Why take the square root? An assessment of interstellar magnetic field strength estimation methods

Context. The magnetic field strength in interstellar clouds can be estimated indirectly from measurements of dust polarization by assuming that turbulent kinetic energy is comparable to the fluctuating energy, and using spread angles estimate latter. method developed Davis (1951, Phys. Rev., 81, 890) Chandrasekhar Fermi (1953, ApJ, 118, 1137) (DCF) assumes incompressible magnetohydrodynamic (MHD) fluctuations induce observed dispersion angles, deriving B ? 1? ?? (or, equivalently, M A , terms Alfvénic Mach number). However, observations show medium highly compressible. Recently, two us (ST) relaxed incompressibility assumption derived instead 1/??? (equivalently, 2 ). Aims. We explored what correct scaling compressible magnetized turbulence through theoretical arguments, tested assumptions accuracy methods with numerical simulations. Methods. used 26 magnetized, isothermal, ideal-MHD simulations without self-gravity different types forcing. range sonic numbers s are 0.1 ? 2.0 0.5 20. created synthetic maps methods. Results. data have a remarkable consistency scaling, which inferred ST, while DCF failed follow data. Similarly, ST root-mean-square (rms) coupling term between mean valid within factor for all (with exception solenoidally driven at high where fails 10). In contrast, rms second-order factors several hundreds sub-Alfvénic shows an better than 50% over entire explored; performs adequately only it has been optimized use “fudge factor”. For low inaccurate tens, since omits term, first order corresponds modes. found no dependence on . Conclusions. reflect physical reality turbulence, this reason provides much method. Even super-Alfvénic cases might outperform still adequate strength, reverse not true.