  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 Garraffo et al. 2016 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.
