Formation of giant globular cluster G1 and the origin of the M31 stellar halo

We first demonstrate that globular cluster G1 could have been formed by tidal interaction between M31 and a nucleated dwarf galaxy (dE,N). Our fully self-consistent numerical simulations show that during tidal interaction between M31 and G1's progenitor dE,N with $M_{\rm B}$ $\sim$ -15 mag and its nucleus mass of $\sim$ $10^7$ $M_{\odot}$, the dark matter and the outer stellar envelope of the dE,N are nearly completely stripped whereas the nucleus can survive the tidal stripping because of its initially compact nature. The naked nucleus (i.e., G1) has orbital properties similar to those of its progenitor dE,N. The stripped stars form a metal-poor ([Fe/H] $\sim$ -1) stellar halo around M31 and its structure and kinematics depend strongly on the initial orbit of G1's progenitor dE,N. We suggest that the observed large projected distance of G1 from M31 ($\sim$ 40 kpc) can give some strong constraints on the central density of the dark matter halo of dE,N. We discuss these results in the context of substructures of M31's stellar halo recently revealed by Ferguson et al. (2002).