A Prescription for Building the Milky Way's Halo from Disrupted Satellites

We develop a semi-analytic method for determining the phase-space population of tidal debris along the orbit of a disrupting satellite galaxy and illustrate its use with a number of applications. We use this method to analyze Zhao's proposal that the microlensing events towards the Large Magellanic Cloud (LMC) might be explained by an appropriately placed tidal streamer, and find that his scenarios lead either to unacceptably high overdensities (10 -- 100%) in faint star counts (apparent magnitudes 17.5 -- 20.5) away from the Galactic plane or short timescales for the debris to disperse (10^8 years). We predict that the tidal streamers from the LMC and the Sagittarius dwarf galaxy currently extend over more than $2\pi$ in azimuth along their orbits. Assuming that each satellite has lost half of its primordial mass, we find that the streamers will have overdensities in faint star counts of 10 -- 100% and < 1% respectively, and conclude that this mass loss rate is unlikely for the LMC, but possible for Sagittarius. If the Galaxy has accreted one hundred $10^5-10^6 M_{\odot}$ objects (comparable to its current population of globular clusters) at distances of 20 -- 100 kpc during its lifetime then 10% of the sky will now be covered by tidal streamers.