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PSR J0636+5128 is a millisecond pulsar in one of the most compact pulsarbinaries known, with a 96\,min orbital period. The pulsar mass functionsuggests a very low-mass companion, similar to that seen in so-called "blackwidow" binaries. Unlike in most of those, however, no radio eclipses bymaterial driven off from the companion were seen leading to the possibilitythat the companion was a degenerate remnant of a carbon-oxygen white dwarf. Wereport the discovery of the optical counterpart of its companion in imagestaken with the Gemini North and Keck~I telescopes. The companion varies between$r=25$ and $r=23$ on the 96\,min orbital period of the binary, caused byirradiation from the pulsar's energetic wind. We modeled the multi-colorlightcurve using parallax constraints from pulsar timing and determine acompanion mass of $(1.71\pm0.23)\times 10^{-2}\,M_\odot$, a radius of$(7.6\pm1.4)\times 10^{-2}\,R_\odot$, and a mean density of $54\pm26\,{\rmg\,cm}^{-3}$, all for an assumed neutron star mass of $1.4\,M_\odot$. Thismakes the companion to PSR J0636+5128 one of the densest of the "black widow"systems. Modeling suggests that the composition is not predominantly hydrogen,perhaps due to an origin in an ultra-compact X-ray binary.

A Dense Companion to the Short-Period Millisecond Pulsar Binary PSR J0636+5128