The Evolution Of The Inner Regions of Protoplanetary Disks

We present a study of the evolution of the inner few astronomical units of protoplanetary disks around low-mass stars. We consider nearby stellar groups with ages spanning from 1 to 11 Myr, distributed into four age bins. Combining PANSTARSS photometry with spectral types, we derive the reddening consistently for each star, which we use (1) to measure the excess emission above the photosphere with a new indicator of IR excess and (2) to estimate the mass accretion rate ($\dot{M}$) from the equivalent width of the H$\alpha$ line. Using the observed decay of $\dot{M}$ as a constrain to fix the initial conditions and the viscosity parameter of viscous evolutionary models, we use approximate Bayesian modeling to infer the dust properties that produce the observed decrease of the IR excess with age, in the range between 4.5 and $24\,\mu$m. We calculate an extensive grid of irradiated disk models with a two-layered wall to emulate a curved dust inner edge and obtain the vertical structure consistent with the surface density predicted by viscous evolution. We find that the median dust depletion in the disk upper layers is $\epsilon \sim 3 \times 10^{-3}$ at 1.5 Myr, consistent with previous studies, and it decreases to $\epsilon \sim 3 \times 10^{-4}$ by 7.5 Myr. We include photoevaporation in a simple model of the disk evolution and find that a photoevaporative wind mass-loss rate of $\sim 1 -3 \times 10 ^{-9} \, M_{\odot}yr^{-1}$ agrees with the decrease of the disk fraction with age reasonably well. The models show the inward evolution of the H$_2$O and CO snowlines.