The effect of the atmospheric refractive index on the radio signal of extensive air showers

For the interpretation of measurements of radio emission from extensive air showers, an important systematic uncertainty arises from natural variations of the atmospheric refractive index n. At a given altitude, the refractivity N=10⁶(n−1) can have relative variations on the order of 10% depending on temperature, humidity, and air pressure. Typical corrections to be applied to N are about 4%. Using CoREAS simulations of radio emission from air showers, we have evaluated the effect of varying N on measurements of the depth of shower maximum X_max. For an observation band of 30–80 MHz, a difference of 4% in refractivity gives rise to a systematic error in the inferred X_max between 3.5 and 11 g/cm², for proton showers with zenith angles ranging from 15 to 50°. At higher frequencies, from 120 to 250 MHz, the offset ranges from 10 to 22 g/cm². These offsets were found to be proportional to the geometric distance to X_max. We have compared the results to a simple model based on the Cherenkov angle. For the 120−250 MHz band, the model is in qualitative agreement with the simulations. In typical circumstances, we find a slight decrease in X_max compared to the default refractivity treatment in CoREAS. While this is within commonly treated systematic uncertainties, accounting for it explicitly improves the accuracy of X_max measurements.