Magnetically active stars possess stellar winds whose interaction with planetary magnetic fields produces radio auroral emission .
We examine the detectability of radio auroral emission from Proxima b , the closest known exosolar planet orbiting our nearest neighboring star , Proxima Centauri .
Using the Radiometric Bode ’ s Law , we estimate the radio flux produced by the interaction of Proxima Centauri ’ s stellar wind and Proxima b ’ s magnetosphere for different planetary magnetic field strengths .
For plausible planetary masses , Proxima b produces 6-83 mJy of auroral radio flux at frequencies of 0.3-0.8 MHz for planetary magnetic field strengths of 1-3 B _ { \oplus } .
According to recent MHD models that vary the orbital parameters of the system , this emission is expected to be highly variable .
This variability is due to large fluctuations in the size of Proxima b ’ s magnetosphere as it crosses the equatorial streamer regions of the dense stellar wind and high dynamic pressure .
Using the MHD model of for the variation of the magnetosphere radius during the orbit , we estimate that the observed radio flux can vary nearly by an order of magnitude over the 11.2 day period of Proxima b .
The detailed amplitude variation depends on the stellar wind , orbital , and planetary magnetic field parameters .
We discuss observing strategies for proposed future space-based observatories to reach frequencies below the ionospheric cut off ( \sim 10 MHz ) as would be required to detect the signal we investigate .