A detailed dive into fitting strategies for GRB afterglows with contamination: A case study with kilonovae

Observations of gamma-ray burst afterglows have begun to readily reveal contamination from a kilonova or a supernova. This contamination presents significant challenges towards traditional methods of inferring the properties of these phenomena from observations. Given current knowledge of kilonova and afterglow modelling, observations (as expected) with near-infrared bands and at early observing times provide the greatest diagnostic power for both observing the presence of a kilonova and inferences on its properties in gamma-ray burst afterglows. However, contemporaneous observations in radio and X-ray are critical for reducing the afterglow parameter space and for more efficient parameter estimation. We compare different methods for fitting joint kilonova and afterglow observations under different scenarios. We find that ignoring the contribution of one source (even in scenarios where the source is sub-dominant) can lead to significantly biased estimated parameters but could still produce great light curve fits that do not raise suspicion. This bias is also present for analyses that fit data where one source is "subtracted". In most scenarios, the bias is smaller than the systematic uncertainty inherent to kilonova models but significant for afterglow parameters, particularly in the absence of high-quality radio and X-ray observations. Instead, we show that the most reliable method for inference in any scenario where contamination can not be confidently dismissed is to jointly fit for both an afterglow and kilonova/supernova, and showcase a Bayesian framework to make this joint analysis computationally feasible.