Anomalous compressible mode generation by global frame projections of pure Alfven mode

TL;DR

This paper investigates how global frame projections of pure Alfven modes can generate apparent compressible modes, revealing the importance of frame choice in analyzing MHD turbulence and providing a geometric interpretation of local versus global Alfven wave fluctuations.

Contribution

It introduces a geometric framework relating local and global Alfven waves, demonstrating that global frame projections can produce misleading compressible signals.

Findings

Local Alfven wave is an orthogonal transformation of the global frame wave.

Global frame projections can cause Alfven waves to appear as compressible waves.

Frame choice significantly impacts the analysis of MHD turbulence properties.

Abstract

Alfven wave is the single most important physical phenomenon of magneto-hydrodynamic turbulence and has far-reaching impact to almost all studies related to astrophysical magnetic field. Yet the restoration of the Alfven wave fluctuations from a given magnetic field, aka the local Alfven wave problem, is never properly addressed in literature albeit its importance. Previous works model the Alfven wave fluctuation as the perturbation along a straight-line, constant magnetic field. However, Lazarian & Pogosyan (2012) suggested that the decomposition of Alfven wave along a straight line, aka. the global frame decomposition, has a factor of discrepancy to the true local Alfven wave fluctuation. Here we provide a geometric interpretation on how the local Alfven wave is related to the global frame through the use of vector frame formulation. We prove both analytically and numerically that the local frame Alfven wave is an orthogonal transformation of that of the global frame and related by the local Alfvenic Mach number. In other words, when we observe Alfven wave in the global frame of reference, some of the Alfven wave will be mistaken as compressible waves. The importance of frame choices have a far-reaching impact to the analytical studies of MHD turbulence. Combining the frame formalism and the new techniques we can have accurate measurement to some of the fundamental turbulence properties like the inclination angle of mean magnetic field relative to the line of sight.