A 3D framework to explore the propagation effects in stars exhibiting electron cyclotron maser emission

Recently, coherent radio emission has been discovered from a number of hot magnetic stars, via the process of electron cyclotron maser emission (ECME). This emission, observed in the form of highly circularly polarized pulses, have interesting properties which contain information about the host star. One of the important properties of ECME is the frequency dependence of the pulse arrival time. This has been attributed to propagation effect by Trigilio et al. (2011), and could explain the sequence observed for CU Vir qualitatively (Lo et al. 2012). However no quantitative treatment exists for this phenomenon which is a promising tool to estimate the density in the stellar magnetosphere. Besides, the effect of propagation through the magnetosphere on ECME has been thought to be limited to giving rise to a particular sequence of arrival of pulses, and in some cases producing the upper cut-off frequency for ECME (Leto et al. 2019). Here, we present a framework to deal with the propagation effect by considering continuous refraction in the inner magnetosphere of the star. This framework is capable of incorporating any type of density distribution, and in principle any type of magnetic field, though we limit ourselves to a dipolar magnetic field for this work. We show by simulation that for stars with high obliquity, the propagation effect can influence not only the sequence of arrival of pulses drastically, but also the pulse shapes, and the observability of a pulse from a particular magnetosphere.