An Optical Study of the Black Widow Population

The optical study of the heated substellar companions of `Black Widow' (BW) millisecond pulsars (MSP) provides unique information on the MSP particle and radiation output and on the neutron star mass. Here we present analysis of optical photometry and spectroscopy of a set of relatively bright BWs, many newly discovered in association with Fermi $\gamma$-ray sources. Interpreting the optical data requires sophisticated models of the companion heating. We provide a uniform analysis, selecting the preferred heating model and reporting on the companion masses and radii, the pulsar heating power and neutron star mass. The substellar companions are substantially degenerate, with average densities $15-30\times$ Solar, but are inflated above their zero temperature radii. We find evidence that the most extreme recycled BW pulsars have both large $>0.8M_\odot$ accreted mass and low $<10^8$G magnetic fields. Examining a set of heavy BWs, we infer that neutron star masses larger than $2.19 M_\odot$ ($1\sigma$ confidence) or $2.08 M_\odot$ ($3\sigma$ confidence) are required; these bounds exclude all but the stiffest equations of state in standard tabulations.