On the Radio Emission from $\epsilon$ Eridani

Some solar-type stars are known to present faint, time-variable radio continuum emission whose nature is not clearly established. We report on Jansky Very Large Array observations of the nearby star $\epsilon$ Eridani at 10.0 and 33.0 GHz. We find that this star has flux density variations on scales down to days, hours and minutes. On 2020 Apr 15 it exhibited a radio pulse at 10.0 GHz with a total duration of about 20 minutes and a peak four times larger than the plateau of 40 $\mu$Jy present in that epoch. We were able to model the time behavior of this radio pulse in terms of the radiation from shocks ramming into the stellar wind. Such shocks can be produced by the wind interaction of violently expanding gas heated suddenly by energetic electrons from a stellar flare, similar to the observed solar flares. Because of the large temperature needed in the working surface to produce the observed emission, this has to be non thermal. It could be gyrosynchrotron or synchrotron emission. Unfortunately, the spectral index or polarization measurements from the radio pulse do not have enough signal-to-noise ratio to determine its nature.