Estimation of Magnetic Fields from Synchrotron Emission: Numerical Tests

We use models of spectrally resolved cosmic-ray (CR) transport in TIGRESS MHD simulations of the local interstellar medium to produce synthetic synchrotron emission and to test, on scales from a few kiloparsecs down to similar to 10 pc, the traditional estimate of magnetic field strength based on the assumption of equipartition between the magnetic and total CR energy densities. Our analysis shows that the traditional equipartition estimate works well at the kiloparsec scale of the simulation box, but breaks down at smaller scales. We find that the predicted magnetic field strength can be improved at small scales by assuming a constant CR energy density across each mock radio observation. The large-scale mean CR energy density can be estimated by assuming equipartition with the large-scale mean magnetic energy density, or as a function of additional observable quantities such as the star formation rate surface density or gas weight. In addition to estimating the magnetic field strength, we use synthetic polarized emission to create maps of the magnetic field direction. We find that the true magnetic field direction can be recovered well from the mock observations.