Spitzer Space Telescope infrared measurements are presented for 24 members of the TW Hydrae association (TWA). High signal-to-noise 24-micron (um) photometry is presented for all of these stars, including 20 stars that were not detected by IRAS. Among these 20 stars, only a single object, TWA 7, shows excess emission at 24um and at the level of only 40% above the stars photosphere. TWA 7 also exhibits a strong 70um excess that is a factor of 40 brighter than the stellar photosphere at this wavelength. At 70um, an excess of similar magnitude is detected for TWA 13, though no 24um excess was detected for this binary. For the 18 stars that failed to show measurable IR excesses, the sensitivity of the current 70um observations does not rule out substantial cool excesses at levels 10-40x above their stellar continua. Measurements of two T Tauri stars, TW Hya and Hen 6-300, confirm that their spectacular IR spectral energy distributions (SEDs) do not turn over even by 160um, consistent with the expectation for their active accretion disks. In contrast, the Spitzer data for the luminous planetary debris systems in the TWA, HD 98800B and HR 4796A, are consistent with single-temperature blackbody SEDs. The major new result of this study is the dramatic bimodal distribution found for the association in the form of excess emission at a wavelength of 24um, indicating negligible amounts of warm (>100 K) dust and debris around 20 of 24 stars in this group of very young stars. This bimodal distribution is especially striking given that the four stars in the association with strong IR excesses are >100x brighter at 24um than their photospheres.
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