  We delineate equilibrium phase structure and topological charge distribution
of dense two-colour QCD at low temperature by using a lattice simulation with
two-flavour Wilson fermions that has a chemical potential $\mu$ and a diquark
source $j$ incorporated. We systematically measure the diquark condensate, the
Polyakov loop, the quark number density and the chiral condensate with improved
accuracy and $j\to0$ extrapolation over earlier publications; the known
qualitative features of the low temperature phase diagram, which is composed of
the hadronic, Bose-Einstein condensed (BEC) and BCS phases, are reproduced. In
addition, we newly find that around the boundary between the hadronic and BEC
phases, nonzero quark number density occurs even in the hadronic phase in
contrast to the prediction of the chiral perturbation theory (ChPT), while the
diquark condensate approaches zero in a manner that is consistent with the ChPT
prediction. At the highest $\mu$, which is of order the inverse of the lattice
spacing, all the above observables change drastically, which implies a lattice
artifact. Finally, at temperature of order $0.45T_c$, where $T_c$ is the chiral
transition temperature at zero chemical potential, the topological
susceptibility is calculated from a gradient-flow method and found to be almost
constant for all the values of $\mu$ ranging from the hadronic to BCS phase.
This is a contrast to the case of $0.89T_c$ in which the topological
susceptibility becomes small as the hadronic phase changes into the quark-gluon
plasma phase.
