What can Gaia (with TMT) say about Sculptor's Core?

Walker et al.'s Magellan/MMFS Survey survey identified 1355 red giant candidates in the dwarf spheroidal galaxy Sculptor. We find that the Gaia satellite will be able to measure the proper motions of 139 of these with a precision of between 13 and 20 km/s. Using a Jeans analysis and 5-parameter density model we show that this allows a determination of the mass within the deprojected half-light radius to within 16% and a measurement of the dark matter density exponent gamma to within 0.68 within that radius. If, even at first light, the TMT observes Sculptor then the combined observations will improve the precision on these proper motions to about 5 km/s, about 5 years earlier than would be possible without Gaia, further improving the precision of gamma to 0.27. Using a bimodal stellar population model for Sculptor the precision of gamma improves by about 30%. This suggests that Gaia (with TMT) is capable of excluding a cored profile of the kind predicted by CDM simulations with 2 sigma (4 sigma) of confidence.