Heated Poles on the Companion of Redback PSR J2339$-$0533

We analyze photometry and spectra of the redback millisecond pulsar binary J2339$-$0533. These observations include new measurements from Keck and GROND, as well as archival measurements from the OISTER, WIYN, SOAR, and HET telescopes. The parameters derived from GROND, our primary photometric data, describe well the rest of the datasets, raising our confidence in our fitted binary properties. Our fit requires hot-spots (likely magnetic poles) on the surface of the companion star, and we see evidence that these spots move over the 8 yr span of our photometry. The derived binary inclination $i = 69.3^circpm 2.3^circ$, together with the center-of-mass velocity (from the radial-velocity fits) $K_{rm C} = 347.0pm 3.7,$ $mathrm{km,s}^{-1}$, give a fairly typical neutron star mass of $1.47pm 0.09,M_odot$.