A Deep Spitzer Survey of Circumstellar Disks in the Young Double Cluster, h and chi Persei

We analyze very deep IRAC and MIPS photometry of $\sim$ 12,500 members of the 14 Myr old Double Cluster, h and $\chi$ Persei, building upon on our earlier, shallower Spitzer studies (Currie et al. 2007a, 2008a). Numerous likely members show infrared (IR) excesses at 8 {\mu}m and 24 $\mu$m indicative of circumstellar dust. The frequency of stars with 8 $\mu$m excess is at least 2% for our entire sample, slightly lower (higher) for B/A stars (later type, lower-mass stars). Optical spectroscopy also identifies gas in about 2% of systems but with no clear trend between the presence of dust and gas. Spectral energy distribution (SED) modeling of 18 sources with detections at optical wavelengths through MIPS 24 $\mu m$ reveals a diverse set of disk evolutionary states, including a high fraction of transitional disks, although similar data for all disk-bearing members would provide better constraints. We combine our results with those for other young clusters to study the global evolution of dust/gas disks. For nominal cluster ages, the e-folding times ($\tau_{o}$) for the frequency of warm dust and gas are 2.75 Myr and 1.75 Myr respectively. Assuming a revised set of ages for some clusters (e.g. Bell et al. 2013), these timescales increase to 5.75 and 3.75 Myr, respectively, implying a significantly longer typical protoplanetary disk lifetime. The transitional disk duration, averaged over multiple evolutionary pathways, is $\sim$ 1 Myr. Finally, 24 $\mu$m excess frequencies for 4-6 M$_{\odot}$ stars appear lower than for 1-2.5 M$_{\odot}$ stars in other 10-30 Myr old clusters.