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

Astronomy and Astrophysics
 Pub Date:
 December 2021
 DOI:
 10.1051/00046361/202142045
 arXiv:
 arXiv:2109.10925
 Bibcode:
 2021A&A...656A.118S
 Keywords:

 magnetohydrodynamics (MHD);
 ISM: magnetic fields;
 polarization;
 turbulence;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 Accepted for publication in A&