[abridged] We describe the first results from the NOAO Outer Limits Survey. The survey consists of deep images of 55 0.6x0.6 degree fields at distances up to 20 degrees from the LMC/SMC, and 10 controls. The fields probe the outer structure of the Clouds, the Magellanic Stream, the Leading Arm, and the wake of the new LMC orbit. Images were taken in 5 filters on the CTIO Blanco 4-m and Mosaic2 camera, with calibration at the CTIO 0.9-m. The CRI images reach depths below the oldest LMC/SMC main sequence (MS) turnoffs, yielding probes of structure combined with ability to measure stellar ages and metallicities. M and DDO51 images allow for discrimination of LMC and SMC giant stars from foreground dwarfs, allowing us to use giants as additional probes. From photometry of 8 fields at radii of 7-19 degrees N of the LMC bar, we find MS stars associated with the LMC to 16 degrees from the LMC center, while the much rarer giants can only be convincingly detected out to 11 degrees. In one control field, we see the signature of the Milky Way globular cluster NGC 1851. The CMDs show that while at 7-degree radius LMC populations as young as 500 Myr are present, at radii more than 11 degrees only the underlying old metal-poor population remains, demonstrating the existence of a population gradient. Even at extreme distances, the dominant age is much less than "globular Cluster age." MS star counts follow an exponential decline with a scale length of 1.15 kpc, essentially the same scale length as gleaned for the inner LMC disk from prior studies. While we cannot rule out tidal structure elsewhere, detection of ordered structure to 12 disk scale lengths is unprecedented, and adds to the puzzle of the LMC's interaction history. Our results do not rule out the possible existence of an LMC stellar halo, which may only dominate the disk at yet larger radii.

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