Curvature of Magnetic Field Lines in Compressible Magnetized Turbulence: Statistics, Magnetization Predictions, Gradient Curvature, Modes, and Self-gravitating Media

Magnetic field lines in interstellar media have a rich morphology, which could be characterized by geometrical parameters such as curvature and torsion. In this paper we explore the statistical properties of magnetic field line curvature kappa in compressible magnetized turbulence. We see that both the mean and standard deviation of magnetic field line curvature obey power-law relations to the magnetization. Moreover, the power-law tail of the curvature probability distribution function is also proportional to the Alfvenic Mach number. We also explore whether the curvature method could be used in the field-tracing velocity gradient technique. In particular, we observe that there is a relation between the mean and standard deviation of the curvature probed by velocity gradients toM(A). Finally, we discuss how curvature is contributed by different MHD modes in interstellar turbulence and suggests that the eigenvectors of MHD modes could be possibly represented by the natural Frenet-Serret frame of the magnetic field lines. We discuss possible theoretical and observational applications of the curvature technique, including the extended understanding on a special length scale that characterizes the importance of magnetic field curvature in driving MHD turbulence, and how it could be potentially used to study a self-gravitating system.