Simulations of un-equal binary collisions embedded in a turbulent gas
  cloud far away of a massive gravitational center
  We simulate the collapse of a turbulent gas cloud with the particle-based
code Gadget2. We choose two sub-clouds, formed by those particles located
around the centers $\vec{r}_L$ and $\vec{r}_R$ and within the radii $r_L$ and
$r_R$, respectively. A translational velocity $\vec{v}_L$ or $\vec{v}_R$ is
added, so that the sub-clouds move towards each other to collide. The radius
and pre-collision velocity of the sub-clouds are chosen to be un-equal, and
both head-on and oblique collisions are considered. The simulations are all
calibrated to have the same total mass and the initial energy ratio
$\alpha=0.16$, which is defined as the ratio of thermal energy to gravitational
energy. We compare low-$\beta$ models to a high-$\beta$ models, where $\beta$
is defined as the ratio of kinetic energy to gravitational energy. Finally, we
consider the turbulent cloud to be under the gravitational influence of an
object located far enough, in order to approximate the tidal effects by means
of an azimuthal velocity $V_{\rm cir}$ added to the cloud particles in addition
to the translational and turbulent velocities mentioned above. We compare a
low-$V_{\rm cir}$ model with a high-$V_{\rm cir}$ one.
