  Filamentary molecular clouds are regarded as the place where newborn stars
are formed. In particular, a hub region, a place where it appears as if several
filaments are colliding, often indicates active star formation. To understand
the star formation in filament structures, we investigate the collisions
between two filaments using two-dimensional magnetohydrodynamical simulations.
As a model of filaments, we assume that the filaments are in magnetohydrostatic
equilibrium under a global magnetic field perpendicular to the filament axis.
We set two identical filaments with an infinite length and collided them with a
zero-impact parameter (head-on). When the two filaments collide while sharing
the same magnetic flux, we found two types of evolution after a merged filament
is formed: runaway radial collapse and stable oscillation with a finite
amplitude. The condition for the radial collapse is independent of the
collision velocity and is given by the total line mass of the two filaments
exceeding the magnetically critical line mass for which no magnetohydrostatic
solution exists. The radial collapse proceeds in a self-similar manner,
resulting in a unique distribution irrespective of the various initial line
masses of the filament, as the collapse progresses. When the total line mass is
less massive than the magnetically critical line mass, the merged filament
oscillates, and the density distribution is well-fitted by a magnetohydrostatic
equilibrium solution. The condition necessary for the radial collapse is also
applicable to the collision whose direction is perpendicular to the global
magnetic field.
