We present infrared (IR) and optical echelle spectra of the Classical T Tauri star TW Hydrae. Using the optical data, we perform detailed spectrum synthesis to fit atomic and molecular absorption lines and determine key stellar parameters: Teff = 4126 pm 24 K, log g = 4.84 pm 0.16, [M/H] = -0.10 pm 0.12, vsini = 5.8 pm 0.6 km/s. The IR spectrum is used to look for Zeeman broadening of photospheric absorption lines. We fit four Zeeman sensitive Ti I lines near 2.2 microns and find the average value of the magnetic field over the entire surface is 2.61 pm 0.23 kG. In addition, several nearby magnetically insensitive CO lines show no excess broadening above that produced by stellar rotation and instrumental broadening, reinforcing the magnetic interpretation for the width of the Ti I lines. We carry out extensive tests to quantify systematic errors in our analysis technique which may result from inaccurate knowledge of the effective temperature or gravity, finding that reasonable errors in these quantities produce a 10% uncertainty in the mean field measurement.
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