  We examine the feasibility of detecting auroral emission from the potentially
habitable exoplanet Proxima Centauri b. Detection of aurorae would yield an
independent confirmation of the planet's existence, constrain the presence and
composition of its atmosphere, and determine the planet's eccentricity and
inclination, thereby breaking the mass-inclination degeneracy. If Proxima
Centauri b is a terrestrial world with an Earth-like atmosphere and magnetic
field, we estimate the power at the 5577\AA\ OI auroral line is on the order of
0.1 TW under steady-state stellar wind, or ${\sim} 100 {\times}$ stronger than
that on Earth. This corresponds to a planet-star contrast ratio of
$10^{-6}-10^{-7}$ in a narrow band about the 5577\AA\ line, although higher
contrast ($10^{-4}-10^{-5}$) may be possible during periods of strong
magnetospheric disturbance (auroral power $1-10$ TW). We searched the Proxima
Centauri b HARPS data for the 5577\AA\ line and for other prominent oxygen and
nitrogen lines, but find no signal, indicating that the OI auroral line
contrast must be lower than $2\times 10^{-2}$ (with power $\lesssim$ 3,000 TW),
consistent with our predictions. We find that observations of 0.1 TW auroral
emission lines are likely infeasible with current and planned telescopes.
However, future observations with a space-based coronagraphic telescope or a
ground-based extremely large telescope (ELT) with a coronagraph could push
sensitivity down to terawatt oxygen aurorae (contrast $7\times 10^{-6}$) with
exposure times of ${\sim} 1$ day. If a coronagraph design contrast of $10^{-7}$
can be achieved with negligible instrumental noise, a future concept ELT could
observe steady-state auroral emission in a few nights.
