Conjuring Radar Meteor Head-Echoes

The argument surrounding under-dense vs. over-dense radar meteors has raged for decades. Here we consider the head-echo case by the noting that the two limiting scattering regimes for the same radar scattering cross-section (RCS) are each easily described. We give a synopsis of scattering from a perfectly conducting (PC) sphere that represents the manifestly over-dense limit. We contrast this with coherent (in-phase) scattering from an ensemble of N electrons all located within a and sim;1/4-wavelength diameter volume containing the meteoroid. Note that N is the absolute minimum number of electrons yielding a given RCS and that the continuum of equal RCS electron distributions leading to the PC-sphere all require more electrons and thus higher energy to assemble. Here we find the loci of equal RCS for these two limiting cases at three wavelengths - 70 cm, 1.29 m, and 6 m - corresponding to the Arecibo Observatory (AO), EISCAT-3D, and Jicamarca Radio Observatory (JRO) radars, respectively. We also plot on each of these curves the location of a single-pulse (unaveraged), 100 km range, SNR=1 event. In all cases the over-dense (Rayleigh scatter) meteor would correspond to an improbably large object while the number of electrons, N, yielding the same RCS is reasonable. Invoking Occam's Razor, we conclude that the vast majority of head-echo radar meteors are under-dense. This conclusion is important to many aspects of meteoroid physics including mass flux determinations as N is relatively easy to link to meteoroid physics and thus to meteoroid mass. This remains largely true when meteoroid inhomogeneity and fragmentation are considered.