Gas surface density (top), pebble surface density (middle), and heavy element content Σ_gas,Y ∕Σ_gas (bottom) of the gas surface density as a function of radius for different times using the evaporation and condensation treatment described in Sect. 2.3 in the case of either no planet or planets fixed at 0.5 or 5 AU. These planets are either located interior (0.5 AU) or exterior (5 AU) to the water ice line. Disk parameters can be found in Table 3; here we use α = 0.0005.