A Gaia view of the optical and X-ray luminosities of compact binary millisecond pulsars

In this paper, we study compact binary millisecond pulsars with low- and very low-mass companion stars (spiders) in the Galactic field, using data from the latest Gaia data release (DR3). We infer the parallax distances of the optical counterparts to spiders, which we use to estimate optical and X-ray luminosities. We compare the parallax distances to those derived from radio pulse dispersion measures and find that they have systematically larger values, by 40% on average. We also test the correlation between X-ray and spin-down luminosities, finding that most redbacks have a spin-down to X-ray luminosity conversion efficiency of $\sim$0.1%, indicating a contribution from the intrabinary shock. On the other hand, most black widows have an efficiency of $\sim$0.01%, similar to the majority of the pulsar population. Finally, we find that the bolometric optical luminosity significantly correlates with the orbital period, with a large scatter due to different irradiated stellar temperatures and binary properties. We interpret this correlation as the effect of the increasing size of the Roche Lobe radius with the orbital period. With this newly found correlation, an estimate of the optical magnitude can be obtained from the orbital period and a distance estimate.