Hydrodynamical simulations of wind interaction in spider systems. A step toward understanding transitional millisecond pulsars

The detected population of "spiders", referring to millisecond pulsar binaries, has significantly grown in the past decade thanks to multiwavelength follow-up investigations of unidentified Fermi sources. These systems consist of low-mass stellar companions orbiting rotation-powered millisecond pulsars in short periods of a few hours up to day. Among them, a subset of intriguing objects called transitional millisecond pulsars (tMSPs) has been shown to exhibit a remarkable behavior, transitioning between pulsar-binary and faint low-mass X-ray binary states over a span of a few years. Our objective is to study the interaction of stellar winds in tMSPs in order to understand their observational properties. To this end we focus on the parameter range that places the system near Roche-lobe overflow. Employing the adaptative mesh refinement (AMR) AMRVAC 2.0 code, we performed 2D hydrodynamical (HD) simulations of the interaction between the flows from both stars, accounting for the effects of gravity and orbital motion. By studying the mass loss and launch speed of the winds, we successfully recreated two phenomenologically distinct regimes: the accretion stream and the pulsar radio state. We also identified the tipping point that marks the sharp transition between these two states. In the accretion stream state, we discover a very strong variability induced by the pulsar wind. In the pulsar state, we reconstructed the corresponding X-ray light curves of the system that produces the characteristic double-peak pattern of these systems. The position of the peaks is shifted due to orbital motion and the leading peak is weaker due to eclipsing by the companion. This study highlights the importance of gravity and orbital motion in the interaction between the companion and pulsar winds. Our setup allows the study of the complex interaction between the pulsar wind and an accretion stream during mass transfer. We suggest that a smaller leading peak in X-rays is indicative of a nearly edge-on system.