Hunting for exoplanets via magnetic star-planet interactions: geometrical considerations for radio emission

Recent low-frequency radio observations suggest that some nearby M dwarfs could be interacting magnetically with undetected close-in planets, powering the emission via the electron cyclotron maser (ECM) instability. Confirmation of such a scenario could reveal the presence of close-in planets around M dwarfs, which are typically difficult to detect via other methods. ECM emission is beamed, and is generally only visible for brief windows depending on the underlying system geometry. Due to this, detection may be favoured at certain orbital phases, or from systems with specific geometric configurations. In this work, we develop a geometric model to explore these two ideas. Our model produces the visibility of the induced emission as a function of time, based on a set of key parameters that characterise magnetic star-planet interactions. Utilising our model, we find that the orbital phases where emission appears are highly dependent on the underlying parameters, and does not generally appear at the quadrature points in the orbit as is seen for the Jupiter-Io interaction. Then using non-informative priors on the system geometry, we show that untargeted radio surveys are biased towards detecting emission from systems with planets in near face-on orbits. While transiting exoplanets are still likely to be detectable, they are less likely to be seen than those in near face-on orbits. Our forward model serves to be a powerful tool for both interpreting and appropriately scheduling radio observations of exoplanetary systems, as well as inverting the system geometry from observations.