  When comet nuclei approach the Sun, the increasing energy flux through the
surface layers leads to sublimation of the underlying ices and subsequent
outgassing that promotes the observed emission of gas and dust. The ejection of
dust requires that the forces binding the dust particles to the comet nucleus
must be overcome by the forces caused by the sublimation process. This relates
to the question of how large the tensile strength of the overlying dust layer
is. Homogeneous layers of micrometer-sized dust particles reach tensile
strengths of typically $10^3$ to $10^4$ Pa. This exceeds by far the maximum
sublimation pressure of water ice in comets. It is therefore unclear how
cometary dust activity is driven. To solve this paradox, we used the model by
Skorov and Blum (Icarus 221, 1-11, 2012), who assumed that cometesimals formed
by gravitational instability of a cloud of dust and ice aggregates and
calculated for the corresponding structure of comet nuclei tensile strength of
the dust-aggregate layers on the order of 1 Pa. Here we present evidence that
the emitted cometary dust particles are indeed aggregates with the right
properties to fit the model by Skorov and Blum. Then we experimentally measure
the tensile strengths of layers of laboratory dust aggregates and confirm the
values derived by the model. To explain the comet activity driven by the
evaporation of water ice, we derive a minimum size for the dust aggregates of
$\sim 1$ mm, in agreement with meteoroid observations and dust-agglomeration
models in the solar nebula. Finally we conclude that cometesimals must have
formed by gravitational instability, because all alternative formation models
lead to higher tensile strengths of the surface layers.
