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Magnetic field lines in interstellar media have a rich morphology, whichcould be characterized by geometrical parameters such as curvature and torsion.In this paper, we explore the statistical properties of magnetic field linecurvature $\kappa$ in compressible magnetized turbulence. We see that both themean and standard deviation of magnetic field line curvature obey power-lawrelations to the magnetization. Moreover, the power-law tail of the curvatureprobability distribution function is also proportional to the Alfvenic Machnumber. We also explore whether the curvature method could be used in thefield-tracing Velocity Gradient Technique. In particular, we observe that thereis a relation between the mean and standard deviation of the curvature probedby velocity gradients to $M_A$. Finally we discuss how curvature is contributedby different MHD modes in interstellar turbulence, and suggests that theeigenvectors of MHD modes could be possibly represented by the naturalFernet-Serrat frame of the magnetic field lines. We discuss possibletheoretical and observational applications of the curvature technique,including the extended understanding on a special length scale thatcharacterize the importance of magnetic field curvature in driving MHDturbulence, and how it could be potentially used to study self-gravitatingsystem.

astrophysical journal/the astrophysical journal

Curvature of magnetic field lines in compressible magnetized turbulence:  Statistics, magnetization predictions, gradient curvature, modes and  self-gravitating media