  The overall shape, internal structure and surface morphology of small bodies
such as asteroids and comets are determined to a large degree by the last
global-scale impact or disruption event. Depending on the specific energy,
impacts lead to a large spectrum of outcomes. Sub-catastrophic disruptions take
place in an energy range between cratering impacts and catastrophic
disruptions. Although less energetic than catastrophic events, they can still
significantly alter the overall shape and structure of the target body. This
has been demonstrated recently in the case of bi-lobe cometary nuclei (Jutzi
and Benz, 2017). Here we present results of a subsequent study on the shapes of
asteroids resulting from such collisions. Sizes ranging from a few hundred
meters to a few kilometers are considered.
  We show that impacts on elongated rotating asteroids frequently lead to the
formation of contact binaries. Our results confirm that this mechanism is
robust and works for a large range of asteroid sizes and impact velocities.
Scaling-laws for the prediction of the size and velocity dependent specific
energies required for successful bi-lobe formation are presented. Based on
these scaling laws, the expected frequency of such sub-catastrophic impacts is
calculated and is compared to the one of catastrophic disruptions, which
require much higher specific energies and are more rare.
  Our analysis suggest that the shapes and structures of a large fraction of
small asteroids as observed today may be the result of the last major
sub-catastrophic impact.
