  The nature of the accreting companion to Mira --- the prototypical pulsating
asymptotic giant branch star --- has been a matter of debate for more than 25
years. Here we use a quantitative analysis of the rapid optical brightness
variations from this companion, Mira B, which we observed with the Nickel
telescope at Lick Observatory, to show that it is a white dwarf (WD). The
amplitude of aperiodic optical variations on time scales of minutes to tens of
minutes (approximately 0.2 mag) is consistent with that of accreting WDs in
cataclysmic variables on these same time scales. It is significantly greater
than that expected from an accreting main-sequence star. With Mira B identified
as a WD, its ultraviolet (UV) and optical luminosities, along with constraints
on the WD effective temperature from the UV, indicate that it accretes at
~1e-10 solar masses per year. We do not find any evidence that the accretion
rate is higher than predicted by Bondi-Hoyle theory. The accretion rate is high
enough, however, to explain the weak X-ray emission, since the accretion-disk
boundary layer around a low-mass WD accreting at this rate is likely to be
optically thick and therefore to emit primarily in the far or extreme UV.
Furthermore, the finding that Mira B is a WD means that it has experienced, and
will continue to experience nova explosions, roughly every million years. It
also highlights the similarity between Mira AB and other jet-producing
symbiotic binaries such as R Aquarii, CH Cygni, and MWC 560, and therefore
raises the possibility that Mira B launched the recently discovered bipolar
streams from this system.
