MOVES V. Modelling star-planet magnetic interactions of HD 189733

Magnetic interactions between stars and close-in planets may lead to a detectable signal on the stellar disk. HD 189733 is one of the key exosystems thought to harbor magnetic interactions, which may have been detected in August 2013. We present a set of twelve wind models at that period, covering the possible coronal states and coronal topologies of HD 189733 at that time. We assess the power available for the magnetic interaction and predict its temporal modulation. By comparing the predicted signal with the observed signal, we find that some models could be compatible with an interpretation based on star-planet magnetic interactions. We also find that the observed signal can be explained only with a stretch-and-break interaction mechanism, while that the Alfv\'en wings scenario cannot deliver enough power. We finally demonstrate that the past observational cadence of HD 189733 leads to a detection rate of only between 12 to 23%, which could explain why star-planet interactions have been hard to detect in past campaigns. We conclude that the firm confirmation of their detection will require dedicated spectroscopic observations covering densely the orbital and rotation period, combined with scarcer spectropolarimetric observations to assess the concomitant large-scale magnetic topology of the star.