Erosion of Icy Interstellar Objects by Cosmic Rays and Implications for
  `Oumuamua
  We study the destruction and modification 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 \citet{jackson2021}
to explain the composition of `Oumuamua should be at least 0.5 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. This
implies an initial N$_2$ mass that is at least an order of magnitude larger
than the final value, exacerbating the N$_2$ mass budget deficiency for
explaining `Oumuamua. 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. We also find that
cosmic-ray and gas heating could entirely modify the ice structure before
destroying interstellar objects.
