The Distance to M54 using Infrared Photometry of RR Lyrae Variable Stars and the Implications of its Relation to the Sagittarius Dwarf Galaxy

CDM cosmological models predict that dark matter halo density profiles will have central cusps. Yet for many dwarf spheroidal galaxies (dSphs), this expectation is in contrast with observations of cored, rather than cusped, halos. This 'cusp-core problem' is apparent in the Sagittarius Dwarf Galaxy (Sgr), one of the largest satellites of the Milky Way. The globular cluster M54, one of several clusters associated with Sgr, coincides in on-sky position with the center of the main body of Sgr. While several studies find that M54 lies within the center of Sgr, other findings show that M54 is offset from the center by several kiloparsecs along our line of sight. The latter requires Sgr to have a cored dark matter distribution. In the presence of a cuspy halo, the orbit of M54 would have decayed via dynamical friction and the cluster would have fallen to the center of Sgr. A clear determination of the relation of the two bodies may help us better understand the distribution of dark matter in Sgr and other dSphs. Here we present a measurement of the distance modulus to M54 using a set of RR Lyrae variable stars in near-infrared Magellan data mid-infrared Spitzer data. The magnitudes of individual stars are measured using multi-epoch PSF photometry and light curve fitting. From precise RR Lyrae period-luminosity relations at these wavelengths, we then find the mean M54 distance modulus to be 17.126 ± 0.023 (ran) ± 0.080 (sys). Our result is consistent with a distance measurement to Sgr derived via nearly identical methods and thus also consistent with the expectation of a central cusp in the dark matter density profile of Sgr.