Diagonalization of the velocity variance/covariance matrix as a diagnostic of maser proper motions

A new computational technique is presented for analyzing the velocity fields mapped by VLBI proper-motion studies of astrophysical masers. Such studies, despite yielding kinematic information of great detail on unprecedented spatial scales, generally cannot determine the absolute motions of maser spots through the sky, or with respect to other nearby objects. The resulting ambiguity hinders physical interpretation, but can be partially overcome by constructing and diagonalizing the velocity variance/covariance matrix (VVCM) for a set of relative maser motions. Applied to the OH masers in W3(OH), VVCM diagonalization provides strong support for the cometary bow-shock model.