The Dark Matter Halo of M54
  M54 is a prototype of a globular cluster embedded in a dark matter halo. Gaia
EDR3 photometry and proper motions separate the old, metal-poor stars from the
more metal rich and younger dwarf galaxy stars. The metal poor stars dominate
the inner 50 pc, with a velocity dispersion profile that declines to a minimum
around 30 pc then rises back to nearly the central velocity dispersion, as
expected for a globular cluster at the center of a dark matter halo. The Jeans
analysis of the three separate stellar populations give consistent masses that
rise approximately linearly with radius to 1 kpc, implying a small core or
cuspy halo. These data are compatible with an infalling CDM dark matter halo
reduced to 3x10^8 M_sun at the 50 kpc apocenter 2.3 Gyr ago, with a central
globular cluster surrounded by the remnant of a dwarf galaxy. Tides gradually
remove material beyond 1 kpc but have little effect on the stars and dark
matter within 300 pc of the center. M54 appears to be a transitional system
between globular clusters with and without local dark halos, whose evolution
within the galaxy depends sensitively on the time of accretion and orbital
pericenter.
