Comparison of simulation results for a fully simulated gas giant (blue) and simulations using the fitted mass function (orange) presented for different α-values. The top panel shows the mass of the gas giant over time, with the green vertical line denoting the pebble isolation mass. The center panel displays the reduced disk surface density due to the gas giant. The bottom panel shows the water vapor content of the disk inside water-ice line at 0.3 AU.