Obtaining strength of magnetic field from E and B modes of dust polarization

We perform numerical simulations of supersonic magnetohydrodynamic (MHD) turbulence and calculate Fourier power spectra of E and B modes arising from dust polarization. We pay close attention to the ratio of E-mode to B-mode spectra (a.k.a. E/B power asymmetry) on small spatial scales. We find that the ratio depends on the strength of the mean magnetic field: the stronger the mean magnetic field is, the smaller the ratio is. More precisely speaking, the ratio scales with the Alfv\'en Mach number $M_A$, the root-mean-square velocity divided by the Alfv\'en speed of the mean magnetic field, when it lies in the range $1\lesssim M_A \lesssim 30$. This result implies that we can use the E/B power asymmetry to constrain the strength of the mean magnetic field in supersonic and super-Alfv\'enic MHD turbulence.