On the size, shape, and density of dwarf planet Makemake

A recent stellar occultation by dwarf planet Makemake provided an excellent opportunity to measure the size and shape of one of the largest objects in the Kuiper belt. The analysis of these results provided what were reported to be precise measurements of the lengths of the projected axes, the albedo, and even the density of Makemake, but these results were, in part, derived from qualitative arguments. We reanalyzed the occultation timing data using a quantitative statistical description, and, in general, find the previously reported results on the shape of Makemake to be unjustified. In our solution, in which we use our inference from photometric data that Makemake is being viewed nearly pole-on, we find a 1 sigma upper limit to the projected elongation of Makemake of 1.02, with measured equatorial diameter of 1434 +/- 14 km and a projected polar diameter of 1422 +/- 14 km, yielding an albedo of 0.81+0.01/-0.02$. If we remove the external constraint on the pole position of Makemake, we find instead a 1 sigma upper limit to the elongation of 1.06, with a measured equatorial diameter of 1434+48/-18 km and a projected polar diameter of 1420+18/-24 km, yielding an albedo of 0.81+0.03/-0.05. Critically, we find that the reported measurement of the density of Makemake was based on the misapplication of the volatile retention models. A corrected analysis shows that the occultation measurements provide no meaningful constraint on the density of Makemake.