Globular cluster ejection, infall and the host dark matter halo of the Pegasus dwarf galaxy

Recent photometric observations revealed a massive, extended (M-GC greater than or similar to 10(5) M-circle dot); R-h similar to 14 pc) globular cluster (GC) in the central region (D-3D less than or similar to 100 pc) of the low-mass (M(*)5 similar to x 10(6) M-circle dot) dwarf irregular galaxy Pegasus. This massive GC offers a unique opportunity to study star cluster inspiral as a mechanism for building up nuclear star clusters, and the dark matter (DM) density profile of the host galaxy. Here, we present spectroscopic observations indicating that the GC has a systemic velocity of Delta V = 3 + 8 km s(-1) relative to the host galaxy, and an old, metal -poor stellar population. We run a suite of orbital evolution models for a variety of host potentials (cored to cusped) and find that the GC's observed tidal radius (which is similar to 3 times larger than the local Jacobi radius), relaxation time, and relative velocity are consistent with it surviving inspiral from a distance of D-gal greater than or similar to 700 pc (up to the maximum tested value of D-gal = 2000 pc). In successful trials, the GC arrives to the galaxy centre only within the last similar to 1.4 1 Gyr. Orbits that arrive in the centre and survive are possible in DM haloes of nearly all shapes, however to satisfy the GC's structural constraints a galaxy DM halo with mass M-DM similar or equal to 6 +/- 2 x 10(9) M-circle dot, concentration c similar or equal to 13.7 +/- 0.6, and an inner slope to the DM density profile of -0.9 <= gamma <= -0.5 is preferred. The gas densities necessary for its creation and survival suggest the GC could have formed initially near the dwarfs centre, but then was quickly relocated to the outskirts where the weaker tidal field permitted an increased size and relaxation time - with the latter preserving the former during subsequent orbital decay.