Investigating the Andromeda stream — I. Simple analytic bulge—disc—halo model for M31

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 the calculation of orbits in M31's halo. We use a Navarro, Frenk and White (NFW) dark halo, an exponential disc, 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 modelling 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 disc 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 mass-to-light ratio (M/L R ), finding a smaller region where the parameters are physically plausible. Our proposed mass model for M31 has M bulge = 3.2 x 10 10 M ⊙ , M disc = 7.2 x 10 10 M ⊙ , and M 200 = 7.1 x 10 11 M ⊙ , with uncorrected (for internal and foreground extinction) mass-to-light ratios of M/L R = 3.9 and 3.3 for the bulge and disc, 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 disc and halo masses.