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We study the destruction and modification of icy interstellar objects bycosmic rays and gas collisions. Using the cosmic-ray flux measured in the localinterstellar medium as well as inferred from gamma-ray observations at thedifferent galactocentric radii, we find that cosmic-ray erosion is significantfor interstellar objects made of common types of ices. Interestingly,cosmic-ray heating might destroy icy interstellar objects very efficiently suchthat the initial size of an N$_2$ fragment as suggested by \citet{jackson2021}to explain the composition of `Oumuamua should be at least 0.5 km in size inorder to survive the journey of about 0.5 Gyr in the ISM and might be evenlarger if it originated from a region with an enhanced cosmic-ray flux. Thisimplies an initial N$_2$ mass that is at least an order of magnitude largerthan the final value, exacerbating the N$_2$ mass budget deficiency forexplaining `Oumuamua. The erosion time due to cosmic-ray heating and gascollisions also allows us to set approximate limits on the initial size forother types of icy interstellar objects, e.g. composed of CO, CO$_2$, orCH$_4$. For a given initial size, we constrain the maximum distance to thebirth site for interstellar objects with different speeds. We also find thatcosmic-ray and gas heating could entirely modify the ice structure beforedestroying interstellar objects.

Erosion of Icy Interstellar Objects by Cosmic Rays and Implications for `Oumuamua