Line defects of a two-component vector order parameter.

The line density of line defects in terms of a two-component vector order parameter are obtained from the definition of topological charges of line defects. The spatial structure and bifurcation of line defects in three-dimensional space are also studied from the topological properties of the two-component vector order parameter. The branch conditions for generating, annihilating, colliding, splitting, and merging of line defects are obtained according to the properties of the two-component vector order parameter itself. It is found that the velocities of line defects are infinite when they are being annihilated or generated, which is obtained only from the topological properties of the two-component vector order parameter.