Optical Study of TRAPUM Pulsars and Modelling of the Redbacks: PSR J1036$-$4353 and PSR J1803$-$6707
The Transients and Pulsars with MeerKAT (TRAPUM) project discovered eight binary millisecond pulsars in its first shallow \textit{L}-band survey of unidentified \textit{Fermi} $γ$-ray sources using the MeerKAT radio telescope. We conducted follow-up observations using ULTRACAM on the New Technology Telescope at the La Silla Observatory to search for the optical counterpart to the pulsar companions. We found two redback companions, in PSRs J1803$-$6707 and J1036$-$4353, and provided upper limits for the other pulsar binaries. We used the \texttt{Icarus} code to fit the redback's light curves using various irradiation models. The asymmetric double-peak light curves of PSR~J1036$-$4353 are best fit with diffusion and convection models. Comparing the two prescriptions of irradiation and gravity darkening, models with post-irradiation gravity darkening provide superior fits (particularly for lower gravity-darkening exponents), suggesting that the irradiation energy is deposited deep in the stellar photosphere. PSR~J1803$-$6707, on the other hand, displayed variability in the amplitude of its irradiation-dominated light curves over a time scale of a few months. This effect can be modelled only if the companion's filling, irradiation temperature, and convection coefficients are allowed to vary over time. Had the star been closer to filling its Roche lobe, like in the cases of the known transitional millisecond pulsars J1023+0038 and J1227$-$4853, this 4.1 per~cent variation in the volume-averaged filling of the star would have caused it to experience a state change to form an active accretion disc.