We have examined both the upstream waves and waves at Polar and mid-latitude ground stations in the Pc 3-4 band on May 11, 1999, when the solar wind density was well below 1 cm-3, and compared with those in the control day of May 14, when the solar wind density was normal and the IMF conditions were similar. The near absence of upstream ULF waves on May 11 appears to be the result of a weakened bow shock, due to the low Mach number of the solar wind flow past the Earth. We expect that the low Mach number shock reflected very few backstreaming particles into the foreshock. Thus, the resulting upstream waves were one order of magnitude weaker in power than usual and had little compressional power. The Pc 3-4 waves, clearly seen in the dayside magnetosphere on May 14, were nearly absent on May 11 both in space as observed by Polar and on the ground at mid-latitudes, even though the foreshock geometry was favorable for the generation of Pc 3-4 waves in the magnetosphere for both days.
The simultaneous observations of Pc 3-4 waves in the upstream region, in the magnetosphere and on the ground in this study provide further support to the solar wind source of magnetospheric Pc 3-4 waves. Previous observations have established the relationship between the IMF magnitude and the Pc 3-4 wave (as well as upstream wave) frequency and between the IMF cone angle and the Pc 3-4 wave occurrence [Bol'shakova and Troitskaya, 1968, Troitskaya et al., 1971, Gulèlmi, 1974]. Previous work also found correlations between the wave power and the solar wind velocity, which correlation was attributed to the presence of the Kelvin-Helmholtz instability acting at the magnetopause [Singer et al., 1977]. This study does not address the role of the solar wind velocity in stimulating the Kelvin-Helmholtz instability because the solar wind velocity was nearly the same on the two days examined. Nevertheless it does raise the issue of whether the solar wind Mach number, which depends on both the solar wind density and velocity, may be responsible for both the number density and velocity correlations. If true, the physical process that controls the wave amplitude take places at the bow shock rather than the magnetopause. The effect of solar wind Mach number on the amplitude of upstream waves and magnetic pulsations in the magnetosphere should be considered in future studies, and control studies using intervals with similar solar wind Mach number but different solar wind velocities should be undertaken.