Emission Lines from the Gas Disk around TW Hydra and the Origin of the Inner Hole

We compare line emission calculated from theoretical disk models with optical to sub-millimeter wavelength observational data of the gas disk surrounding TW Hya and infer the spatial distribution of mass in the gas disk. The model disk that best matches observations has a gas mass ranging from $\sim10^{-4}-10^{-5}$\ms\ for $0.06{\rm AU} <r<3.5$AU and $\sim 0.06$\ms\ for $ 3.5 {\rm AU} <r<200$AU. We find that the inner dust hole ($r<3.5$AU) in the disk must be depleted of gas by $\sim 1-2$ orders of magnitude compared to the extrapolated surface density distribution of the outer disk. Grain growth alone is therefore not a viable explanation for the dust hole. CO vibrational emission arises within $r\sim 0.5$AU from thermal excitation of gas. [OI] 6300\AA\ and 5577\AA\ forbidden lines and OH mid-infrared emission are mainly due to prompt emission following UV photodissociation of OH and water at $r\lesssim0.1$AU and at $r\sim 4$AU. [NeII] emission is consistent with an origin in X-ray heated neutral gas at $r\lesssim 10$AU, and may not require the presence of a significant EUV ($h\nu>13.6$eV) flux from TW Hya. H$_2$ pure rotational line emission comes primarily from $r\sim 1-30$AU. [OI]63$\mu$m, HCO$^+$ and CO pure rotational lines all arise from the outer disk at $r\sim30-120$AU. We discuss planet formation and photoevaporation as causes for the decrease in surface density of gas and dust inside 4 AU. If a planet is present, our results suggest a planet mass $\sim 4-7$M$_J$ situated at $\sim 3$AU. Using our photoevaporation models and the best surface density profile match to observations, we estimate a current photoevaporative mass loss rate of $4\times10^{-9}$\ms\ yr$^{-1}$ and a remaining disk lifetime of $\sim 5$ million years.