Diagnosis of 3D magnetic field and modes composition in MHD turbulence with Y-parameter

Magnetic field is ubiquitous in interstellar media and channels turbulent flow from kilo-parsec to sub-parsec scales in both diffuse ISM and molecular clouds. The determination of magnetohydrodynamic (MHD) turbulence and 3D magnetic field properties in ISM is notoriously difficult. In this study, we establish a statistical recipe `Y-parameter' based on the recent development of turbulence statistical theory, namely the turbulence anisotropy analysis, to reconstruct 3D magnetic fields in MHD simulations and understand the mode-decomposition of MHD turbulence. In our analysis, we used 25 MHD turbulence datacubes simulated using ZEUS-MP and Athena++ codes. We found that the anisotropy of Stokes parameters can act as a diagnostic for retrieving the magnetic field inclination in ISM and identifying dominating mode. It is supported by the value space separation of the Y-parameter for decomposed Alfvenic and compressible MHD cubes and which is decreasing and increasing with mean field inclination angle, $\theta_{\lambda}$, respectively. In the total cube analysis, Y$\sim 1.5$ (with Y$>1.5$ for A-mode and Y$<1.5$ for C-mode) provides a statistical demarcation to obtain the dominant fraction of MHD turbulence modes. Furthermore, we have found that the (i) if Y$\gtrsim 2.5$, $10^\circ<\theta_{\lambda}< 30^\circ$ and A mode or $5^\circ<\theta_{\lambda}< 10^\circ$ and C-mode (ii) if Y$ \lesssim 1.0 $, $\theta_{\lambda} \lesssim 5^\circ$ and C-mode or $\theta_{\lambda} \gtrsim 60^\circ$ and A-mode (iii) $40^\circ \lesssim \theta_{\lambda} \lesssim 60^\circ$ with A-mode or $\theta_{\lambda} \gtrsim 70^\circ$ with C-mode, if Y-parameter is in the intermediate range. As a consequence, in the future with the availability of vast radio polarisation surveys, this technique can play a leading role in detecting 3D magnetic field in ISM and characterizing the nature of the interstellar turbulence.