SDSS-V Local Volume Mapper (LVM): The Integrated Light and Internal Rotation of Omega Centauri

The SDSS-V Local Volume Mapper (LVM) is a wide-field integral field spectroscopic survey of the Southern Milky Way plane, the Magellanic Clouds, and nearby Local Group galaxies. We use Early Science observations of the whole body of the nearest nuclear cluster, Omega Centauri, to extend the LVM beyond its primary interstellar-medium science case. The wide LVM field allows us to precisely map $\omega$ Cen's line-of-sight rotation out to $\sim 3r_{HL}$ or $15^\prime$, reaching a maximum value of $(8.4 \pm 0.8)$ km s$^{-1}$ at $r \approx 4.7^\prime$. Within the central region, comparisons with existing VLT MUSE oMEGACat data show explicitly that the unresolved-light signal is dominated by a small number of bright stars, with an effective sample size of only $\sim$12 per resolution element. Using Gaia DR3 as an external reference, we verify that the SDSS-V's LVM reduction pipeline recovers integrated stellar fluxes to 1-4 % across six magnitudes of surface brightness. Our resulting total spectrum of $\omega$ Cen is one of the highest S/N integrated spectrum for any globular or nuclear star cluster. We use it to test four widely-used SSP template libraries against resolved age-metallicity ground truth from oMEGACat. All templates recover an old, metal-poor population. But, even at S/N $\sim$1300, the inferred mean ages and mean [Fe/H] vary by $\sim$7 Gyr and $\sim$0.4 dex, respectively, across libraries and wavelength ranges, reflecting a systematic floor for integrated-light studies of old multi-population systems.