We investigate the dependence of polar mesosphere summer echoes (PMSE) and mesosphere summer echoes (MSE) on the background electron number density. Both a lower and upper limit are quantified below and above which PMSE cannot exist. The result is that PMSE occur for a very wide range of electron number densities between ~300--500/cm3 and ~105/cm3. A comparison of the diurnal variation of MSE observed at K¿hlungsborn (54¿N) with current model estimates of the electron number density at midlatitudes shows that at least ~300--500 electrons /cm3 are necessary for PMSE to exist. This lower limit is consistent with all available electron number density measurements obtained from sounding rockets in the vicinity of PMSE. It is shown that the existence of a lower electron number density limit can be understood in terms of the standard theory of the scattering of VHF waves in the D region. We have then analyzed PMSE observations during the major solar proton event on 14 July 2000. We have estimated the electron number density at PMSE altitudes based on proton and electron flux measurements obtained with detectors on board the GOES-8 and ACE spacecrafts in combination with an ion-chemical model. Comparing the electron number densities at 87 km altitude with the average PMSE signal to noise observations (SNR) we find a significant negative correlation between SNR and the electron number densities for densities on the order of ~105/cm3. We propose that this negative correlation is due to a limited amount of aerosol particles: current PMSE theories assume that electron irregularities in the VHF band can only exist if more than ~50% of the free electrons are bound to aerosol particles which thus reduce the electron diffusivity due to ambipolar forces. If, however, the electron number density increases significantly above the aerosol number density, this condition can no longer be fulfilled. On the other hand, the fact that PMSE is present up to electron number densities of ~105/cm3 raises several important questions on our current understanding of aerosol particles around the polar summer mesopause and their role in the creation of PMSE: either many more aerosol particles exist than has been anticipated so far (with corresponding implications for the nucleation of these particles) or our current understanding of the role of aerosol particles in the creation of PMSE is not complete.