Evidence for a Weak Galactic Center Magnetic Field from Diffuse Low Frequency Nonthermal Radio Emission

New low-frequency 74 and 330 MHz observations of the Galactic center (GC) region reveal the presence of a large-scale ($6\arcdeg\times 2\arcdeg$) diffuse source of nonthermal synchrotron emission. A minimum energy analysis of this emission yields a total energy of $\sim (\phi^{4/7}f^{3/7})\times 10^{52}$ ergs and a magnetic field strength of $\sim 6(\phi/f)^{2/7}$ \muG (where $\phi$ is the proton to electron energy ratio and $f$ is the filling factor of the synchrotron emitting gas). The equipartition particle energy density is $1.2(\phi/f)^{2/7}$ \evcm, a value consistent with cosmic-ray data. However, the derived magnetic field is several orders of magnitude below the 1 mG field commonly invoked for the GC. With this field the source can be maintained with the SN rate inferred from the GC star formation. Furthermore, a strong magnetic field implies an abnormally low GC cosmic-ray energy density. We conclude that the mean magnetic field in the GC region must be weak, of order 10 \muG (at least on size scales $\ga 125\arcsec$).