We present high resolution (R ~ 60,000) circular spectropolarimetry of the classical T Tauri star TW Hydrae. We analyze 12 photospheric absorption lines and measure the net longitudinal magnetic field for 6 consecutive nights. While no net polarization is detected the first five nights, a significant photospheric field of Bz = 149 pm 33 G is found on the sixth night. To rule out spurious instrumental polarization, we apply the same analysis technique to several non-magnetic telluric lines, detecting no significant polarization. We further demonstrate the reality of this field detection by showing that the splitting between right and left polarized components in these 12 photospheric lines shows a linear trend with Lande g-factor times wavelength squared, as predicted by the Zeeman effect. However, this longitudinal field detection is still much lower than that which would result if a pure dipole magnetic geometry is responsible for the mean magnetic field strength of 2.6 kG previously reported for TW Hya. We also detect strong circular polarization in the He I 5876 and the Ca II 8498 emission lines, indicating a strong field in the line formation region of these features. The polarization of the Ca II line is substantially weaker than that of the He I line, which we interpret as due to a larger contribution to the Ca II line from chromospheric emission in which the polarization signals cancel. However, the presence of polarization in the Ca II line indicates that accretion shocks on Classical T Tauri stars do produce narrow emission features in the infrared triplet lines of Calcium.
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