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 to $M_A$. 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
Fernet-Serrat 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
characterize the importance of magnetic field curvature in driving MHD
turbulence, and how it could be potentially used to study self-gravitating
system.
