence on B(z) that is stronger and functionally different for B(z) southward as compared to B(z) northwa rd (i.e., the behavior of a ''half-wave rectifier''). In contrast, all these changes are much less sensitive to IMF B(z) at the highest pres sures. As an application of these new results, we use a pressure balan ce relationship to estimate the difference between the magnetic field strength just inside the subsolar magnetopause and that of the dipole field, and we find that this difference decreases rapidly as B(z) beco mes more negative (although it is relatively insensitive to northward changes in B(z)). Quantitative comparison shows that Region 1 Birkelan d currents could make the dominant contribution to this depression in the inferred magnetic field at the subsolar point.