Robust magnetic field estimates in star-forming galaxies with the equipartition formula in the absence of equipartition

The equipartition model is widely used to estimate magnetic field strength from synchrotron intensity in radio galaxies, yet the validity of its underlying assumptions remains uncertain. Using an simulation which incorporates a two-moment cosmic ray (CR) transport scheme and a multiphase interstellar medium, we compare magnetic fields inferred from synthetic synchrotron emission maps with the true fields in the simulation. Starting from the derivation of the equipartition formula, we find that the deviation between the equipartition magnetic field and the true magnetic field depends only weakly on the ratio of the magnetic to the CR energy density. In practice, for both face-on and edge-on projections, the equipartition model slightly overestimates the total synchrotron-weighted magnetic field with mean offsets of 32% (0.17 dex) and 36% (0.2 dex), even though the energy equipartition between CR protons and magnetic fields does not hold locally. Beyond these average offsets, a clear trend emerges in edge-on projections that the model underestimates the field in the disk and overestimates it in the halo. Our results demonstrate that the validity of the equipartition model depends only weakly on the strict fulfillment of energy equipartition, and that the equipartition model remains a practical method for estimating magnetic field strengths in face-on projection maps based on our CR-magnetohydrodynamics simulation. Arepo