Cepheid Period-Luminosity Relations in the Near-Infrared and the Distance to M31 from the Hubble Space Telescope Wide Field Camera 3

We present measurements of 68 classical Cepheids with periods from 10 to 78 days observed in the near-infrared by the PHAT Program using the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST). The combination of HST's resolution and the use of near-infrared measurements provides a dramatic reduction in the dispersion of the Period--Luminosity relation over the present optical, ground-based data. Even using random-phase magnitudes we measure a dispersion of just 0.17 mag, implying a dispersion of just 0.12 mag for mean magnitudes. The error in the mean for this relation is 1% in distance. Combined with similar observations of Cepheids in other hosts and independent distance determinations, we measure a distance to M31 of mu_0=24.42 +/- 0.05 (statistical) +/- 0.03 (systematic), 765 +/- 28 kpc, in good agreement with past measurements though with a better, 3% precision here. The result is also in good agreement with independent distance determinations from two detached eclipsing binaries allowing for an independent calibration of the Cepheid luminosities and a determination of the Hubble constant.