We examine the nature of the progenitor of the giant stellar stream in M31
using as constraints new radial velocity measurements of stream red giant stars
(presented in the companion paper by Guhathakurta et al. 2005,
astro-ph/0406145) along with other M31 data sets available in the literature.
We find that the observations are best fit by orbits that are highly eccentric
and close to edge-on, with apo- to peri-center ratios of order 25 - 30, and
with apocenters at or only slightly beyond the southern edge of the current
data. Among these orbits, we are able to find a few that plausibly connect the
stream with the northern spur or with the low-surface-brightness feature of
similar high metallicity as the stream (originally reported by Ferguson et al.
2002) to the east of M31's center. In the latter case, if the connection is
real, then the eastern debris should lie well in front of M31 near the
apocenter of the orbit. Both the width of the debris and velocity dispersion
measurements imply a rough lower limit on the mass of the progenitor of 10^8
M_sun. We use this limit and our orbits to discuss which of M31's satellites
could be plausibly associated with the stream. In addition, we predict that the
width of the stream should increase beyond the southern edge of the current
data around the apocenter of the orbit and that the line-of-sight velocity
dispersion should exhibit significant variations along the stream.Comment: 20 pages, 6 figures, 1 table; submitted to the Astronomical Journal;
includes revisions suggested by the refere