We report results of a sensitive search for cold dust and molecular gas in the disks around eight T Tauri stars in the high-latitude cloud MBM 12. Interferometric observations of 3 mm continuum emission in five fields containing six of the objects and literature values for the remaining two limit the disk masses to Mdisk < 0.04–0.09 M⊙ (gas plus dust), for a gas-to-dust mass ratio of 100 and a distance of 275 pc. By co-adding the 3 mm data of our five fields, we set an upper limit to the average disk mass of disk(N = 5) < 0.03 M⊙. Simultaneous observation of the CS J = 2–1 and the N2H+ 1–0 lines show no emission. Single-dish observations of the 13CO 2–1 line limit the disk mass to (5–10) × 10-4 M⊙ for a standard CO abundance of 2 × 10-4. Depletion of CO by up to 2 orders of magnitude through freezing out or photodissociation can reconcile these limits. These mass limits lie within the range found in the Taurus-Auriga and ρ Oph star-forming regions (0.001–0.3 M⊙) and preclude conclusions about possible decrease in disk mass over the 1–2 Myr age range spanned by the latter two regions and MBM 12. Our observations can exclude the presence in MBM 12 of T Tauri stars with relatively bright and massive disks such as T Tau, DG Tau, and GG Tau.
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