Dust dissipation timescales in the intermediate and outer regions of protoplanetary disks

Dust and gas in protoplanetary disks dissipate as central stars evolve. In order to estimate the dust dissipation timescales in the protoplanetary disks, we stacked the WISE 12, 22, and the AKARI 90 $\mu$m survey images of known T Tauri stars and derived the average fluxes, well below the survey flux limit in the 90 $\mu$m band. We classified 4,783 T Tauri stars into three age groups, which are young ($ $6 Myr) groups, and stacked the WISE 12 and 22 and the AKARI 90 $\mu$m images in each group. The photometry of the stacked image shows the flux decay timescales of 1.4$\pm$0.2, 1.38$\pm$0.05, and 1.4$^{+0.6}_{-0.5}$ Myr in the 12, 22, and 90 $\mu$m bands, respectively. In optically thin disks with one-solar luminosity central stars, the 12 and 22 $\mu$m fluxes are attributed to the emission from the intermediate ($\sim$ 1 au) region and the 90 $\mu$m flux corresponds to that from the outer ($\sim$ 10 au) region in the disk. We hence conclude the dust dissipation timescale is $\tau_{\rm med,dust}\sim$1.4 Myr in the intermediate disks and is $\tau_{\rm outer, dust}=$1.4$^{+0.6}_{-0.5}$ Myr in the outer disks. The dust-dissipation time difference between the outer and intermediate disks is $\Delta\tau_{\rm dust} = \tau_{\rm outer,dust} -\tau_{\rm med,dust}=0.0^{+0.6}_{-0.5}$ Myr, indicating that the dust in the intermediate and outer disks dissipates on almost the same timescale.