Optical Study of TRAPUM Pulsars and Modelling of the Redbacks: PSR J1036$-$4353 and PSR J1803$-$6707

TL;DR

The paper addresses irradiation and atmospheric dynamics in redback MSP companions by combining multi-band ULTRACAM photometry, SOAR spectroscopy, and Bayesian light-curve modelling with the Icarus code. It employs Direct Heating and heat-redistribution (diffusion+convection) prescriptions, comparing Pre- and Post-irradiation gravity-darkening to determine how deeply MSP energy is deposited. For PSR J1036$-$4353 and PSR J1803$-$6707, the diffusion+convection model with Post-IGD provides the best fits, yielding $M_p=1.4\pm0.1\,M_{\odot}$, $M_c=0.24\pm0.01\,M_{\odot}$ and $M_p=1.7\pm0.2\,M_{\odot}$, $M_c=0.44_{-0.04}^{+0.05}\,M_{\odot}$, respectively. J1803$-$6707 shows epoch-dependent light-curve amplitudes, indicating evolving companion structure, while J1036$-$4353 supports deep energy deposition beneath the photosphere, consistent with recent theoretical expectations. These findings advance understanding of irradiation physics in spider binaries and illuminate potential evolutionary paths toward transitional millisecond pulsars (tMSPs), underscoring the value of long-term optical/radio monitoring to capture state changes.

Abstract

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.

Figures (10)

• Figure 1: Five-minute stacked ULTRACAM images of the MSP binaries are shown with different localisation ellipses representing 95-per cent confidence. If the ellipses are smaller than a pixel, they are indicated by two strips pointing at the centres of the ellipses. The SeeKAT localisations are shown in red ellipses. The blue strips indicate the timing localisation obtained during the follow-up timing campaign from Burgay2024+timing.
• Figure 2: The top panel shows the optical light curves of PSR J1036$-$4353, observed in $r_s$, $g_s$, and $u_s$ bands. The bottom panel shows the light curves of PSR J1803$-$6707 in $i_s$, $g_s$, and $u_s$. The data points are re-binned to 300s and 900s for PSRs J1036$-$4353 and J1803$-$6707, respectively. This is to clearly display the discrepancy between observational epochs as shown in the two subpanels (a) and (b). In both panels, if data points fall below the two-sigma detection threshold, the upper limits are shown with downward arrows.
• Figure 3: The radial velocity curves of PSRs J1036$-$4353 and J1803$-$6707 are shown as crosses with vertical bars of uncertainties. The blue solid lines are the results of cross-correlating model spectra with a template (defined as the model at orbital phase = 0.25) to reproduce the measured radial velocities. The red dotted lines are the sine curves which are approximately radial velocities tracing the centre of mass of the companions. The discrepancy between the model of PSR J1803$-$6707 and the sine curve shows the clear effect of how radial velocity is shifted from the centre of mass to the 'centre of light' toward the brighter, hotter region of the star.
• Figure 4: Different models are compared using their Bayesian evidence relative to the best-fitting model. As described in Section \ref{['sec:modelling']}, a decisively better model will have a log-evidence higher by 4.6 compared to another model. The log-evidence values are labelled according to the set of parameters that were separately fitted to different datasets. This implies that the D+C model with Post-IGD are the best-fitting models for both PSR J1036$-$4353 and PSR J1803$-$6707. Specifically, the D+C model with Post-IGD and separate $f_{\rm RL}$, $T_{\rm irr}$, $\kappa$, and $\nu$ parameters for different datasets best describes the modulation changes in PSR J1803$-$6707.
• Figure 5: The Hertzsprung--Russell diagram displays PSR J1036$-$4353, PSR J1803$-$6707, and upper limits for other pulsars. The vertical axis denotes the absolute magnitude $M_{\rm G}$ in the Gaia G band, while the horizontal axis represents the Gaia colour ($G_{\rm BP}-G_{\rm RP}$). Black dots denote Gaia sources within a 200 pc distance, with the orange circle marking the Sun's position. Magnitudes are uncorrected for interstellar extinction. The black arrow shows the shift from the intrinsic to the observed position of a star with E(B$-$V) $\simeq 0.3$ mag. ULTRACAM $i_s$ and $g_s$ magnitudes at the signal-to-noise ratio of unity are approximately 25.253 and 26.256, respectively Dhillon2001. These limits are converted to Gaia magnitudes, establishing 1-sigma upper limits at various distances, depicted as grey dashed lines. One of these lines serves as an approximate boundary, distinguishing detectable sources above it from undetectable ones below. Upper limits for other TRAPUM pulsars are estimated from DM distance YMW2016 and represented as dashed lines in different colours.