With hydrodynamical simulations we examine the evolution of a protoplanetary disc around \alpha Centauri B including the effect of the eccentric orbit binary companion \alpha Centauri A .
The initially circular orbit disc undergoes two types of eccentricity growth .
First , the eccentricity oscillates on the orbital period of the binary , P _ { orb } , due to the eccentricity of the binary orbit .
Secondly , for a sufficiently small disc aspect ratio , the disc undergoes global forced eccentricity oscillations on a time-scale of around 20 P _ { orb } .
These oscillations damp out through viscous dissipation leaving a quasi-steady eccentricity profile for the disc that oscillates only on the binary orbital period .
The time-averaged global eccentricity is in the range 0.05-0.1 , with no precession in the steady state .
The periastrons of the gas particles are aligned to one another .
The higher the disc viscosity , the higher the disc eccentricity .
With N -body simulations we examine the evolution of a disc of planetesimals that forms with the orbital properties of the quasi-steady protoplanetary disc .
We find that the average magnitude of the eccentricity of particles increases and their periastrons become misaligned to each other once they decouple from the gas disc .
The low planetesimal collision velocity required for planet formation suggests that for planet formation to have occurred in a disc of planetesimals formed from a protoplanetary disc around \alpha Centauri B , said disc ’ s viscosity must be have been small and planet formation must have occurred at orbital radii smaller than about 2.5 au .
Planet formation may be easier with the presence of gas .