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We apply an order-of-magnitude model of gas-assisted growth, known as pebbleaccretion, in a turbulent medium to suggest a reason why some systems form wideorbital separation gas giants while others do not. In contrast to traditionalgrowth by ballistic collisions with planetesimals, growth by pebble accretionis not necessarily limited by doubling times at the highest core mass.Turbulence, in particular, can cause growth to bottleneck at lower core masses.We demonstrate how a combination of growth by planetesimal and pebble accretionlimits the maximum semi-major axis where gas giants can form. We find that, forfiducial disk parameters, strong turbulence ($\alpha \gtrsim 10^{-2}$)restricts gas giant cores to form interior to $a \lesssim 40 \, \text{AU}$,while for weak turbulence gas giants can form out to $a \lesssim 70 \,\text{AU}$. The correspondence between $\alpha$ and semi-major axis depends onthe sizes of small bodies available for growth. This dependence on turbulenceand small-body size distribution may explain the paucity of wide orbitalseparation gas giants. We also show that while lower levels of turbulence($\alpha \lesssim 10^{-4}$) can produce gas giants far out in the disk, weexpect these gas giants to be low-mass ($M \lesssim \, 1 M_J$). These planetsare not luminous enough to have been observed with the current generation ofdirect-imaging surveys, which could explain why wide orbital separation gasgiants are currently observed only around A stars.

Restrictions on the Growth of Gas Giant Cores via Pebble Accretion