First, we developed a mass model for M31 that fits the observations. This mass model is just the sum of a Hernquist bulge, an exponential disk, and an NFW halo. We found that the parameter space was very tightly constrained in some directions in parameter space, but very poorly constrained in others due to degeneracies and a large uncertainty in the halo mass profile. We can make astrophysical arguments to narrow the allowed region.

• Investigating the Andromeda stream - I. Simple analytic bulge-disc-halo model for M31
  Geehan, J. J., Fardal, M. A., Babul, A., Guhathakurta, P. 2006, 366, 996

Next we developed a method for fitting the orbit of the progenitor of the southern stream. This method recognizes that the stream does not follow a single orbit, but rather each star within the stream is on its own orbit. There is a gradient in orbital energy along the stream: the highest-energy stars take the longest paths, so they wind up at the tail of the stream. We call this phenomenon "stream-orbit tilt". Our approximate formula very accurately predicts the central path of the debris in phase space, as confirmed by N-body simulations with GASOLINE. So we can fit the observations with a quick orbital calculation. To go beyond this central path, we use our N-body simulations to relate the phase space volume (length, width and velocity dispersion of the stream) to the progenitor's mass and size. We found a relation between the unknown orbital phase of the progenitor and its initial mass. Now we need to constrain the orbital phase somehow. To do this, we will have to identify the satellite debris forward of the stream.

• Investigating the Andromeda stream - II. Orbital fits and properties of the progenitor
  Fardal, M. A., Babul, A., Geehan, J. J., Guhathakurta, P. 2006, MNRAS, 366, 1012

The figure shows our current answer to this problem. The count map exhibits a shelf-like feature on the NE side, called the "NE Shelf" (Ferguson et al. 2002). We have identified a similar feature on the W side. Both features are made more easily visible by Sobel-filtering the published count map (version shown is from Irwin et al. 2005).

By choosing an appropriate orbit for our N-body satellite, we can produce a very good match to this pair of structures. The figure color-codes the particles by the number of pericentric passages they have undergone since the beginning of the run (green=1, red=2, blue=3, purple=4). The simulation reproduces not only these shell-like structures, but also some kinematic anomalies observed in red giant stars (Kalirai et al, Ibata et al) and planetary nebulae (Merrett et al) in the region covered by the simulated shelves.

Our identification of these "shelf" structures with the debris further forward of the stream provides the constraint we need to estimate the mass and orbital phase of the progenitor. Our best fit gives 2 x 10⁹ M_sun as the initial stellar mass. The orbit implies the initial collision took place 0.7 Gyr ago, and the central bulk of the progenitor currently occupies the NE shelf region.

• Investigating the Andromeda Stream: III. A Young Shell System in M31
  Fardal, M. A., Guhathakurta, P., Babul, A., McConnachie, A. W. 2006, submitted to MNRAS, astro-ph/0609050
• Movie of collision
• another movie of collision
• same, mpeg format
• Movie showing current debris structure

• Match the transversely-skewed surface density of the southern stream using rotating satellites
• Look for further kinematic and spatial confirmation of the shelf model
• Tighten observational constraints on the orbital model
• Precisely measure the potential in M31's halo
• Understand impact of collision on M31 itself!