Title: Breakthrough revisited: investigating the requirements for growth of dust beyond the bouncing barrier,
Abstract: 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.