Optical photometry of two transitional millisecond pulsars in the radio pulsar state

We present ULTRACAM multiband optical photometry of two transitional millisecond pulsars, PSR J1023+0038 and PSR J1227$-$4853, taken while both were in their radio pulsar states. The light curves show significant asymmetry about the flux maxima in all observed bands, suggesting an asymmetric source of heating in the system. We model the light curves using the Icarus binary code, using models with an additional "hot spot" heating contribution and an anisotropic heat redistribution model to treat the asymmetry. Our modelling reveals companion stars with under-filled Roche lobes in both PSRs J1023+0038 and J1227$-$4853, with Roche lobe filling factors in the range $f \sim 0.82-0.92$. While the volume-averaged filling factors are closer to unity, significant under-filling is unexpected from tMSPs as they must rapidly over-fill their Roche lobes to start transferring mass, which occurs on timescale of weeks or months. We discuss the motivation and validity of our extensions to the models and the implications of the under-filled Roche lobe, and suggest future work to further investigate the role of the filling factor in the tMSP cycle.