What frequencies of standing surface waves can the subsolar magnetopause support?

It is has been proposed that the subsolar magnetopause may support its own eigenmode, consisting of propagating surface waves which reflect at the northern/southern ionospheres forming a standing wave. While the eigenfrequencies of these so-called Kruskal-Schwartzschild (KS) modes have been estimated under typical conditions, the potential distribution of frequencies over the full range of solar wind conditions is not know. Using models of the magnetosphere and magnetosheath applied to an entire solar cycle\textquoterights worth of solar wind data, we perform time-of-flight calculations yielding a database of KS mode frequencies. Under non-storm times or northward interplanetary magnetic field (IMF), the most likely fundamental frequency is calculated to be inline image mHz, consistent with previous estimates and indirect observational evidence for such standing surface waves of the subsolar magnetopause. However, the distributions exhibit significant spread (of order \textpm0.3 mHz) demonstrating that KS mode frequencies, especially higher harmonics, should vary considerably depending on the solar wind conditions. The implications of such large spread on observational statistics are discussed. The subsolar magnetopause eigenfrequencies are found to be most dependent on the solar wind speed, southward component of the IMF and the Dst index, with the latter two being due to the erosion of the magnetosphere by reconnection and the former an effect of the expression for the surface wave phase speed. Finally, the possible occurrence of KS modes is shown to be controlled by the dipole tilt angle.