Planet Formation in Binaries - Planetary Exploration and Science: Recent Results and Advances - page 311

Fig. 13.4 Planetesimal disc around Ǜ Cen B. Numerical simulations with gas drag. Relative
importance of different type of mutual impacts as a function of radial distance. Red : impacts for
which v s 1 ;s 2 v eroM ,wherev eroM is the threshold velocity beyond which an impact between

two objects of sizes s 1 and s 2 always results in net mass loss. Yellow : v escm v eroM ,

where v escm is the erosion threshold considering poorly collision-resistant material. Green :
v s 1 ;s 2

v s 1 ;s 2

v esc where v esc is the escape velocity of the (s 1 ;s 2 ) pair. Accretion can here proceed
unimpedended, in a “runaway growth” way, as around a single star. Light blue : v esc v s 1 ;s 2

v erom . Collisions result in net accretion, but v are high enough to cancel off the fast runaway
growth mode. The two thick blue lines denote the location of the inner limit of the “empirical”
and “narrow” habitable zones (see Sect. 13.7 ). The planetesimal size distribution is assumed to be
a Maxwellian centred on 5 km (Modified from Thebault et al. 2009 )

prescription. In recent years, new studies have investigated this issue by considering
increasingly sophisticated gas-disc models. For the most part, these studies have
confirmed the accretion-hostile effect of the gas. Paardekooper et al. ( 2008 )have
considered a system with an evolving gas disc that also feels the pull of the binary.
They have shown that the situation gets even worse for planetesimal accretion: gas
streamlines follow paths very different from the planetesimal orbits, so that gas drag
is enhanced, and so is the accretion-hostile differential phasing effect (see Fig. 13.5 ).
Another important mechanism that had been neglected in most early planetesi-
mal+gas studies is that of the gas disc's gravity. Due to the difficulty of incorporating
this effect, there have only been two attempts at numerically investigating this issue
and only for very small populations of test planetesimals. The pioneering study
by Kley and Nelson ( 2007 ) have shown that for many setups, the effect of gas-
disc gravity can dominate that of gas drag in controlling planetesimal dynamics.
A later study by the same team (Fragner et al. 2011 ) found that the net effect of
disc gravity is to further increase impact speeds between planetesimals and this even
between equal-sized bodies. The recent analytical exploration of Rafikov ( 2013 )has