  M31 has a giant stream of stars extending far to the south and a great deal
of other tidal debris in its halo, much of which is thought to be directly
associated with the southern stream. We model this structure by means of
Bayesian sampling of parameter space, where each sample uses an N-body
simulation of a satellite disrupting in M31's potential. We combine constraints
on stellar surface densities from the Isaac Newton Telescope survey of M31 with
kinematic data and photometric distances. This combination of data tightly
constrains the model, indicating a stellar mass at last pericentric passage of
log(M_s / Msun) = 9.5+-0.1, comparable to the LMC. Any existing remnant of the
satellite is expected to lie in the NE Shelf region beside M31's disk, at
velocities more negative than M31's disk in this region. This rules out the
prominent satellites M32 or NGC 205 as the progenitor, but an overdensity
recently discovered in M31's NE disk sits at the edge of the progenitor
locations found in the model. M31's virial mass is constrained in this model to
be log(M200) = 12.3+-0.1, alleviating the previous tension between
observational virial mass estimates and expectations from the general galactic
population and the timing argument. The techniques used in this paper, which
should be more generally applicable, are a powerful method of extracting
physical inferences from observational data on tidal debris structures.
