Multiband Optical Light Curves of Black-Widow Pulsars

We collect new and archival optical observations of nine "black-widow" millisecond pulsar binaries. New measurements include direct imaging with the Keck, Gemini-S, MDM, and LCO 2~m telescopes. This is supplemented by synthesized colors from Keck long-slit spectra. Four black-widow optical companions are presented here for the first time. Together these data provide multicolor photometry covering a large fraction of the orbital phase. We fit these light curves with a direct (photon) heating model using a version of the ICARUS light-curve modeling code. The fits provide distance and fill-factor estimates, inclinations, and heating powers. We compare the heating powers with the observed GeV luminosities, noting that the ratio is sensitive to pulsar distance and to the gamma-ray beaming. We make a specific correction for "outer-gap" model beams, but even then some sources are substantially discrepant, suggesting imperfect beaming corrections and/or errors in the fit distance. The fits prefer large metal abundance for half of the targets, a reasonable result for these wind-stripped secondaries. The companion radii indicate substantial Roche-lobe filling, $f_c \approx 0.7-1$ except for PSR J0952$-$0607, which with $f_c< 0.5$ has a companion density $\rho \approx 10\,{\rm g\,cm^{-3}}$, suggesting unusual evolution. We note that the direct-heating fits imply large heating powers and rather small inclinations, and we speculate that unmodeled effects can introduce such bias.