  All cometary nuclei that formed in the early Solar System incorporated
radionuclides and therefore were subject to internal radiogenic heating.
Previous work predicts that if comets have a pebble-pile structure internal
temperature build-up is enhanced due to very low thermal conductivity, leading
to internal differentiation. An internal thermal gradient causes widespread
sublimation and migration of either ice condensates, or gases released from
amorphous ice hosts during their crystallisation. Overall, the models predict
that the degree of differentiation and re-distribution of volatile species to a
shallower near-surface layer depends primarily on nucleus size. Hence, we
hypothesise that cometary activity should reveal a correlation between the
abundance of volatile species and the size of the nucleus. To explore this
hypothesis we have conducted a thorough literature search for measurements of
the composition and size of cometary nuclei, compiling these into a unified
database. We report a statistically significant correlation between the
measured abundance of CO/H$_{2}$O and the size of cometary nuclei. We further
recover the measured slope of abundance as a function of size, using a
theoretical model based on our previous thermophysical models, invoking
re-entrapment of outward migrating high volatility gases in the near-surface
pristine amorphous ice layers. This model replicates the observed trend and
supports the theory of internal differentiation of cometary nuclei by early
radiogenic heating. We make our database available for future studies, and we
advocate for collection of more measurements to allow more precise and
statistically significant analyses to be conducted in the future.
