Breakthrough revisited: investigating the requirements for growth of dust beyond the bouncing barrier

For grain growth to proceed effectively and lead to planet formation a number of barriers to growth must be overcome. One such barrier, relevant for compact grains in the inner regions of the disc, is the `bouncing barrier' in which large grains ($\sim$ mm size) tend to bounce off each other rather than sticking. However, by maintaining a population of small grains it has been suggested that cm-size particles may grow rapidly by sweeping up these small grains. We present the first numerically resolved investigation into the conditions under which grains may be lucky enough to grow beyond the bouncing barrier by a series of rare collisions leading to growth (so-called `breakthrough'). Our models support previous results, and show that in simple models breakthrough requires the mass ratio at which high velocity collisions transition to growth instead of causing fragmentation to be low, $\phi \lesssim 50$. However, in models that take into account the dependence of the fragmentation threshold on mass-ratio, we find breakthrough occurs more readily, even if mass transfer is relatively inefficient. This suggests that bouncing may only slow down growth, rather than preventing growth beyond a threshold barrier. However, even when growth beyond the bouncing barrier is possible, radial drift will usually prevent growth to arbitrarily large sizes.