The differential lifetimes of protostellar gas and dust disks

We construct a protostellar disk model that takes into account the combined effect of viscous evolution, photoevaporation, and the differential radial motion of dust grains and gas. For T Tauri disks, the lifetimes of dust disks that are mainly composed of millimeter-sized grains are always shorter than the gas disks' lifetimes and become similar only when the grains are fluffy (density less than or similar to 0.1 g cm(-3)). If grain growth during the classical T Tauri phase produces plenty of millimeter-sized grains, such grains completely accrete onto the star in 10(7) yr, before photoevaporation begins to drain the inner gas disk and the star evolves to the weak-line T Tauri phase. In the weak-line phase, only dust-poor gas disks remain at large radii (greater than or similar to 10 AU), without strong signs of gas accretion or of millimeter thermal emission from the dust. For Herbig Ae/Be stars, the strong photoevaporation clears the inner disks in 10(6) yr, before the dust grains in the outer disk migrate to the inner region. In this case, the grains left behind in the outer gas disk accumulate at the disk inner edge (at 10-100 AU from the star). The dust grains remain there even after the entire gas disk has been photoevaporated and form a gas-poor dust ring similar to that observed around HR 4796A. Hence, depending on the strength of the stellar ionizing flux, our model predicts opposite types of products around young stars. For low- mass stars with a low photoevaporation rate, dust-poor gas disks with an inner hole would form, whereas for high-mass stars with a high photoevaporation rate, gas-poor dust rings would form. This prediction should be examined by observations of gas and dust around weak-line T Tauri stars and evolved Herbig Ae/Be stars.