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

We study the destruction of icy interstellar objects by cosmic rays and gas collisions. Using the cosmic-ray flux measured in the local interstellar medium as well as inferred from gamma-ray observations at the different galactocentric radii, we find that cosmic-ray erosion is significant for interstellar objects made of common types of ices. Interestingly, cosmic-ray heating might destroy icy interstellar objects very efficiently such that the initial size of an N$_2$ fragment as suggested by Jackson & Desch (2021) to explain the composition of `Oumuamua should be at least 10 km in size in order to survive the journey of about 0.5 Gyr in the ISM and might be even larger if it originated from a region with an enhanced cosmic-ray flux. The erosion time due to cosmic-ray heating and gas collisions also allows us to set approximate limits on the initial size for other types of icy interstellar objects, e.g. composed of CO, CO$_2$, or CH$_4$. For a given initial size, we constrain the maximum distance to the birth site for interstellar objects with different speeds.