Some fraction of the solar wind energy is transferred to Earth magnetosphere and ionosphere. Sometimes this transfer of energy is exceptionally large, producing a magnetic storm. Storms occur when the Interplanetary Magnetic Field (IMF) turns southward and remains southward for an extended period of time. During the main phase of many magnetic storms the solar wind Mach number is low and IMF magnitude is large. Under these conditions, the ionospheric potential saturates and it becomes relatively insensitive to further increases in the IMF magnitude. On the other hand, the dayside merging rate and the potential become sensitive to the solar wind density. This should result in a correlation between the intensity of the auroral electrojets and the solar wind density. In this study we found several storm events to examine the effect of the solar wind density on the intensity of the auroral electrojets (as measured by the SME index) under the condition of low Mach number and steady IMF. As expected, there is a positive correlation between the solar wind density and SME index. We showed this correlation coefficient gets larger for smaller Mach number when one would expect the effect of density to be greater. We also use the LFM global magnetohydrodynamic simulation to reproduce the correlation between ionospheric current and the solar wind density and to examine the physical cause of the correlation.