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The Cepheid Period-Luminosity Relation (The Leavitt Law) at Mid-Infrared Wavelengths: III. Cepheids in NGC 6822

We present the first application of mid-infrared Period-Luminosity relations to the determination of a Cepheid distance beyond the Magellanic Clouds. Using archival IRAC imaging data on NGC 6822 from Spitzer we were able to measure single-epoch magnitudes for sixteen long-period (10 to 100-day) Cepheids at 3.6um, fourteen at 4.5um, ten at 5.8um and four at 8.0um. The measured slopes and the observed scatter both conform to the relations previously measured for the Large Magellanic Cloud Cepheids, and fitting to those relations gives apparent distance moduli of mod{3.6} = 23.57 +/- 0.06, mod{4.5} = 23.55 +/- 0.07, mod{5.8} = 23.60 +/- 0.09 and mod{8.0} = 23.51 +/-0.08 mag. A multi-wavelength fit to the new IRAC moduli, and previously published BVRIJHK moduli, allows for a final correction for interstellar reddening and gives a true distance modulus of 23.49 +/- 0.03 mag with E(B-V) = 0.26 mag, corresponding to a metric distance of 500 +/-8 kpc.