The Spitzer c2d survey of weak-line T Tauri stars.: II.: New constraints on the timescale for planet building

One of the central goals of the Spitzer Legacy Project From Cores to Disks'' (c2d) is to determine the frequency of circumstellar disks around weak-line T Tauri stars (WTTSs) and to study the properties and evolutionary status of these disks. Here we present a census of disks for a sample of over 230 WTTSs located in the c2d IRAC and MIPS maps of the Ophiuchus, Lupus, and Perseus Molecular Clouds. We find that similar to 20% of the WTTSs in a magnitude-limited subsample have IR excesses at IRAC wavelengths. These disks frequencies are similar to 3-6 times larger than that recently found for a sample of relatively isolated WTTSs located outside the highest extinction regions covered by the c2d maps. The disk fractions we find are more consistent with those obtained in recent Spitzer studies of WTTSs in young clusters such as IC 348 and Tr37. According to their location in the H-R diagram, the WTTSs with excesses in our sample are among the younger part of the age distribution. Still, up to similar to 50% of the apparently youngest stars in the sample show no evidence of IR excess, suggesting that the circumstellar disks of a sizable fraction of pre-main-sequence stars dissipate in a timescale of similar to 1 Myr. We also find that none of the stars in our sample apparently older than similar to 10 Myr have detectable circumstellar disks at wavelengths < 24 mu m. The WTTS disks in our sample exhibit a wide range of properties (SED morphology, inner radius, L-disk/L-*, etc.) that bridge the gaps observed between the CTTSs and the debris disk regimes.