  Context: In protoplanetary disks, dust grains coagulate with each other and
grow to form aggregates. As these aggregates grow by coagulation, their filling
factor \phi decreases down to \phi << 1. However, comets, the remnants of these
early planetesimals, have \phi ~ 0.1. Thus, static compression of porous dust
aggregates is important in planetesimal formation. However, the static
compression strength has been investigated only for relatively high density
aggregates (\phi > 0.1). Aims: We investigate and find the compression strength
of highly porous aggregates (\phi << 1). Methods: We perform three dimensional
N-body simulations of aggregate compression with a particle-particle
interaction model. We introduce a new method of static compression: the
periodic boundary condition is adopted and the boundaries move with low speed
to get closer. The dust aggregate is compressed uniformly and isotropically by
themselves over the periodic boundaries. Results: We empirically derive a
formula of the compression strength of highly porous aggregates (\phi << 1). We
check the validity of the compression strength formula for wide ranges of
numerical parameters, such as the size of initial aggregates, the boundary
speed, the normal damping force, and material. We also compare our results to
the previous studies of static compression in the relatively high density
region (\phi > 0.1) and confirm that our results consistently connect to those
in the high density region. The compression strength formula is also derived
analytically.
