Detection of 2$-$4 GHz Continuum Emission from $\epsilon$ Eridani

The nearby star $\rm \epsilon \ Eridani$ has been a frequent target of radio surveys for stellar emission and extraterrestial intelligence. Using deep $\rm 2-4 \ GHz$ observations with the Very Large Array, we have uncovered a $29 \ \mu {\rm Jy}$ compact, steady continuum radio source coincident with $\rm \epsilon \ Eridani$ to within 0.06 arcseconds ($\lesssim 2\sigma$; 0.2 au at the distance of the star). Combining our data with previous high frequency continuum detections of $\rm \epsilon \ Eridani$, our observations reveal a spectral turnover at $\rm 6 \ GHz$. We ascribe the $\rm 2-6 \ GHz$ emission to optically thick, thermal gyroresonance radiation from the stellar corona, with thermal free-free opacity likely becoming relevant at frequencies below $\rm 1 \ GHz$. The steep spectral index ($\alpha \simeq 2$) of the $\rm 2-6 \ GHz$ spectrum strongly disfavors its interpretation as stellar wind-associated thermal bremsstrahlung ($\alpha \simeq 0.6$). Attributing the entire observed $\rm 2-4 \ GHz$ flux density to thermal free-free wind emission, we thus, derive a stringent upper limit of $3 \times 10^{-11} \ M_{\odot} \ {\rm yr}^{-1}$ on the mass loss rate from $\rm \epsilon \ Eridani$. Finally, we report the non-detection of flares in our data above a $5\sigma$ threshold of $\rm 95 \ \mu Jy$. Together with the optical non-detection of the most recent stellar maximum expected in 2019, our observations postulate a likely evolution of the internal dynamo of $\rm \epsilon \ Eridani$.