  Model of a partial current-carrying torus loop anchored to the photosphere is
analyzed. Conditions of the catastrophic loss of equilibrium are considered and
corresponding value of the critical decay index of external magnetic field is
found. Taking into account line-tying conditions leads to non-monotonous
dependence of the critical decay index on the height of the apex and length of
the flux rope (its endpoints separation). For relatively short flux ropes, the
critical decay index is significantly lower than unity, which is in contrast to
widespread models with the typical critical decay index above unity. The steep
decrease of the critical index with height at low heights is due to the sharp
increase of the curvature of the flux-rope axis that transforms from a nearly
straight line to a crescent.
