Synchrotron emission on FIRE: equipartition estimators of magnetic fields in simulated galaxies with spectrally resolved cosmic rays

Synchrotron emission is one of few observable tracers of galactic magnetic fields (B) and cosmic rays (CRs). Much of our understanding of B in galaxies comes from utilizing synchrotron observations in conjunction with several simplifying assumptions of equipartition models, however, it remains unclear how well these assumptions hold, and what B these estimates physically represent. Using Feedback in Realistic Environments project simulations which self-consistently evolve CR proton, electron, and positron spectra from MeV to TeV energies, we present the first synthetic synchrotron emission predictions from simulated L-* galaxies with 'live' spectrally resolved CR-magnetohydrodynamic. We find that synchrotron emission can be dominated by relatively cool and dense gas, resulting in equipartition estimates of B with fiducial assumptions underestimating the 'true' B in the gas that contributes the most emission by factors of 2-3 due to small volume-filling factors. Motivated by our results, we present an analytical framework that expands upon equipartition models for estimating B in a multiphase medium. Comparing our spectrally resolved synchrotron predictions to simpler spectral assumptions used in galaxy simulations with CRs, we find that spectral evolution can be crucial for accurate synchrotron calculations towards galactic centres, where loss terms are large.