The evolution of the Sun's birth cluster and the search for the solar
  siblings with Gaia
  We use self-consistent numerical simulations of the evolution and disruption
of the Sun's birth cluster in the Milky Way potential to investigate the
present-day phase space distribution of the Sun's siblings. The simulations
include the gravitational N-body forces within the cluster and the effects of
stellar evolution on the cluster population. In addition the gravitational
forces due to the Milky Way potential are accounted for in a self-consistent
manner. Our aim is to understand how the astrometric and radial velocity data
from the Gaia mission can be used to pre-select solar sibling candidates. We
vary the initial conditions of the Sun's birth cluster, as well as the
parameters of the Galactic potential. We show that the disruption time-scales
of the cluster are insensitive to the details of the non-axisymmetric
components of the Milky Way model and we make predictions, averaged over the
different simulated possibilities, about the number of solar siblings that
should appear in surveys such as Gaia or GALAH. We find a large variety of
present-day phase space distributions of solar siblings, which depend on the
cluster initial conditions and the Milky Way model parameters. We show that
nevertheless robust predictions can be made about the location of the solar
siblings in the space of parallaxes ($\varpi$), proper motions ($\mu$) and
radial velocities ($V_\mathrm{r}$). By calculating the ratio of the number of
simulated solar siblings to that of the number of stars in a model Galactic
disk, we find that this ratio is above 0.5 in the region given by: $\varpi \geq
5$mas, $4 \leq \mu \leq 6$masyr$^{-1}$, and $-2\leq V_\mathrm{r} \leq
0$kms$^{-1}$. Selecting stars from this region should increase the probability
of success in identifying solar siblings through follow up observations
[Abridged].
