Exploring Halo Substructure with Giant Stars. VI. Extended Distributions of Giant Stars around the Carina Dwarf Spheroidal Galaxy: How Reliable Are They?

The question of the existence of active and prominent tidal disruption around various Galactic dwarf spheroidal (dSph) galaxies remains controversial. That debate often centers on the nature (bound vs. unbound) of extended populations of stars claimed to lie outside the bounds of single King profiles fitted to the density distributions of dSph centers. However, the more fundamental issue of the very existence of the previously reported extended populations is still contentious. We present a critical evaluation of the debate centering on one particular dSph, Carina, for which claims both for and against the existence of stars beyond the King limiting radius have been made. Our review includes a detailed examination of all previous studies bearing on the Carina radial profile and shows that among the previous survey methods used to study Carina, that which achieves the highest detected dSph signal-to-background ratio in the diffuse, outer parts of the galaxy is the Washington M, T2 + DDO51 filter approach from Paper II in this series, which depends on the stellar surface gravity sensitivity of the DDO51 filter to remove the bulk of contaminating foreground stars and leave predominantly stars on the Carina red giant branch. The second part of the paper addresses statistical methods used to evaluate the reliability of M, T2, DDO51 surveys in the presence of photometric errors and for which a new a posteriori statistical analysis methodology is provided. This analysis demonstrates that the expected level of contamination due to photometric error among the photometrically selected candidate Carina giant sample stars in Paper II is no more than 13%-27%, i.e., only slightly higher than originally predicted in Paper II. In the third part of this paper, these statistical methods are tested by new Blanco + Hydra multifiber spectroscopy of stars in the M, T2, DDO51-selected Carina candidate sample. The results of both the new a posteriori and the previous Paper II contamination predictions are generally borne out by the spectroscopy: Of 73 candidate giants with follow-up spectroscopy, the M, T2, DDO51 technique successfully identified 61 new Carina members, including 8 stars outside the photometrically defined King profile limiting radius. In addition, among a sample of 29 stars that were not initially identified as candidate Carina giants but that lie just outside of our selection criteria, 12 have radial velocities consistent with membership in Carina, including fiv