The overestimation of equipartition magnetic field strengths from synchrotron emission using synthetically observed galaxies

Understanding the role that magnetic fields play on the stage of galaxy formation requires accurate methods for inferring the properties of extragalactic magnetic fields. Radio synchrotron emission has been the most promising avenue to infer magnetic field strengths across galaxies, with the application of a central assumption: that galactic cosmic rays are in energy equipartition with the magnetic field. In this work, we leverage flexible synthetic observations of a high-resolution magnetohydrodynamic simulation of a Milky Way-like galaxy to review whether true equipartition is capable of reproducing radio observations of galaxies, and investigate its impact on the inference of magnetic field strengths when varying the properties and density distribution of the cosmic rays. We find that imposing equipartition (regardless of scale length) results in cosmic ray electron densities that are unable to generate either the amplitude or the shape of the radio intensity profiles typically observed in spiral galaxies. Instead, observationally motivated smooth distributions of cosmic ray electrons across the galaxy provide a remarkable match to observations. We further demonstrate that assuming equipartition with those mock observations can lead to significant overestimation of the magnetic field strength ($\sim10-50\times$). This overestimation varies with cosmic ray electron densities, cosmic ray spectrum power-law index, and galactic environment, aggravated in inter-arm regions and attenuated in star-forming regions. Our results promote caution when assuming equipartition in observations, and suggest that additional theoretical and numerical work is required to leverage the upcoming generation of radio observations poised to revolutionize our understanding of astrophysical magnetic fields.