Flat Spectrum Radio Continuum Emission Associated with $\epsilon$ Eridani

We present Very Large Array observations at 33.0 GHz that detect emission coincident with $\epsilon$ Eridani to within $0\rlap.{"}07$ (0.2 AU at the distance of this star), with a positional accuracy of $0\rlap.{"}05$. This result strongly supports the suggestion of previous authors that the quiescent centimeter emission comes from the star and not from a proposed giant exoplanet with a semi-major axis of $\sim1\rlap.{"}0$ (3.4 AU). The centimeter emission is remarkably flat and is consistent with optically thin free-free emission. In particular, it can be modeled as a stellar wind with a mass loss rate of the order of $6.6 \times 10^{-11}~ M_\odot ~yr^{-1}$, which is 3,300 times the solar value, exceeding other estimates of this star's wind. However, interpretation of the emission in terms of other thermal mechanisms like coronal free-free and gyroresonance emission cannot be discarded.