We present results from an ongoing Keck spectroscopic survey of red giant stars in a field located along the major axis of M31, ≈34 kpc in projection from the nucleus and near the luminous globular cluster G1. We use multislit LRIS spectroscopy to measure the Ca II near-infrared triplet in 41 stars ranging in apparent magnitude from 20 < I < 22. Of these, 23 stars are found to have radial velocities v < -200 km s-1, indicating that they are giants in M31; the rest are likely to be foreground Galactic dwarf stars. Roughly two-thirds of the M31 members concentrate at v = -451 km s-1, with a relatively small velocity spread [σ(Gaussian) = 27 km s-1], which suggests that they belong to the outer disk or possibly a cold debris trail in the halo. The mean velocity of this group of red giants is consistent with that of nearby neutral hydrogen and models of the velocity field of M31's disk, rather than with G1 or the systemic velocity of M31. We use V, I photometry to estimate a mean metallicity of [Fe/H]phot = -0.8 for this group of potential M31 outer disk stars. Six stars out of the 23 M31 member giants have metallicities and velocities consistent with those of G1 (after accounting for its intrinsic spread in v and [Fe/H]): one of these stars lies within the projected tidal radius of G1 and is a likely member; the remaining five stars are not physically close to G1 and may represent tidal debris from G1. However, more data are needed to confirm the nature of these five stars, as it is likely that they simply represent M31's field halo population. We might have expected to detect tidal debris if G1 were the remnant core of a dwarf galaxy being accreted by M31; instead, the majority of M31 giants in this field are metal-rich and belong to what is evidently the outer disk of M31, and only a small fraction (20%) could possibly have originated in G1.
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