This paper is the first in a series which studies interactions between M31 and its satellites , including the origin of the giant southern stream .
We construct accurate yet simple analytic models for the potential of the M31 galaxy to provide an easy basis for calculation of orbits in M31 ’ s halo .
We use an NFW dark halo , an exponential disk , a Hernquist bulge , and a central black hole point mass to describe the galaxy potential .
We constrain the parameters of these functions by comparing to existing surface brightness , velocity dispersion , and rotation curve measurements of M31 .
Our description provides a good fit to the observations , and agrees well with more sophisticated modeling of M31 .
While in many respects the parameter set is well constrained , there is substantial uncertainty in the outer halo potential and a near-degeneracy between the disk and halo components , producing a large , nearly two-dimensional allowed region in parameter space .
We limit the allowed region using theoretical expectations for the halo concentration , baryonic content , and stellar M / L ratio , finding a smaller region where the parameters are physically plausible .
Our proposed mass model for M31 has M _ { bulge } = 3.2 \times 10 ^ { 10 } { M } _ { \odot } , M _ { disk } = 7.2 \times 10 ^ { 10 } { M } _ { \odot } , and M _ { 200 } = 7.1 \times 10 ^ { 11 } { M } _ { \odot } , with uncorrected ( for internal and foreground extinction ) mass-to-light ratios of M / L _ { R } = 3.9 and 3.3 for the bulge and disk , respectively .
We present some illustrative test particle orbits for the progenitor of the stellar stream in our galaxy potential , highlighting the effects of the remaining uncertainty in the disk and halo masses .