  Context. Breathtaking imagery recorded during the European Space Agency's
Rosetta mission confirmed the bilobate nature of comet
67P/Churyumov-Gerasimenko's nucleus. Its peculiar appearance is not unique
among comets. The majority of cometary cores imaged at high resolution exhibit
a similar build. Various theories have been brought forward as to how cometary
nuclei attain such peculiar shapes.
  Aims. We illustrate that anisotropic mass loss and local collapse of
subsurface structures caused by non-uniform exposure of the nucleus to solar
irradiation can transform initially spherical comet cores into bilobed ones.
  Methods. A mathematical framework to describe the changes in morphology
resulting from non-uniform insolation during a nucleus' spin-orbit evolution is
derived. The resulting partial differential equations that govern the change in
the shape of a nucleus subject to mass loss and consequent collapse of depleted
subsurface structures are solved analytically for simple insolation
configurations and numerically for more realistic scenarios.
  Results. The here proposed mechanism is capable of explaining why a large
fraction of periodic comets appear to have peanut-shaped cores and why
light-curve amplitudes of comet nuclei are on average larger than those of
typical main belt asteroids of the same size.
