We present Multiband Imaging Photometer for Spitzer (MIPS) observations at 24 and 70 microns for 30 stars, and at 160 microns for a subset of 12 stars, in the nearby (~30 pc), young (~12 Myr) Beta Pictoris Moving Group (BPMG). In several cases, the new MIPS measurements resolve source confusion and background contamination issues in the IRAS data for this sample. We find that 7 members have 24 micron excesses, implying a debris disk fraction of 23%, and that at least 11 have 70 micron excesses (disk fraction of >=37%). Five disks are detected at 160 microns (out of a biased sample of 12 stars observed), with a range of 160/70 flux ratios. The disk fraction at 24 and 70 microns, and the size of the excesses measured at each wavelength, are both consistent with an inside-out infrared excess decrease with time, wherein the shorter-wavelength excesses disappear before longer-wavelength excesses, and consistent with the overall decrease of infrared excess frequency with stellar age, as seen in Spitzer studies of other young stellar groups. Assuming that the infrared excesses are entirely due to circumstellar disks, we characterize the disk properties using simple models and fractional infrared luminosities. Optically thick disks, seen in the younger TW Hya and eta Cha associations, are entirely absent in the BPMG. Additional flux density measurements at 24 and 70 microns are reported for nine Tucanae-Horologium Association member stars. Since this is <20% of the association membership, limited analysis on the complete disk fraction of this association is possible.
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