  We analyze Ly-alpha fluoresced H2 lines observed in the UV spectrum of Mira
B. We identify 13 different sequences fluoresced by 13 different H2 transitions
within the Ly-alpha line. The observed H2 line ratios within these sequences
imply significant line opacity, so we use a Monte Carlo radiative transfer code
to model the line ratios, correcting for opacity effects. We find the observed
line ratios can best be reproduced by assuming that the H2 is fluoresced in a
layer between the observer and Mira B with a temperature and column density of
T=3600 K and log N(H2)=17.3, respectively. The strengths of H2 absorption
features within the Ly-alpha line are roughly consistent with this temperature
and column. We use the total flux fluoresced within the 13 sequences to infer
the Ly-alpha profile seen by the H2. In order to explain differences between
the shape of this and the observed profile, we have to assume that the observed
profile suffers additional interstellar (or circumstellar) H I Ly-alpha
absorption with a column density of about log N(H I)=20.35. We also have to
assume that the observed profile is about a factor of 2.5 lower in flux than
the profile seen by the H2, and a couple possible explanations for this
behavior are presented. Several lines of evidence lead us to tentatively
attribute the fluoresced emission to H2 that is heated in a photodissociation
front within Mira A's wind a few AU from Mira B, although it is possible that
interaction between the winds of Mira A and B may also play a role in heating
the H2. We estimate a Mira B mass loss rate of 5e-13 solar masses per year and
a terminal velocity of 250 km/s, based on wind absorption features in the Mg II
h & k lines. We note, however, that the wind is variable and IUE Mg II spectra
suggest significantly higher mass loss rates during the IUE era.
